2018-07-17 | Tue | David Spencer (Sheffield) | Number Theory seminar |
14:00 | J11 | Congruences of local origin for higher levels | |
Abstract: There are many kinds of congruences between different types of modular forms. The most well known of which is Ramanujan's mod 691 congruence. This is a congruence between the Hecke eigenvalues of the weight 12 Eisenstein series and the Hecke eigenvalues of the weight 12 cusp form (both at level 1). This type of congruence can be extended to give congruences of ''local origin''. In this talk I will explain what is meant by such a congruence while focusing on the case of weight 1. The method of proof in this case is very different to that of higher weights and involves working with Galois representations and ray class characters. |
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2018-07-06 | Fri | Christian Voigt (Glasgow) | K-Theory, Hecke Algebras and Representation Theory |
09:30 | Lecture Theatre C | Categorification and Hecke algebras | |
Abstract: The idea of categorification is to replace set theoretic constructions and theorems by category theoretic analogues, recovering the original constructions via taking isomorphism classes or K-groups. In this talk I’ll discuss some examples of this procedure related to Hecke algebras and connections to noncommutative geometry. |
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2018-07-06 | Fri | Maarten Solleveld (Nijmegen) | K-Theory, Hecke Algebras and Representation Theory |
11:00 | Lecture Theatre C | Topological K-theory of affine Hecke algebras | |
Abstract: An affine Hecke algebra can be completed to a C*-algebra. These algebras appear in the theory of reductive p-adic groups, and they are of interest in representation theory and in relation with the Baum--Connes conjecture.They provide typical examples of C*-algebras which are close to commutative. In this talk I will discuss results about the K-theory of such C*-algebras, and techniques used to study it. In particular, I will show that the K-theory does not depend on the deformation parameter of the Hecke algebra. In the end all calculations will be reduced to equivariant K-theory of topological spaces, with respect to certain nice actions of finite groups. I will show that under mild conditions these equivariant K-groups are torsion-free. |
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2018-07-06 | Fri | Sergio Mendes (ISCTE Lisbon) | K-Theory, Hecke Algebras and Representation Theory |
14:00 | Lecture Theatre C | On L-packets and depth for SL2(K) and its inner forms | |
Abstract: An invariant that makes sense on both sides of the local Langlands correspondence is depth. In this talk we survey the notion of depth and study depth-preservation under the local Langlands correspondence. Examples will be provided with special emphasis to the group SL2 over a local field with characteristic 2. This talk is based on joint work with Anne-Marie Aubert, Roger Plymen and Maarten Solleveld. |
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2018-07-06 | Fri | Anne-Marie Aubert (Paris 6) | K-Theory, Hecke Algebras and Representation Theory |
15:30 | Lecture Theatre C | Affine Hecke algebras on the Galois side | |
Abstract: We will explain a way to attach affine Hecke algebras to certain Langlands parameters on Levi subgroups of a given p-adic reductive group in relation with the ABPS-conjecture. This is joint work with Ahmed Moussaoui and Maarten Solleveld. |
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2018-07-05 | Thu | Peter Hochs (Adelaide) | K-Theory, Hecke Algebras and Representation Theory |
09:30 | Lecture Theatre C | K-types of tempered representations and index theory | |
Abstract: Let G be a semisimple Lie group. Tempered representations of G are the ones occurring in the Plancherel decomposition of $L^2$(G). They are also relevant to the Langlands classification of the more general admissible representations. In joint work with Yanli Song and Shilin Yu, we realise the restriction of any tempered representation to a maximal compact subgroup K as an equivariant index. This is a concrete expression of Kirillov's orbit method. A consequence of this realisation is a geometric expression for the multiplicities of the irreducible representations of K in that restriction. (The irreducible representations that occur are the K-types of the representation.) This helps to study the general behaviour of those multiplicities. As an example, we show that admissible representations of SU(p,1) and SO_0(p,1) restrict multiplicity-freely to maximal compact subgroups. That was proved earlier by Koornwinder, but now illustrates our multiplicity formula. |
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2018-07-05 | Thu | Henrik Schlichtkrull (Copenhagen) | K-Theory, Hecke Algebras and Representation Theory |
11:00 | Lecture Theatre C | Harmonic analysis on real spherical spaces | |
Abstract: Let G be a real reductive Lie group. A homogeneous space Z of G is called real spherical if the minimal parabolic subgroups of G have only finitely many orbits on Z. For example, the Bruhat decomposition of G implies that Z=G is real spherical for the two-sided action of G$\times$G. A survey will be given of some recent progress (by F. Knop, B. Krötz, and others) on the generalization of Harish-Chandra's harmonic analysis to such spaces. |
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2018-07-05 | Thu | Beth Romano (Cambridge) | K-Theory, Hecke Algebras and Representation Theory |
14:00 | Lecture Theatre C | The local Langlands correspondence in small residue characteristic | |
Abstract: Through explicit examples, I'll discuss why the local Langlands correspondence becomes mysterious for small residue characteristic. I'll focus on examples and conjectures related to ``epipelagic" representations, which have minimal positive depth. |
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2018-07-05 | Thu | Tyrone Crisp (Nijmegen) | K-Theory, Hecke Algebras and Representation Theory |
15:30 | Lecture Theatre C | Parabolic induction over the p-adic integers | |
Abstract: For p-adic reductive groups like GL(n,Q_p), the right-hand side of the Baum-Connes conjecture --- i.e., the K-theory of the group C*-algebra --- is in many respects better understood than the left-hand side. This unusual state of affairs is due to the extremely complicated representation theory of compact p-adic groups like GL(n,Z_p). In this talk I shall present an ongoing program, joint with Ehud Meir and Uri Onn, that aims to understand the representations of these compact groups in terms of parabolic induction from Levi subgroups, analogously to the way one usually studies representations of real, complex, p-adic, and finite reductive groups. |
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2018-07-04 | Wed | Hang Wang (Adelaide / East China Normal) | K-Theory, Hecke Algebras and Representation Theory |
09:30 | Lecture Theatre C | Role of local Langlands correspondence in K-theory of group C*-algebras | |
Abstract: K-theory of C*-algebras associated to a Lie group can be understood both from the geometric point of view via Baum-Connes assembly map and from the representation theoretic point of view via harmonic analysis of Lie groups. Inspired by the local Langlangds correspondence and work by Plymen and collaborators, one can study relations between two groups, where their L-parameters are related in a nice way, from the aspects of K-theory and index theory of invariant elliptic operators. I will introduce two examples I investigated with Peter Hochs (when the two groups are inner forms to each other) and with Kuok Fai Chao (when there is a base change involved between the L-parameters of the two groups). |
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2018-07-04 | Wed | Alexandre Afgoustidis (Paris 9) | K-Theory, Hecke Algebras and Representation Theory |
11:00 | Lecture Theatre C | On the tempered dual of a real reductive group and that of its Cartan motion group | |
Abstract: Given a reductive Lie group G and a maximal compact subgroup K, one can consider the isometry group of the (flat) tangent space to G/K at the identity coset: this is a first-order approximation of G near K, called the Cartan motion group of G. George Mackey’s early work on semi-direct products describes its unitary representations in very simple and concrete terms. In the 1970s, Mackey noticed that his parametrization for the representations of the motion group showed unexpected similarities with Harish-Chandra’s more subtle parametrization for the tempered representations of G. Motivated by quantum-mechanical considerations related with the existence of a one-parameter family of Lie groups interpolating between both groups, he suggested that a kind of rigidity of representation theory along the deformation may be observed in general. Alain Connes and Nigel Higson later pointed out that the Baum-Connes-Kasparov isomorphism in operator K-theory can be viewed, for real reductive groups, as a cohomological reflection of Mackey’s ideas. For the special case of complex semisimple groups, Nigel Higson gave in 2008 a precise form to Mackey’s analogy and its relationship with the Baum-Connes-Kasparov isomorphism. For real reductive groups, I will describe a natural one-to-one correspondence between the tempered and admissible duals of both groups, and discuss some geometrical (or topological) aspects of the rigidity revealed by the correspondence along the deformation from one group to the other. |
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2018-07-04 | Wed | Pierre Clare (William&Mary) | K-Theory, Hecke Algebras and Representation Theory |
14:00 | Lecture Theatre C | On the reduced C*-algebra of real reductive groups | |
Abstract: I will report on joint work with Nigel Higson regarding the description up to Morita equivalence of the reduced C*-algebra of a class of real reductive groups. The results build on previous work, joint with Tyrone Crisp, and are related to the approach to the Connes-Kasparov isomorphism promoted by Roger Plymen and others. |
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2018-07-04 | Wed | Nigel Higson (PennState) | K-Theory, Hecke Algebras and Representation Theory |
15:30 | Lecture Theatre C | On (some of) the work of Roger Plymen | |
Abstract: I shall give an appreciation of some of the fundamental contributions of Roger Plymen to the themes of this conference, focusing on his studies of the C*-algebras of real and p-adic groups, and their K-theory groups. |
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2018-07-03 | Tue | Bram Mesland (MPIM Bonn) | K-Theory, Hecke Algebras and Representation Theory |
14:30 | Lecture Theatre C | A Hecke module structure on the KK-theory of arithmetic groups | |
Abstract: Let G be a locally compact group, H a discrete subgroup and C(G,H) the commensurator of H in G. The cohomology of H is a module over the Shimura Hecke ring of the pair (H,C(G,H)). This construction recovers the action of the Hecke operators on modular forms for SL(2,Z) as a particular case. In this talk I will discuss how the Shimura Hecke ring of a pair (H, C(G,H)) maps into the KK-ring associated to an arbitrary H-C*-algebra. From this we obtain a variety of K-theoretic Hecke modules. In the case of manifolds the Chern character provides a Hecke equivariant transformation into cohomology, which is an isomorphism in low dimensions. We discuss Hecke equivariant exact sequences arising from possibly noncommutative compactifications of H-spaces. Examples include the Borel-Serre and geodesic compactifications of the universal cover of an arithmetic manifold, and the totally disconnected boundary of the Bruhat-Tits tree of SL(2,Z). This is joint work with M.H. Sengun (Sheffield). |
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2018-07-03 | Tue | Heath Emerson (Victoria) | K-Theory, Hecke Algebras and Representation Theory |
16:00 | Lecture Theatre C | Noncommutative Lefshetz fixed-point formulas via KK-theory | |
Abstract: Using the idea of K-theoretic Poincaré duality, it is possible to formulate an analogue of the classical Lefschetz fixed-point formula from basic algebraic topology, which applies to KK-endomorphisms (e.g. ordinary C*-algebra endomorphisms) of a C*-algebra equipped with such a duality. We discuss the general methodology and apply it in the example of the C*-algebra crossed-product of a discrete group acting properly, smoothly and co-compactly on a smooth manifold. The result is an `orbifold' Lefschetz formula of some interest; our hope is that many other examples should exist. |
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2018-06-28 | Thu | Adel Betina (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | Hida families (a la Pilloni) | |
2018-06-27 | Wed | Ariel Weiss (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | Hida families (classical treatment) | |
2018-06-26 | Tue | Algebra / Algebraic Geometry seminar | |
14:00 | J11 | ||
2018-06-25 | Mon | Adel Betina (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | Classicality of overconvergent modular forms | |
2018-06-21 | Thu | Adel Betina (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | Classicality | |
2018-06-19 | Tue | Algebra / Algebraic Geometry seminar | |
14:00 | J11 | ||
2018-06-18 | Mon | Adel Betina (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | The canonical subgroup | |
2018-06-14 | Thu | Adel Betina (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | Introduction to rigid analytic geometry- Part (3) | |
2018-06-12 | Tue | Algebra / Algebraic Geometry seminar | |
14:00 | J11 | ||
2018-06-11 | Mon | Adel Betina (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | Introduction to rigid analytic geometry- Part (2) | |
2018-06-07 | Thu | Adel Betina (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | Introduction to rigid analytic geometry- Part (1) | |
2018-06-06 | Wed | Ciaran Schembri (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | Fuchsian group | |
Abstract: Fuchsian groups are discrete subgroups of the special projective linear group. They act as isometries on the hyperbolic plane and are studied because of their role in generating Riemann surfaces among other things. In this talk I will outline their geometric properties and if time permits will discuss how they relate to modern number theory. |
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2018-06-05 | Tue | Algebra / Algebraic Geometry seminar | |
14:00 | J11 | ||
2018-06-04 | Mon | Ariel Weiss (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | Hasse invariant | |
2018-05-31 | Thu | S. Shelyag (Northumbria University) | |
10:00 | LT 10 | Do photospheric non-magnetic bright points exist? | |
Abstract: Recent high-resolution simulations of non-magnetic solar photospheric convection suggest the presence of a separate class of small-scale photospheric brightenings, which coincide with intergranular vortex tubes. In contrast to well-known magnetic bright points, these brightenings are not related to magnetic fields. In our presentation, using high-resolution simulations with MURaM and detailed radiative diagnostics of the simulated models, I will analyse the physical characteristics of these brightenings and their observability with current and future instruments for solar observations. |
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2018-05-31 | Thu | Adel Betina (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | Modular curve- Part 2 | |
2018-05-30 | Wed | Nebojsa Pavic (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | Intersection theory in algebraic geometry: History and motivation. | |
Abstract: In this talk I'm going to motivate the notion of intersection theory in algebraic geometry by considering the example of Riemannian surfaces and only requiring a basic knowledge of complex analysis and a little bit of complex differential geometry. If time permits, I will give a rigorous definition of intersection groups, so called Chow groups, and relate them to the example. |
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2018-05-29 | Tue | Scott Balchin (Sheffield) | Magnitude Homology |
13:00 | J11 | Mangitude homology and persistent homology?? | |
2018-05-29 | Tue | Elisa Postinghel (University of Loughborough) | Algebra / Algebraic Geometry seminar |
14:00 | J11 | ||
2018-05-29 | Tue | Jessie Durk (Queen Mary UL) | Cosmology, Relativity and Gravitation |
16:00 | LT09, Hicks | Black hole lattices as inhomogeneous cosmological models | |
Abstract: The standard model of cosmology, ΛCDM, is based on the assumption that the Universe can be described by the homogeneous and isotropic FLRW solution to the Einstein field equations. The need to test whether the large-scale expansion of space is that of FLRW, or is instead modified by the presence of inhomogeneities, has lead to this assumption being relaxed. An interesting subset of inhomogeneous cosmologies include those dubbed black hole lattices. These are exact, fully-relativistic treatments of universes with a discretised matter content. We generalise an existing family of these to include a cosmological constant, structure formation and electric charge. For each new generalisation, we find a common behaviour of tending towards FLRW-like as the number of masses is increased, and for the addition of structures, we investigate the effect of gravitational interaction energies between clustered masses. |
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2018-05-24 | Thu | Adel Betina (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | The modular curve | |
2018-05-23 | Wed | Ciaran Meachan (University of Glasgow) | Algebra / Algebraic Geometry seminar |
13:00 | Hicks LT09 | Derived equivalent Hilbert schemes of points on K3 surfaces which are not birational | |
Abstract: Starting with two non-birational derived equivalent K3 surfaces, one can ask whether their Hilbert schemes of points are birational. In this talk, we will show that in some cases they are but in most cases they are not. This is joint work with Giovanni Mongardi and Kota Yoshioka. |
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2018-05-23 | Wed | Daniil Proskurin (Kiev Taras Shevchenko University) | Pure Maths Colloquium |
14:00 | J11 | $C^*$-algebras generated by quonic commutation relations and extensions of non-commutative tori | |
Abstract: We consider $C^*$-algebras $A_{q_i}\Theta$ generated by relations of the following form $$a_i^*a_i=1+q_i a_ia_i^* a_i^*a_j=e^{2\pi\theta_{ij}} a_ja_i^*, \quad i\ne j i, \quad j=1,\ldots,d $$ where $-1 \lt q_i \lt 1$, $\theta_{ij}=-\theta_{ji}$, $i\ne j$. We show that $A_{q_i}\Theta \simeq A_{0}\Theta$ is an extension of higher-dimensional non-commutative tori and study its properties. |
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2018-05-23 | Wed | Xiaolei Zhao (Northeastern University) | Algebra / Algebraic Geometry seminar |
15:00 | Hicks LT09 | Twisted cubics on cubic fourfolds and stability conditions | |
Abstract: It is a classical result of Beauville and Donagi that Fano varieties of lines on cubic fourfolds are hyper-Kahler. More recently, Lehn, Lehn, Sorger and van Straten constructed a hyper-Kahler eightfold out of twisted cubics on cubic fourfolds. In this talk, I will explain a new approach to these hyper-Kahler varieties via moduli of stable objects on the Kuznetsov components. Along the way, we will derive several properties of cubic fourfolds as consequences. This is based on a joint work with Chunyi Li and Laura Pertusi. |
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2018-05-23 | Wed | Chunyi Li (University of Warwick) | Algebra / Algebraic Geometry seminar |
16:15 | Hicks LT09 | Bogomolov type inequality for Fano varieties with Picard number 1 | |
Abstract: I will talk about some basic facts about slope stable sheaves and the Bogomolov inequality. New techniques from stability conditions will imply new stronger bounds on Chern characters of stable sheaves on some special varieties, including Fano varieties, quintic threefolds and etc. I will discuss the progress in this direction and some related open problems. |
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2018-05-22 | Tue | Paolo Stellari (Universita' degli studi di Milano) | Algebra / Algebraic Geometry seminar |
14:00 | J11 | TBA | |
Abstract: TBA |
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2018-05-22 | Tue | Joseph Fernandez (Liverpool John Moores) | Cosmology, Relativity and Gravitation |
16:00 | J11, Hicks | Tidal encounters of compact binaries with massive black holes as a source of gravitational waves | |
Abstract: Massive black holes (MBHs) are ubiquitous in galactic centres. The extreme potential due to these objects dominates the surrounding dynamics, giving rise to physics not possible in other regions. These regions are of particular interest for gravitational wave astronomy, as several dynamical processes which can give rise to black hole (BH) binary mergers have been postulated. We show that compact binaries can survive close encounters with the MBH without being disrupted, and that they tend to become hard and eccentric. Since the GW merger time of binaries is sensitive to the semi-major axis length and eccentricity, we find that this leads to a reduction of the merger time by several orders of magnitude in some cases. Therefore, tidal encounters of stellar mass BH binaries with a MBH at the centre of galaxies can provide a new formation channel of BH mergers. We use Monte Carlo simulations to evaluate the effective spin of the binaries after the encounter We also provide a description of a simple scenario to understand how this process could take place the a larger astrophysical context. |
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2018-05-21 | Mon | Angelo Rendina (Sheffield) | Number Theory Learning Seminar |
14:00 | J-11 | Geometric definition of modular forms | |
2018-05-17 | Thu | Frazer Jarvis (Sheffield) | Number Theory seminar |
14:00 | F24 | $p$-adic periods of genus 2 curves via the AGM | |
Abstract: The arithmetic-geometric mean provides the fastest way to compute periods of elliptic curves, both over the complex and $p$-adic numbers. There is an isogeny of genus 2 curves which looks like it might play the same role to compute periods for curves of genus 2. In this talk, we will discuss progress in developing an algorithm for the $p$-adic case, where $p$-adic periods were defined and first investigated in Teitelbaum's thesis. It is as yet incomplete, but the only missing step is an explicit Tate uniformisation for genus 2 curves. This is joint work with Rudolf Chow, and relates to the final chapter of his PhD thesis. |
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2018-05-16 | Wed | Shaun Stevens (University of East Anglia) | Pure Maths Colloquium |
14:00 | J11 | Towards an explicit local Langlands correspondence for classical groups | |
Abstract: The local Langlands correspondence is a web of sometimes conjectural correspondences between, on the one hand, irreducible representations of reductive groups over a p-adic field F and, on the other hand, certain representations of the absolute Weil group of F (which is almost the absolute Galois group). I will try to explain what the objects involved here are, some of what the correspondence predicts and what is known/unknown, as well as work (particularly due to Bushnell and Henniart for general linear groups) towards making the correspondence explicit. Hopefully I will also explain some joint work (with Blondel and Henniart) where we describe the "wild part'' of the correspondence for symplectic groups. |
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2018-05-16 | Wed | Ati Sharma (Southampton) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 9 | Some recent developments in the low-order modelling of fluid flows | |
Abstract: Modelling fluid flows is a difficult problem. Fluid flows are well described by the Navier-Stokes equations, but these are nonlinear PDEs, which are difficult to solve in a general way. Much recent work has focused on finding low-dimensional approximations to fluid flow systems, either by abstracting them from data generated from experiment and simulation or by finding suitable approximations to the equations. This talk will discuss two such approaches, Dynamic Mode Decomposition (DMD) and resolvent analysis. The approaches will be explained, and a variety of recent applications to flow analysis and estimation will be presented. |
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2018-05-16 | Wed | Arend Bayer (University of Edinburgh) | Algebra / Algebraic Geometry seminar |
15:30 | J11 | Families of Hyperkaehler varieties via families of stability conditions | |
Abstract: Abstract: Stability conditions on derived categories of algebraic varieties and their wall-crossings have recently been used extensively to study the geometry of moduli spaces of stable sheaves. In work in progress with Macri, Lahoz, Nuer, Perry and Stellari, we are extending this toolkit to the "relative" setting, i.e. for a family of varieties. Our construction comes with relative moduli spaces of stable objects; this gives additional ways of constructing new families of varieties from a given family, thereby potentially relating different moduli spaces of varieties. Our main application is for families of cubic fourfolds; in particular, this produces many new examples of algebraically constructed families of Hyperkaehler varieties over a base of maximal dimension 20. |
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2018-05-16 | Wed | *No talk* | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | ||
2018-05-15 | Tue | Simon Willerton (Sheffield) | Magnitude Homology |
13:00 | J11 | A graph with torsion in magnitude homology (after Kaneta and Yoshinaga) | |
2018-05-15 | Tue | Damiano Testa (University of Warwick) | Algebra / Algebraic Geometry seminar |
14:00 | J11 | Plane quartics and their inflection lines | |
Abstract: Let C be a general plane quartic curve. It follows from the Plücker formulas that C admits 24 inflection lines. We address the question of finding all the plane quartics D, having the same 24 inflection lines as C. In joint work with Marco Pacini, we show that, over fields of characteristic coprime with 6, the curve C is uniquely determined by its configuration of inflection lines. |
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2018-05-15 | Tue | Damien Trinh (Manchester) | Cosmology, Relativity and Gravitation |
16:00 | J11, Hicks | The dark sector in light of GW170817 | |
Abstract: Recent observations in the propagation of gravitational waves have seemingly severely restricted viable alternatives to the cosmological constant. Indeed, the stringent constraint that gravitational waves must propagate at the speed of light is not something which many modified gravity theories predict. Using the Equation of State approach, I will discuss its implications to some theories and also highlight some caveats to the recent observations which may yield a slightly more optimistic outlook for this field. |
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2018-05-14 | Mon | Kayla King (Oxford) | Mathematical Biology Seminar Series |
13:00 | Alfred Denny LT1 | ||
2018-05-11 | Fri | Siung Ghai (University of Sheffield) | SP2RC seminar |
12:00 | LT 11 | A statistical study of ionopause perturbation and associated boundary wave formation at Venus. | |
2018-05-10 | Thu | Fredrik Stromberg (Nottingham) | Number Theory seminar |
14:00 | F24 | Spectral theory and Maass forms for noncongruence subgroups | |
Abstract: The spectral theory for congruence subgroups of the modular group is fairly well understood since Selberg and the development of the Selberg trace formula. In particular it is known that congruence subgroups has an infinite number of discrete eigenvalues (corresponding to Maass cusp forms) and there is extensive support towards Selberg’s conjecture that there are no small eigenvalues for congruence subgroups. In contrast to this setting, much less is known for noncongruence subgroups of the modular group even though these groups are clearly arithmetic. In fact, it can be shown that under certain circumstances small eigenvalues must exist. And even the existence of infinitely many “new” discrete eigenvalues is not known for these groups. The main obstacle for developing the spectral theory here is that there is in general no explicit formula for the scattering determinant. In this talk I will present sufficient conditions for an “odd” discrete spectrum to exist and I will also give experimental support for the conjecture that these conditions are also necessary. I will also present an experimental version of Turing’s method for certifying correctness of the spectral counting. |
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2018-05-09 | Wed | Shunsuke Takagi (University of Tokyo) | Pure Maths Colloquium |
14:00 | J11 | General hyperplane sections of 3-folds in positive characteristic | |
Abstract: Miles Reid proved that in characteristic zero, a general hyperplane section of a canonical (resp. klt) 3-hold has only rational double points (resp. klt singularities). His proof heavily depends on the Bertini theorem for free linear series, which fails in positive characteristic. Thus, it is natural to ask whether the same statement holds in positive characteristic or not. In this talk, I will present an affirmative answer to this question when the characteristic is larger than 5. This is joint work with Kenta Sato. |
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2018-05-09 | Wed | Riccardo Vanon (Sheffield) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 9 | The role of zonal flows in self-gravitating astrophysical disc turbulence | |
Abstract: Astrophysical discs whose mass is not negligible compared to their central object (ie. self-gravitating discs) can be induced to fragment or settle into a turbulent-like state due to the de-stabilising action of self-gravity. Although the fragmentation process is well studied, the mechanism allowing the gravitational turbulent state to sustain itself is poorly understood, as this requires a continuous extraction of energy from the background flow to prevent its decay. In this talk I will present numerical simulations, carried out using a bespoke pseudo-spectral code, that will show how the gravitational turbulent state and the formation of zonal flows in the disc are strongly connected thanks to the action of axisymmetric and non-axisymmetric instabilities. |
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2018-05-09 | Wed | Matthew Bisatt (King's College) | Number Theory seminar |
15:00 | LT 9 | The generalised Birch--Swinnerton-Dyer conjecture and twisted L-functions | |
Abstract: The Birch and Swinnerton-Dyer conjecture famously connects the rank of an elliptic curve to the order of vanishing of its L-function. We combine this with a conjecture of Deligne to study twisted L-functions and derive several interesting properties of them using tools from representation theory. We show that, under certain conditions, these conjectures predict that the order of vanishing of the twisted L-function is always a multiple of a given prime and provide analogous statements for L-functions of modular forms. |
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2018-05-09 | Wed | Davide Spriano (ETH Zurich) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | What is geometric group theory (and why people care about it) | |
Abstract: Geometric group theory is an area of mathematics that focuses on understanding a group by understanding its geometric properties, which are typically expressed in terms of actions on metric spaces. The advantage of the geometric group theory approach is that it provides a better understanding of groups of great interest on which more classical approach would fail. A prominent example is given by "automorphism groups of certain objects". They can be easily defined, but it is not at all clear when they are, for instance, finitely generated. The first part of the talk will be concerned in providing example of such groups motivating why are they interesting and which are the main difficulties that arises in the study of them. In the second part, we will introduce some of the fundamental concepts and tools of geometric group theory and coarse geometry. |
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2018-05-08 | Tue | Johannes Nicaise (Imperial College (London)) | Algebra / Algebraic Geometry seminar |
14:00 | J11 | A motivic Fubini theorem for the tropicalization map | |
Abstract: Abstract: This talk is based on joint work with Sam Payne (arXiv:1703.10228). Kontsevich and Soibelman's motivic upgrade of Donaldson-Thomas theory produces refined curve counting invariants by means of motivic vanishing cycles of potential functions. In order to get a coherent theory, Kontsevich-Soibelman and Davison-Meinhardt have conjectured formulas for the motivic vanishing cycles of special types of functions. I will explain how one can deduce these formulas from a combination of Hrushovski-Kazhdan motivic integration and tropical geometry. |
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2018-05-04 | Fri | Mathew Owens (University of Reading) | SP2RC seminar |
13:00 | LT 09 | The changing heliosphere. | |
Abstract: Knowledge of long-term solar variability underpins understanding of the solar dynamo and quantification of potential climate and space weather implications. Prior to direct spacecraft measurements of the heliospheric magnetic field (HMF) and solar wind, accurate annual reconstructions are possible using geomagnetic and sunspot records. On longer timescales, information about the HMF can be extracted from cosmogenic radionuclide records, particularly 14C in ancient trees and 10Be in ice sheets. I'll discuss these proxies and what they reveal about the HMF and solar wind, both in terms of space climate and space weather. |
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2018-05-03 | Thu | Salvo Guglielmino (Osservatorio Astrofisico di Catania) | SP2RC seminar |
10:00 | K14 | Interactions between pre-existing and emerging magnetic flux systems observed with IRIS | |
Abstract: We report multi-wavelength ultraviolet observations taken with the IRIS satellite, concerning the emergence phase in the upper chromosphere and transition region of an emerging flux region (EFR) embedded in the unipolar plage of active region NOAA 12529. IRIS data are complemented by full-disk, simultaneous observations of the Solar Dynamics Observatory satellite, relevant to the photosphere and the corona. The photospheric configuration of the EFR is also analysed by measurements taken with the spectropolarimeter onboard the Hinode satellite, when the EFR was fully developed. Recurrent intense brightenings that resemble UV bursts, with counterparts in all coronal passbands, are identified at the edges of the EFR. Jet activity is also found at chromospheric and coronal levels, near the observed brightness enhancement sites. Analysis of the IRIS line profiles reveals heating of dense plasma in the low solar atmosphere and the driving of bi-directional, high-velocity flows with speeds up to 100 km/s at the same locations. Comparing these signatures with previous observations and numerical models, we suggest evidence of several long-lasting, small-scale magnetic reconnection episodes between the emerging bipole and the ambient field. This process leads to the cancellation of a pre-existing photospheric flux concentration of the plage with the opposite polarity flux patch of the EFR. Moreover, the reconnection appears to occur higher in the atmosphere than usually found in UV bursts, explaining the observed coronal counterparts. |
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2018-05-03 | Thu | Abhishek Saha (Queen Mary) | Number Theory seminar |
14:00 | J11 | On the critical values for the standard L-function of a Siegel modular form | |
Abstract: I will talk about some joint work with Pitale and Schmidt where we prove an explicit pullback formula that gives an integral representation for the twisted standard L-function for a holomorphic vector-valued Siegel cusp form of degree n and arbitrary level. In contrast to all previously proved pullback formulas in this situation, our formula involves only scalar-valued functions despite being applicable to L-functions of vector-valued Siegel cusp forms. Further, by specializing our integral representation to the case n=2, we prove an algebraicity result for the critical L-values in that case (generalizing previously proved critical-value results for the full level case). Time permitting, I will also talk of some further applications and works in progress. |
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2018-05-02 | Wed | Owen Jones (Cardiff) | Probability in the North East |
13:30 | LT D | Runoff processes on trees | |
Abstract: The volume of catchment discharge that reaches a stream via the overland flow path is critical for water quality prediction, because it is via this pathway that most particulate pollutants are generated and transported to the stream channel, via surface erosion processes. When it rains, spatial variation in the soil infiltration rate leads to the formation and reabsorption of rivulets on the surface, and local topography determines the coalescence of rivulets. We consider the question of how coalescence facilitates overland flow using a highly abstracted version of the problem, in which the drainage pattern is represented by a Galton-Watson tree. We show that as the rate of rainfall increases there is a distinct phase-change: when there is no stream coalescence the critical point occurs when the rainfall rate equals the infiltration rate, but when we allow coalescence the critical point occurs when the rainfall rate is less than the infiltration rate, and increasing the amount of coalescence increases the total expected runoff. |
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2018-05-02 | Wed | David O'Sullivan (Sheffield Hallam University) | Pure Maths Colloquium |
14:00 | J11 | Isomorphism conjectures and assembly maps via topological categories | |
Abstract: The Baum-Connes conjecture is the "commutative" part of Alain Connes' noncommutative geometry programme, since it forms the bridge to classical geometry and topology. In its classical form, the conjecture identifies two object associated with a countable discrete group: one analytical and one topological. In their 1997 paper, Davis and Lück utilised a (then little known) category theoretic variant of an operator algebra to present a unified approach to this conjecture, and to the Isomorphism Conjecture of Farrell and Jones on the algebraic K- and L-theory of integral group rings. In this talk we will look at how this machinery fits together, what information the machinery gives us about the identifying maps, and how we might go about extending the scope of the techniques to topological groups and groupoids. |
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2018-05-02 | Wed | Vittoria Silvestri (Cambridge) | Probability in the North East |
14:20 | LT D | Recent progress on Laplacian growth models | |
Abstract: The Hastings-Levitov planar aggregation models describe growing random clusters on the complex plane, built by iterated composition of random conformal maps. A striking feature of these models is that they can be used to define natural off–lattice analogues of several fundamental discrete models, such as the Eden model or Diffusion Limited Aggregation, by tuning the correlation between the defining maps appropriately. In this talk I will discuss shape theorems and fluctuations of large clusters in the weak correlation regime. Joint work with James Norris and Amanda Turner. |
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2018-05-02 | Wed | David Penman (Essex) | Probability in the North East |
15:30 | LT D | Probabilistic aspects of comparable pairs and linear extensions of partial orders | |
Abstract: Given a finite partially ordered set $(P,\prec)$, a linear extension of it is a total order on the set which is compatible with the original partial order. A comparable pair of elements is two elements $x,y\in P$ for which we have $x\prec y$ or $y\prec x$. It is reasonable to ask about the extent of any relationship between the number of comparable pairs and the number of linear extensions, with an initial rough intuition being that fewer comparable pairs should correspond to more linear extensions. We will focus in this talk on the case of dense posets where a strictly positive proportion of pairs are comparable, though other cases will be considered as well. I shall focus on probabilistic aspects in this version of the talk, including the original motivating problem of estimating how many linear extensions a random interval order (which has roughly two-thirds of pairs comparable) possesses. This talk is based on joint work with Vasileios Iliopoulos and Colin McDiarmid. |
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2018-05-02 | Wed | *No talk* | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | ||
2018-05-02 | Wed | Andreas Kyprianou (Bath) | Probability in the North East |
16:20 | LT D | Entrance and exit at infinity for stable jump diffusions | |
Abstract: In a seminal work from the 50s of the last century, William Feller classified all one-dimensional diffusions on $-\infty\leq a1$ and $\alpha= 1$ differ significantly in the details by virtue of non-existence of local times for $\alpha=1$. |
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2018-05-01 | Tue | Jordan Williamson (Sheffield) | Magnitude Homology |
13:00 | J11 | Magnitude homology equals Hochschild homology II | |
2018-04-26 | Thu | Emmanuel Lecouturier (Paris) | Number Theory seminar |
14:00 | LT 6 | Higher Eisenstein elements in weight 2 and prime level | |
Abstract: In his classical work, Mazur considers the Eisenstein ideal $I$ of the Hecke algebra $T$ acting on cusp forms of weight $2$ and level $\Gamma_0(N)$ where $N$ is prime. When $p$ is an Eisenstein prime, i.e. $p$ divides the numerator of $\frac{N−1}{12}$, denote by $\mathbf{T}$ the completion of $T$ at the maximal ideal generated by $I$ and $p$. This is a $\mathbb{Z}_p$-algebra of finite rank $g_p ≥ 1$ as a $\mathbb{Z}_p$-module. Mazur asked what can be said about $g_p$. Merel proved a criterion for when $g_p \geq 2$. We will give criteria for $g_p \geq 3, 4$ and prove higher Eichler formulas. |
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2018-04-25 | Wed | Andrew Granville (University College London) | Pure Maths Colloquium |
14:00 | J11 | An alternative approach to analytic number theory | |
Abstract: Ever since Riemann's seminal paper in 1859, analytic approaches to number theory have developed out of an understanding of the zeros of the Riemann zeta-function. In 2009, Soundararajan and I proposed an alternative approach (the "pretentious approach"), piecing together many "ad hoc" ideas from the past into a coherent theory. This new theory has taken on a life of its own in the last few years, providing the framework for some impressive new results by Matomaki, Radziwill, Tao and others. In this talk we will explain the main ideas and try to give some sense of how these new works fit in. |
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2018-04-25 | Wed | Caitlin McAuley (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | Introducing stability conditions | |
Abstract: The space of stability conditions is a complex manifold associated to a triangulated category. The definition of a stability condition was motivated by work in string theory and as such, an understanding of the stability manifold will have important consequences in mirror symmetry. I'll introduce stability conditions on an arbitrary triangulated category and discuss some of their most important features, as well as discussing some examples. |
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2018-04-24 | Tue | Jordan Williamson (Sheffield) | Magnitude Homology |
13:00 | J11 | Magnitude homology equals Hochschild homology I | |
2018-04-19 | Thu | Martine Barrons (Warwick) | Statistics Seminar |
14:00 | LT3 | ||
2018-04-19 | Thu | Gary McConnell (Imperial) | Number Theory seminar |
14:00 | J11 | Empirical connections between "crystals" of complex equiangular lines and Hilbert's twelfth problem for real quadratic fields | |
Abstract: Let K be a real quadratic field of discriminant D or 4D, and set d to be one of the infinitely many integers for which the square-free part of $(d-1)^2 - 4$ is D. Over the past ten years it has become evident from many calculations that there is a profound connection between certain maximal sets of equiangular lines in complex d-dimensional Hilbert space on the one hand, and the ray class field of K of conductor d on the other. I will give a short outline of what has been discovered and where we believe it may be heading. |
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2018-04-18 | Wed | Ilke Canakci (University of Newcastle) | Pure Maths Colloquium |
14:00 | J11 | Cluster algebras and continued fractions | |
Abstract: I will report on a new connection between cluster algebras and continued fractions given in terms of so-called 'Snake graphs'. Snake graphs are planar graphs first appeared in the context of cluster algebras associated to marked surfaces. In their first incarnation, they were used to give formulas for generators of cluster algebras. Along with further investigations and several applications, snake graphs were also studied from a more abstract point of view as combinatorial objects. This talk will focus on a combinatorial realisation of continued fractions in terms of 'perfect matchings' of snake graphs. I will also discuss applications to Cluster algebras, to elementary Number theory and, time permitting, to Knot theory. This is joint work with Ralf Schiffler. |
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2018-04-18 | Wed | Elena Marensi (Sheffield) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 9 | Calculation of minimal seeds in stabilised pipe flows | |
Abstract: Turbulent wall flows exert a much higher friction drag than laminar flows, with consequent increase in energy consumption and carbon emissions. Considerable research effort is thus directed towards the design of control strategies to reduce the turbulent drag or delay the transition to turbulence. Of fundamental interest from this viewpoint is the so-called minimal seed, i.e. the initial perturbation of lowest energy capable to trigger transition. In this talk, variational methods are used to construct fully nonlinear optimisation problems that seek the minimal seed in stabilised pipe flows. The question of how representative the minimal seed is of typical ambient disturbances is addressed here for the first time by performing a statistical study of the critical initial energies for transition with different initial perturbations. A set of initial conditions are thus generated to investigate the stabilising effect of a simple model for the presence of a baffle in the core of the flow. Significant increases in the critical energy and drag reductions are found to be possible. The relevance of the minimal seed in realistic scenarios will be further discussed, as well as a closely-related variational problem for the control of transition. |
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2018-04-18 | Wed | David Spencer (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | Visualising the values of a binary quadratic form | |
Abstract: The solution of Diophantine equations is still a thriving area in number theory. In this talk I will consider binary quadratic forms, those of the form $ax^2 + bxy + cy^2$ with $a,b,c \in\mathbb Z$. I will show how to construct a graph which allows us to see the possible values such a quadratic form can take. This will allow us to determine when the Diophantine equation $ax^2 + bxy + cy^2 = k$ is solvable in integers $(x,y)$, and to find such integers when it is solvable. |
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2018-04-17 | Tue | Igor Sikora (Sheffield) | Magnitude Homology |
13:00 | J11 | Euler Characteristic II | |
2018-04-17 | Tue | Algebra / Algebraic Geometry seminar | |
14:00 | J11 | ||
2018-04-16 | Mon | Natasha Savage (Liverpool) | Mathematical Biology Seminar Series |
14:00 | Hicks LT6 | Where to draw one’s theoretical boundary: One closed question, one experimental data set, two published models, two opposing answers. | |
2018-03-27 | Tue | Prof. Manolis Georgoulis (Academy of Athens) | SP2RC seminar |
13:00 | LT 10 | From Physical Understanding to Forecasting of Solar Flares and Coronal Mass Ejections | |
Abstract: The imperative and pressing nature of an efficient space weather forecasting has spurred multiple efforts around the world to address this problem. A recent realization is that the problem's tackling should not be restricted to heliophysics, but should utilize help provided by the big data and machine learning communities, in a complementary and reinforcing role. This said, we argue that without the lead of solar and heliospheric physicists, these interdisciplinary efforts would be ill-fated. This is because a successful forecasting effort should be driven by an in-depth understanding of the solar pre-eruption phase(s) and evolution of solar source regions. We will provide a few examples of this enhanced-understanding process put to work in the framework of the EU FLARECAST project on solar flare prediction. From flares, we will then take a conceptual step toward an efficient CME forecasting that can be facilitated by what has been already achieved through FLARECAST and other EU projects. Concluding, we will touch on another necessary aspect of efficient space weather forecasting, namely, the input data from solar monitoring. With continuous, near-realtime monitoring of the Sun attempted predominantly from satellites and spacecraft, we discuss a potentially viable, longer-term and better managed alternative such as a strategically built network of ground-based monitoring stations. Such networks can be served, maintained, and expanded / upgraded at will, better adapting to the problem at hand while reflecting progress in its physical understanding. |
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2018-03-26 | Mon | Hans Werner Henn (Strasbourg) | Topology seminar |
16:00 | J11 | The centralizer resolution of the K(2)-local sphere at the prime 2. | |
Abstract: In the last few years two different resolutions of the K(2)-local sphere at the prime 3 have been used very successfully to settle some basic problems in K(2)-local stable homotopy theory like the chromatic splitting conjecture, the calculation of Hopkins' K(2)-local Picard group and determining $K(2)-local Brown-Comentz duality. The focus is now moving towards the prime 2 where one can hope for similar progress. In this talk we concentrate on one of these two resolutions, the centralizer resolution at the prime 2. |
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2018-03-22 | Thu | Petros Syntelis (ESPOS Seminar) (University of St Andrews) | SP2RC seminar |
10:00 | E39 | Recurrent CME-like Eruptions in Flux Emergence Simulations | |
Abstract: We report on three-dimensional MHD simulations of recurrent small-scale Coronal Mass Ejection (CME)-like eruptions using flux-emergence simulations and study their formation and eruption mechanism. These eruptions have the size and energies of small prominence eruptions. The erupting flux ropes are formed due to the reconnection of J-loops (formed by shearing and rotation) and are located inside magnetic envelope field favouring torus instability. The flux rope eruptions are triggered by the action of a tension removal mechanism, such as the typical tether-cutting where the envelope field reconnects with itself. Another side tether-cutting is also found. There, the envelope field reconnected with the J-loops. The two tether-cutting mechanisms transfer hot plasma differently inside the erupting structures. We report similar mechanisms creating three more eruptions in a recurrent manner. |
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2018-03-22 | Thu | Netan Dogra (Imperial) | Number Theory seminar |
14:00 | J11 | Unlikely intersections and the Chabauty-Kim method over number fields | |
Abstract: Chabauty's method is a method for proving finiteness of rational points on curves under assumptions on the rank of the Jacobian. Recently, Kim has shown that one can extend this to prove finiteness of rational points on curves over Q, under slightly weaker assumptions on the dimension of certain Galois cohomology groups. A conjecture of Beilinson-Bloch-Kato implies these assumptions are always satisfied. In this talk I will explain Kim's construction, and how to extend his results to general number fields by proving an 'unlikely intersection' result for the zeroes of p-adic iterated integrals. |
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2018-03-21 | Wed | Evgeny Shinder (Sheffield) | Pure Maths Colloquium |
14:00 | J11 | Rationality in families of algebraic varieties | |
Abstract: I will talk about the following problem in algebraic geometry: given a family of algebraic varieities, if general fibers are rational, are all fibers rational? The talk will be based on recent joint work of myself and Nicaise, and a development by Kontsevich and Tschinkel. |
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2018-03-21 | Wed | Sam Morgan (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | F20 | Lie groupoids and their application in symplectic geometry | |
Abstract: The aim of this talk is to introduce the theory of Lie groupoids and Lie algebroids to a broad audience. It is hoped that the subject can be well motivated, without many prerequisites. In the second part of the talk, we will see why Lie groupoids were first introduced into symplectic and Poisson geometry, and what role they play here. |
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2018-03-20 | Tue | Igor Sikora (Sheffield) | Magnitude Homology |
13:00 | J11 | Euler characteristics | |
2018-03-19 | Mon | Cameline Orlendo (Glasgow) | Mathematical Biology Seminar Series |
14:00 | Hicks F41 | ||
2018-03-15 | Thu | Matthew Bisatt (King's College) | Number Theory seminar |
14:00 | LT A | The generalised Birch--Swinnerton-Dyer conjecture and twisted L-functions- CANCELLED | |
Abstract: The Birch and Swinnerton-Dyer conjecture famously connects the rank of an elliptic curve to the order of vanishing of its L-function. We combine this with a conjecture of Deligne to study twisted L-functions and derive several interesting properties of them using tools from representation theory. We show that, under certain conditions, these conjectures predict that the order of vanishing of the twisted L-function is always a multiple of a given prime and provide analogous statements for L-functions of modular forms. |
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2018-03-15 | Thu | Dr Robert Massey (Royal Astronomical Society) | |
15:00 | Hicks LT A | Funding Blue Skies Research In The Age Of Austerity | |
2018-03-15 | Thu | Simon Wood (Cardiff) | Topology seminar |
16:00 | J11 | Questions in representation theory inspired by conformal field theory | |
Abstract: Two dimensional conformal field theories (CFTs) are conformally invariant quantum field theories on a two dimensional manifold. What distinguishes two dimensions from all others is that the (Lie) algebra of local conformal transformations become infinite dimensional. This extraordinary amount of symmetry allows certain conformal field theories to be solved by symmetry considerations alone. The most intensely studied type of CFT, called a rational CFT, is characterised by the fact that its representation theory is completely reducible and that there are only a finite number isomorphism classes of irreducibles. The representation categories of these CFTs form so called modular tensor categories which have important applications in the construction of 3-manifold invariants. In this talk I will discuss recent attempts at generalising this very rich structure to CFTs whose representation categories are neither completely reducible nor finite. |
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2018-03-14 | Wed | Igor Sikora (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | Could the Philosophy of Mathematics be interesting for mathematicians | |
Abstract: Philosophical reflections of mathematics are concerned with the fundamental problems about mathematics, such as existence of mathematical objects, subject of research of mathematics, how do we extend our mathematical knowledge, what are relations of mathematics with other sciences etc. In this talk I will attempt to describe several classical and modern problems in philosophy an approaches to solve them. |
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2018-03-08 | Thu | Dr Krishna Prasad (Queen's University, Belfast) | |
10:00 | LT 6 | Frequency-dependent Damping of Slow Magneto-acoustic Waves in Sunspots | |
Abstract: Propagating slow magneto-acoustic waves are regularly observed in the solar corona, particularly in sunspot related loop structures. These waves exhibit rapid damping as they propagate along the loops. Several physical and geometrical effects were found to produce the observed decay in the wave amplitude. It has also been shown that the damping is frequency dependent. A majority of the observed characteristics have been attributed to damping by thermal conduction in the solar corona. Although it is believed that these waves originate in the photosphere, their damping behaviour in the sub-coronal layers is relatively less studied. Using high spatial and temporal resolution images of a sunspot, we investigated propagation and damping characteristics of slow magnetoacoustic waves up to transition region heights. The major conclusions from this study will be discussed in the talk which include: 1) The energy flux in slow waves estimated from the relative amplitudes decays gradually right from the photosphere even when the oscillation amplitude is increasing. 2) The damping displayed by slow waves is frequency dependent well below coronal heights. 3) A spatial comparison of power spectra across the umbra highlights enhancement of high-frequency waves near the umbral center. |
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2018-03-08 | Thu | David Spencer (Sheffield) | Number Theory seminar |
14:00 | F35 | Congruences of local origin for higher levels- CANCELLED | |
Abstract: There are many kinds of congruences between different types of modular forms. The most well known of which is Ramanujan's mod 691 congruence. This is a congruence between the Hecke eigenvalues of the weight 12 Eisenstein series and the Hecke eigenvalues of the weight 12 cusp form (both at level 1). This type of congruence can be extended to give congruences of ''local origin''. In this talk I will explain what is meant by such a congruence while focusing on the case of weight 1. The method of proof in this case is very different to that of higher weights and involves working with Galois representations and ray class characters. |
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2018-03-05 | Mon | Justin Travis (Aberdeen) | Mathematical Biology Seminar Series |
14:00 | Hicks F41 | ||
2018-03-02 | Fri | Dr. Jiajia Liu (University of Sheffield) | SP2RC seminar |
12:00 | LT 11 | A New Tool for CME Arrival Time Prediction Using Machine Learning Algorithms: CAT-PUMA | |
Abstract: Coronal Mass Ejections (CMEs) are arguably the most violent eruptions in the Solar System. CMEs can cause severe disturbances in the interplanetary space and even affect human activities in many respects, causing damages to infrastructure and losses of revenue. Fast and accurate prediction of CME arrival time is then vital to minimize the disruption CMEs may cause when interacting with geospace. In this paper, we propose a new approach for partial-/full-halo CME Arrival Time Prediction Using Machine learning Algorithms (CAT-PUMA). Via detailed analysis of the CME features and solar wind parameters, we build a prediction engine taking advantage of 182 previously observed geo-effective partial-/full-halo CMEs and using algorithms of the Support Vector Machine (SVM). We demonstrate that CAT-PUMA is accurate and fast. In particular, predictions after applying CAT-PUMA to a test set, that is unknown to the engine, show a mean absolute prediction error ~5.9 hours of the CME arrival time, with 54% of the predictions having absolute errors less than 5.9 hours. Comparison with other models reveals that CAT-PUMA has a more accurate prediction for 77% of the events investigated; and can be carried out very fast, i.e. within minutes after providing the necessary input parameters of a CME. We have also designed a publicly free User Interface (https://github.com/PyDL/cat-puma), allowing the community to perform their own applications for prediction using CAT-PUMA. |
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2018-03-02 | Fri | Mladen Dimitrov (Lille) | Number Theory seminar |
14:00 | LT-5 | $p$-adic L-functions for nearly finite slope Hilbert modular forms and the Exceptional Zero Conjecture | |
Abstract: We attach $p$-adic L-functions and improved variants theoreof to families of nearly finite slope cohomological Hilbert modular forms, and use them to prove the Greenberg-Benois exceptional zero conjecture at the central point for forms which are Iwahori spherical at $p$. This is a joint work with Daniel Barrera and Andrei Jorza. |
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2018-03-01 | Thu | Mladen Dmitrov (Université de Lille ) | Pure Maths Colloquium |
14:00 | J11 | L-functions of GL(2n): p-adic properties and nonvanishing of twists | |
Abstract: A crucial result in Shimura's work on the special values of L-functions of modular forms concerns the existence of a twisting character to ensure that a twisted L-value is nonzero at the center of symmetry. Even for simple situations involving L-functions of higher degree this problem is open: for example, if $\pi$ is the automorphic representation attached to a holomorphic cusp form, then it has been an open problem to find a character such that the twisted symmetric cube L-function of $\pi$ does not vanish at the center. We will present a recent joint work with F. Januszewski and A. Raghuram in which purely arithmetic methods involving studying p-adic distributions on Galois groups are used to tackle this problem. Given a cohomological unitary cuspidal automorphic representation $\Pi$ on GL(2n) over a totally real field, under a very mild regularity assumption on the infinity type that ensures two critical points for the standard L-function of $\Pi$, supposing $\Pi$ admits a Shalika model, then for any ordinary prime p for $\Pi$, we prove that for all but finitely many Hecke characters the twisted central L-value of $\Pi$ does not vanish. For example, with a classical normalization of $L$-functions, it follows from our results that there are infinitely many Dirichlet characters $\chi$ such that $L(6, \Delta \otimes \chi) L(17, {\rm Sym}^3\Delta \otimes \chi) \neq 0$ for the Ramanujan $\Delta$-function. |
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2018-03-01 | Thu | Christian Wimmer (Bonn) | Topology seminar |
16:00 | J11 | A model for equivariant commutative ring spectra away from the group order | |
Abstract: Stable homotopy theory simplifies drastically if one consider spectra up to rational equivalence. It is a classical result that taking homotopy groups induces an equivalence $$G \text{-} \mathcal{SHC} \simeq_{\mathbb{Q}} \text{gr.} \prod_{(H \leq G)} \mathbb{Q} [WH] \text{-mod}$$ between the genuine $G$-equivariant stable homotopy category ($G$ finite) and the category of graded modules over the Weyl groups $WH$ indexed by the conjugacy classes of subgroups of $G$. However, this approach is too primitive to be useful for the comparison of highly structured ring spectra in this setting. Let $R \subset \mathbb{Q}$ be a subring such that $|G|$ is invertible in $R$. I will explain how geometric fixed points equipped with additional norm maps related to the Hill-Hopkins-Ravenel norms can be used to give an $R$-local model: They induce an equivalence $$\text{Com}(G\text{-Sp}) \simeq_R \text{Orb}_G \text{-Com}(\text{Sp})$$ between the $R$-local homotopy theories of genuine commutative $G$-ring spectra and $\text{Orb}_G$-diagrams in non-equivariant commutative ring spectra, where $\text{Orb}_G$ is the orbit category of the group $G$. As a corollary this gives an algebraic model $$\text{Com}(G\text{-Sp})_\mathbb{Q} \simeq \text{Orb}_G \text{-CDGA}_\mathbb{Q}$$ for rational ring spectra in terms of commutative differential algebras. I will also try to indicate the analogous global equivariant statements. |
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2018-02-28 | Wed | Peter Millington (Nottingham) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 9 | Energy-parity from a bicomplex algebra | |
Abstract: There is a long history of attempts to alleviate the sensitivity of quantum field theory to vacuum fluctuations and ultraviolet divergences by introducing states of negative norm or states of negative energy. This history involves early works by Dirac, Pauli, Pontrjagin and Krein, as well as more recent suggestions by Linde, Kaplan and Sundrum, and ‘t Hooft and Nobbenhuis. In this talk, we will attempt to construct viable scalar quantum field theories that permit positive- and negative-energy states by replacing the field of complex numbers by the commutative ring of bicomplex numbers. The two idempotent zero divisors of the bicomplex numbers partition the algebra into two ideal subalgebras, and we associate one with positive-energy modes and the other with negative-energy modes. In so doing, we avoid destabilising, negative-energy cascades, while realising a discrete energy-parity symmetry that eliminates the vacuum energy. The probabilistic interpretation is preserved by associating expectation values with the Euclidean inner product of the bicomplex numbers, and both the positive- and negative-energy Fock states have positive-definite Euclidean norms. We consider whether this construction can yield transition probabilities consistent with the usual scattering theory and highlight potential limitations. We conclude by commenting on the extension to spinor, vector and tensor fields. |
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2018-02-27 | Tue | Alice Rizzardo (University of Liverpool) | Algebra / Algebraic Geometry seminar |
14:00 | J11 | ||
2018-02-27 | Tue | Christos Aravanis (Sheffield) | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | Hopf algebras in categories of complexes | |
Abstract: I will discuss about a generalization of the notion of a Hopf algebra in monoidal categories due to Brugieres and Virelizier. Of particular interest will be the derived category of coherent sheaves on a smooth complex projective variety. |
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2018-02-26 | Mon | Dwight Barkley (Warwick) | Applied Mathematics Colloquium |
15:00 | Hicks, LT E | Recent Advances in the subcritical transition to turbulence | |
Abstract: Explaining the route to turbulence in wall-bounded shear flows has been a long and tortuous journey. After years of missteps, controversies, and uncertainties, we are at last converging on a unified and fascinating picture of transition in flows such as pipes, channels, and ducts. Classically, subcritical transition (such as in a pipe), was thought to imply a {\em discontinuous} route to turbulence. We now know that this is not the case -- subcritical shear flows may, and often do, exhibit continuous transition. I will discuss recent developments in experiments, simulations, and theory that have established a deep connection between transition in subcritical shear flows and a class of non-equilibrium statistical phase transitions known as directed percolation. From this we understand how to define precise critical points for systems without linear instabilities and how to characterize the onset of turbulence in terms of non-trivial, but universal power laws. I will discuss the physics responsible for the complex turbulent structures ubiquitously observed near transition and end with thoughts on outstanding open questions. |
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2018-02-26 | Mon | Laurette Tuckerman (ESPCI Paris) | Applied Mathematics Colloquium |
15:45 | Hicks, LT E | Exotic patterns of Faraday waves | |
Abstract: When a fluid layer is vibrated at a sufficiently high amplitude, a pattern of standing waves appears at its surface. Because of the imposed periodicity, this is a Floquet problem, but we explain how to easily solve it. Classically, the pattern takes the form of stripes, squares or hexagons, but we also look at more exotic patterns like quasipatterns, heteroclinic orbits, supersquares, and Platonic polyhedra. (Longer version) A standing wave pattern appears on the free surface of a fluid layer when it is subjected to vertical oscillation of sufficiently high amplitude. Like Taylor-Couette flow (TC) and Rayleigh-Benard convection (RB), the Faraday instability is one of the archetypical pattern-forming systems. Unlike TC and RB, the wavelength is controlled by the forcing frequency rather than by the fluid depth, making it easy to destabilize multiple wavelengths everywhere simultaneously. Starting in the 1990s, experimental realizations using this technique produced fascinating phenomena such as quasipatterns and superlattices which in turn led to new mathematical theories of pattern formation. Another difference is that the Faraday instability has been the subject of surprisingly little numerical study, lagging behind TC and RB by several decades. The first 3D simulation reproduced hexagonal standing waves, which were succeeded by long-time recurrent alternation between quasi-hexagonal and beaded striped patterns, interconnected by spatio-temporal symmetries. In a large domain, a supersquare is observed in which diagonal subsquares are synchronized. A liquid drop subjected to an oscillatory radial force comprises a spherical version of the Faraday instability. Simulations show Platonic solids alternating with their duals while drifting. |
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2018-02-22 | Thu | Adel Betina (Sheffield) | Number Theory seminar |
14:00 | F24 | Classical and overconvergent modular forms - CANCELLED | |
Abstract: I will explain the proof of Kassaei of Coleman’s theorem via analytic continuation on the modular curve. |
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2018-02-22 | Thu | Luca Pol (Sheffield) | Topology seminar |
16:00 | J11 | On the geometric isotropy of a compact rational global spectrum | |
Abstract: In this talk I will explain a way to detect groups in the geometric isotropy of a compact rational global spectrum. As an application, I will show that the Balmer spectrum of the rational global stable homotopy category exhibits at least two different types of prime: group and multiplicative primes. |
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2018-02-21 | Wed | Scott Balchin, Caitlin McAuley, Ariel Weiss | ShEAF: postgraduate pure maths seminar |
16:00 | J11 Hicks | What is...? | |
Abstract: Three fifteen minute introductory talks on some important themes from different areas of pure maths, namely Tiling Spaces, Mirror Symmetry, and the Langlands Program. |
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2018-02-20 | Tue | Daniel Graves (Sheffield) | Magnitude Homology |
13:00 | J11 | Hochschild homology of enriched categories | |
2018-02-20 | Tue | Thanasis Bouganis (Durham) | Number Theory seminar |
14:00 | F24 | On the standard L function attached to Siegel-Jacobi modular forms of higher index | |
Abstract: The standard L function attached to a Siegel modular form is one of the most well-studied L functions, both with respect to its analytic properties and to the algebraicity of its special L-values. Siegel-Jacobi modular forms are closely related to Siegel modular forms, and it was Shintani who first studied the standard L function attached to them. In this talk, I will start by introducing Siegel-Jacobi modular forms and then discuss joint work with Jolanta Marzec on the analytic properties of their standard L function, extending results of Murase and Sugano, and on the algebraicity of its special L values. I will also discuss some open questions. |
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2018-02-20 | Tue | RSS Local Group / Michael Wallace (Sheffield) | RSS Seminar Series |
16:30 | Hicks Room I19 | A tribute to the life and work of Nick Fieller | |
Abstract: Join the Sheffield Local Group in a tribute to Nick Fieller, a member of staff at the University of Sheffield from 1974 until his retirement in 2012, a long-standing fellow of the RSS, and an active member of the local RSS committee until just prior to his death in 2017. The meeting will start with memories of Nick, continue with a seminar given by Dr Michael Wallace from the Department of Archaeology at The University of Sheffield, and end with a drinks reception. A geometric morphometric view of early agriculture - Michael Wallace Nick Fieller had a long and rich history of collaboration with several colleagues in the Department of Archaeology, and Michael was fortunate enough to work with him on the ERC project 'The Evolutionary Origins of Agriculture' (PI: Prof. Glynis Jones). The switch from a mobile hunter-gatherer way of life to one based on settled agriculture was perhaps the most fundamental change in the development of our species, and the subsequent spread of agriculture required the use of crops in environments far outside their natural distribution. A key element of the ERC project was to pioneer the use of geometric modern morphometrics (GMM) for the study of ancient crop remains (primarily cereal grains). GMM allows us to enhance our exploration of past crop remains by quantifying the variation within a crop species, which in turn can offer new insights into ancient crop selection. In this seminar, Michael will discuss some of the key research themes to which GMM can contribute in archaeobotany, the implementation of morphometrics using Vincent Bonhomme's "Momocs' (which was expanded as part of the ERC project), and some of the ongoing research that explores the origins and spread of agriculture. |
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2018-02-19 | Mon | David Miller (St Andrews) | Mathematical Biology Seminar Series |
14:00 | Hicks F41 | Accounting for detectability in spatially-explicit abundance models of cetaceans | |
2018-02-15 | Thu | Neil Dummigan (Sheffield) | Number Theory seminar |
14:00 | J11 | Automorphic forms on Feit's Hermitian lattices | |
Abstract: This is joint work with Sebastian Schoennenbeck. Feit showed, in 1978, that the genus of unimodular hermitian lattices of rank 12 over the Eisenstein integers contains precisely 20 classes. Complex-valued functions on this finite set are automorphic forms for a unitary group. Using Kneser neighbours, we find a basis of Hecke eigenforms, for each of which we propose a global Arthur parameter. This is consistent with several kinds of congruences involving classical modular forms and critical L-values, and also produces some new examples of Eisenstein congruences for U(2,2). |
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2018-02-15 | Thu | Jeremy Colman (Sheffield) | Statistics Seminar |
15:00 | F41 | Stan: better faster MCMC - A user review | |
2018-02-15 | Thu | David Barnes (Queen's University Belfast) | Topology seminar |
16:00 | J11 | Cohomological dimension of profinite spaces | |
Abstract: I will introduce the notion of rational cohomological dimension of topological spaces and show a simple way to calculate it when we restrict ourselves to a certain class of topological spaces. Very roughly, the r.c.d of a space X is the largest p such that the pth rational cohomology of X is non-zero. This invariant can be calculated in terms of the more geometric notion of sheaves on X. The category of sheaves on X is an abelian category and the injective dimension of this category is the r.c.d of X. This is a standard way to calculate the the r.c.d. of a space, but can be rather difficult. In this talk, I will describe how for profinite spaces, this injective dimension is related to a simpler notion: the Cantor-Bendixson dimension of the space. There will be a number of pictures and some nice examples illustrating the calculations. |
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2018-02-14 | Wed | Lassina Dembele (University of Sheffield) | Pure Maths Colloquium |
14:00 | J11 | Hilbert modular forms and arithmetic applications | |
Abstract: Hilbert modular forms were introduced by David Hilbert in 1892 in an attempt to generalise so called elliptic modular forms to other settings. Considered to be a notoriously difficult topic, it wasn't until the mid 1970s that they were seriously studied, notably by Goro Shimura. Since then, they have become very central objects to modern number theory. In this talk, we will start with a gentle introduction to Hilbert modular forms. Then, we will discuss various applications to number theory and arithmetic geometry. |
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2018-02-13 | Tue | Scott Balchin (Sheffield) | Magnitude Homology |
13:00 | J11 | Magnitudes of enriched categories and metric spaces | |
2018-02-13 | Tue | TBA | Algebra / Algebraic Geometry seminar |
14:00 | J11 | ||
2018-02-13 | Tue | Tommi Tenkanen (Queen Mary UL) | Cosmology, Relativity and Gravitation |
16:00 | J11, Hicks | Primordial Black Holes as Dark Matter | |
Abstract: I revisit the cosmological and astrophysical constraints on the fraction of dark matter (DM) in primordial black holes (PBHs). I consider a variety of production mechanisms and mass functions for PBHs and discuss whether they can constitute the observed DM abundance or not. I also discuss how one can constrain the physics of the early Universe with the constraints on PBHs, presenting e.g. constraints on the running of the inflaton spectral index which are comparable to those from the Planck satellite. |
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2018-02-12 | Mon | Malte Heuer (Sheffield) | Differential geometry seminar |
14:00 | LT 11 | Decompositions of Triple Vector Bundles | |
Abstract: I will prove that any triple vector bundle is non-canonically isomorphic to a decomposed one. The method relies on del Carpio-Marek's construction of local splittings of double vector bundles. Our method yields a useful definition of triple vector bundles via atlases of triple vector bundle charts. This is joint work with Madeleine Jotz Lean. |
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2018-02-08 | Thu | Christopher Williams (Imperial) | Number Theory seminar |
14:00 | F24 | p-adic Asai L-functions of Bianchi modular forms | |
Abstract: The Asai (or twisted tensor) L-function attached to a Bianchi modular form is the 'restriction to the rationals' of the standard L-function. Introduced by Asai in 1977, subsequent study has linked its special values to the arithmetic of the corresponding form. In this talk, I will discuss joint work with David Loeffler in which we construct a p-adic Asai L-function -- that is, a measure on Z_p* that interpolates the critical values L^As(f,chi,1) -- for ordinary weight 2 Bianchi modular forms. The method makes use of techniques from the theory of Euler systems, namely Kato's system of Siegel units, building on the rationality results of Ghate. I will start by giving a brief introduction to p-adic L-functions and Bianchi modular forms. |
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2018-02-07 | Wed | Ben Ashby (Bath) | Mathematical Biology Seminar Series |
13:00 | Hicks F20 | ||
2018-02-07 | Wed | Dan Lucas (Keele) | Applied Mathematics Colloquium |
14:00 | Hicks, LT 9 | A dynamical systems perspective on layers and mixing in stratified turbulence | |
Abstract: Stably stratified flows, with dense fluid underlying lighter fluid, are commonly observed in nature and industry. In the oceans the behaviour of turbulence when the fluid is strongly stratified is of great importance if we are to understand fundamental processes such as layer formation and mixing. In this work we approach these issues from the so-called ‘dynamical systems perspective’ where we seek unstable simple solutions, or “exact coherent structures”, which are embedded in the chaos of the turbulent flow. First we show that when forcing the flow with a horizontal shear, spontaneous layers form. We are able to associate the coherent structures responsible for the layers with steady states which a bifurcation analysis shows are the finite amplitude product of a sequence of stratified linear instabilities [1]. Secondly we attack the problem of mixing in stratified turbulence by locating unstable periodic orbits embedded in the turbulence in two parameter regimes; one where the mixing is quite efficient and another where the mixing is weak. The periodic orbits represent a reduced description of the flow which we are able to examine in detail, and compare the processes involved in rearranging the buoyancy field in each case [2]. [1] Lucas, Caulfield & Kerswell 2017 J. Fluid Mech. 832 pp 409-437 [2] Lucas & Caulfield 2017 J. Fluid Mech. 832 R1, |
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2018-02-06 | Tue | Simon Willerton (Sheffield) | Magnitude Homology |
13:00 | J11 | Graph magnitude homology + organization | |
2018-02-06 | Tue | Timothy Logvinenko (University of Cardiff) | Algebra / Algebraic Geometry seminar |
14:00 | J11 | P^n-functors and cyclic covers | |
Abstract: I will begin by reviewing the geometry of a cyclic cover branched in a divisor. I will then explain how it gives the first ever example of a non-split P^n-functor. This is a joint work with Rina Anno (Kansas). |
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2018-02-02 | Fri | Dr Jie Chen (National Astronomical Observatories) | SP2RC seminar |
13:00 | LT 11 | Study of solar coronal jets | |
2018-02-01 | Thu | Scott Balchin | Chromatic homotopy theory reading seminar |
14:00 | J11 | Flat modules over M_FG | |
2018-01-30 | Tue | Yu Qiu (Chinese University of Hong Kong) | Algebra / Algebraic Geometry seminar |
14:00 | J11 | Q-stability conditions on Calabi-Yau-X categories of quivers with superpotential | |
Abstract: We introduce X-stability conditions on Calabi-Yau-X categories and spaces of their specializations, the q-stability conditions. The motivating example comes from the Calabi-Yau-X category D(S) associated to a graded marked surface S, constructed from quivers with superpotential. We show that the cluster category of D(S) is Haiden-Katzarkov-Kontsevich's topological Fukaya category C(S) and Bridgeland-Smith type Calabi-Yau-N categories are the orbit quotients of D(S). Moreover, we show that stability conditions on C(S) induce q-stability conditions on D(S). Finally, we are constructing moduli space to realize the fiber of the spaces of q-stabilty conditions for given complex number s. |
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2018-01-26 | Fri | Mihai Barbulescu (Sheffield) | SP2RC seminar |
13:00 | LT 11 | Periodic Counter Streaming Flows as a Model of Transverse Coronal Loop Oscillations | |
Abstract: Recent numerical simulations have demonstrated that non-linear transverse coronal loop oscillations are susceptible to the Kelvin-Helmholtz instability (KHI) due to the counter streaming motions at the boundaries of the loop. We present the first study of this mechanism using an analytical model. The region at the loop boundary where the shearing motions are greatest is treated as a straight interface separating periodic counter-streaming flows. We derive the governing equations for both a straight and a twisted flux tube model, and find that the magnetic twist contributes significantly towards stabilising the system. Establishing the necessary conditions for coronal loops to become unstable due to shearing is important since, it has been shown, the turbulent behaviour due to the instability may lead to heating of the exterior via Ohmic dissipation. |
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2018-01-23 | Tue | Jordan Williamson | Chromatic homotopy theory reading seminar |
14:00 | J11 | The classification of formal groups | |