# Seminars this semester

Series:

 May 21 Mon Angelo Rendina (Sheffield) Number Theory Learning Seminar 14:00 J-11 Geometric definition of modular forms May 22 Tue Paolo Stellari (Universita' degli studi di Milano) Algebra / Algebraic Geometry seminar 14:00 J11 TBA Abstract: TBA May 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. May 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. May 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. May 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. May 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. May 24 Thu Adel Betina (Sheffield) Number Theory Learning Seminar 14:00 J-11 The modular curve May 29 Tue Scott Balchin (Sheffield) Magnitude Homology 13:00 J11 Mangitude homology and persistent homology?? May 29 Tue Elisa Postinghel (University of Loughborough) Algebra / Algebraic Geometry seminar 14:00 J11 May 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. May 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. May 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. May 31 Thu Adel Betina (Sheffield) Number Theory Learning Seminar 14:00 J-11 Modular curve- Part 2 Jun 4 Mon Ariel Weiss (Sheffield) Number Theory Learning Seminar 14:00 J-11 Hasse invariant Jun 5 Tue Algebra / Algebraic Geometry seminar 14:00 J11 Jun 6 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. Jun 7 Thu Adel Betina (Sheffield) Number Theory Learning Seminar 14:00 J-11 Introduction to rigid analytic geometry- Part (1) Jun 11 Mon Adel Betina (Sheffield) Number Theory Learning Seminar 14:00 J-11 Introduction to rigid analytic geometry- Part (2) Jun 12 Tue Algebra / Algebraic Geometry seminar 14:00 J11 Jun 14 Thu Adel Betina (Sheffield) Number Theory Learning Seminar 14:00 J-11 Introduction to rigid analytic geometry- Part (3) Jun 18 Mon Adel Betina (Sheffield) Number Theory Learning Seminar 14:00 J-11 The canonical subgroup Jun 19 Tue Algebra / Algebraic Geometry seminar 14:00 J11 Jun 21 Thu Adel Betina (Sheffield) Number Theory Learning Seminar 14:00 J-11 Classicality Jun 25 Mon Adel Betina (Sheffield) Number Theory Learning Seminar 14:00 J-11 Classicality of overconvergent modular forms Jun 26 Tue Algebra / Algebraic Geometry seminar 14:00 J11 Jun 27 Wed Ariel Weiss (Sheffield) Number Theory Learning Seminar 14:00 J-11 Hida families (classical treatment) Jun 28 Thu Adel Betina (Sheffield) Number Theory Learning Seminar 14:00 J-11 Hida families (a la Pilloni) Jul 3 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). Jul 3 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. Jul 4 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). Jul 4 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. Jul 4 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. Jul 4 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. Jul 5 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. Jul 5 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. Jul 5 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. Jul 5 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. Jul 6 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. Jul 6 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. Jul 6 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. Jul 6 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. Jul 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. Aug 7 Tue Kirill Mackenzie (Sheffield) Differential geometry seminar 14:00 LT 7 Quotients of Lie algebroids Abstract: For a transitive Lie algebroid $A$, and an ideal in the adjoint bundle (= kernel of the anchor), there is a simple construction of a quotient Lie algebroid over the same base, and this has the usual properties. When the base manifold is also quotiented, the situation is more complicated. This talk will describe the general quotient construction, starting with the case of vector bundles. I'll assume a basic familiarity with Lie algebroids. All are welcome.