# Seminars this semester

Series:

 Jan 23 Tue Jordan Williamson Chromatic homotopy theory reading seminar 14:00 J11 The classification of formal groups Jan 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. Jan 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. Feb 1 Thu Scott Balchin Chromatic homotopy theory reading seminar 14:00 J11 Flat modules over M_FG Feb 2 Fri Dr Jie Chen (National Astronomical Observatories) SP2RC seminar 13:00 LT 11 Study of solar coronal jets Feb 6 Tue Simon Willerton (Sheffield) Magnitude Homology 13:00 J11 Graph magnitude homology + organization Feb 6 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). Feb 7 Wed Ben Ashby (Bath) Mathematical Biology Seminar Series 13:00 Hicks F20 Feb 7 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, Feb 8 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. Feb 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. Feb 13 Tue Scott Balchin (Sheffield) Magnitude Homology 13:00 J11 Magnitudes of enriched categories and metric spaces Feb 13 Tue TBA Algebra / Algebraic Geometry seminar 14:00 J11 Feb 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. Feb 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). Feb 15 Thu Jeremy Colman (Sheffield) Statistics Seminar 15:00 F41 Stan: better faster MCMC - A user review Feb 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. Feb 19 Mon David Miller (St Andrews) Mathematical Biology Seminar Series 14:00 Hicks F41 Accounting for detectability in spatially-explicit abundance models of cetaceans Feb 20 Tue Daniel Graves (Sheffield) Magnitude Homology 13:00 J11 Hochschild homology of enriched categories Feb 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. Feb 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. Feb 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. Feb 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. Feb 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. Feb 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. Feb 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. Feb 27 Tue Alice Rizzardo (University of Liverpool) Algebra / Algebraic Geometry seminar 14:00 J11 Feb 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. Feb 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. Mar 1 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. Mar 1 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. Mar 2 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. Mar 2 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. Mar 5 Mon Justin Travis (Aberdeen) Mathematical Biology Seminar Series 14:00 Hicks F41 Mar 6 Tue Paolo Stellari (Universita' degli studi di Milano) Algebra / Algebraic Geometry seminar 14:00 J11 Mar 8 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. Mar 8 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. Mar 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. Mar 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. Mar 15 Thu Dr Robert Massey (Royal Astronomical Society) 15:00 Hicks LT A Funding Blue Skies Research In The Age Of Austerity Mar 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. Mar 19 Mon Cameline Orlendo (Glasgow) Mathematical Biology Seminar Series 14:00 Hicks F41 Mar 20 Tue Igor Sikora (Sheffield) Magnitude Homology 13:00 J11 Euler characteristics Mar 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. Mar 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. Mar 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. Mar 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. Mar 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. Mar 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. Apr 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. Apr 17 Tue Igor Sikora (Sheffield) Magnitude Homology 13:00 J11 Euler Characteristic II Apr 17 Tue Algebra / Algebraic Geometry seminar 14:00 J11 Apr 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. Apr 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. Apr 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)$, and to find such integers when it is solvable. Apr 19 Thu Martine Barrons (Warwick) Statistics Seminar 14:00 LT3 Apr 19 Thu Gary McConnell (Imperial) Number Theory seminar 14:00 J11 Empirical connections between "crystals" of complex equiangular lines and Hilbert's twelfth problem for real quadratic fields Abstract: Let K be a real quadratic field of discriminant D or 4D, and set d to be one of the infinitely many integers for which the square-free part of$(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. Apr 24 Tue Jordan Williamson (Sheffield) Magnitude Homology 13:00 J11 Magnitude homology equals Hochschild homology I Apr 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. Apr 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. Apr 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. May 2 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. May 2 Wed Carys Bebbington, Oliver Southwell (Sheffield) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks May 3 Thu Fabrizio Leisen (Kent) Statistics Seminar 14:00 LT A May 3 Thu Abhishek Saha (Queen Mary) Number Theory seminar 14:00 F24 TBA May 8 Tue Johannes Nicaise (Imperial College (London)) Algebra / Algebraic Geometry seminar 14:00 J11 May 9 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. May 9 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. May 9 Wed Davide Spriano (ETH Zurich) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks May 10 Thu Daniel Williamson (Exeter) Statistics Seminar 14:00 LT A May 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. May 14 Mon Kayla King (Oxford) Mathematical Biology Seminar Series 14:00 Alfred Denny LT1 May 15 Tue Damiano Testa Algebra / Algebraic Geometry seminar 14:00 J11 May 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. May 16 Wed Ati Sharma (Soothampton) Applied Mathematics Colloquium 14:00 Hicks, LT 9 May 16 Wed TBC ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks May 17 Thu Frazer Jarvis (Sheffield) Number Theory seminar 14:00 F24 May 22 Tue Algebra / Algebraic Geometry seminar 14:00 J11 May 23 Wed Daniil Proskurin (Kiev Taras Shevchenko University) Pure Maths Colloquium 14:00 J11 May 23 Wed Ciaran Schembri (Sheffield) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks May 29 Tue Elisa Postinghel (University of Loughborough) Algebra / Algebraic Geometry seminar 14:00 J11 May 30 Wed Nebojsa Pavic (Sheffield) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks Jun 5 Tue Algebra / Algebraic Geometry seminar 14:00 J11