# 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 TBC ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks Feb 22 Thu Adel Betina (Sheffield) Number Theory seminar 14:00 F24 TBA 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 Nobody knew turbulent transition could be so complicated (provisional title) Feb 26 Mon Laurette Tuckerman (ESPCI Paris) Applied Mathematics Colloquium 15:45 Hicks, LT E Frequency prediction by linear stability analysis around mean flow (provisional title) Feb 27 Tue TBA Magnitude Homology 13:00 J11 TBA 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 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 Dimitrov (Lille) Number Theory seminar 14:00 J11 TBA Mar 2 Fri Mladen Dmitrov (Université de Lille ) Pure Maths Colloquium 14:00 LT-5 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 5 Mon Justin Travis (Aberdeen) Mathematical Biology Seminar Series 14:00 Hicks F41 Mar 6 Tue TBA Magnitude Homology 13:00 J11 TBA Mar 6 Tue Paolo Stellari (Universita' degli studi di Milano) Algebra / Algebraic Geometry seminar 14:00 J11 Mar 7 Wed Ati Sharma (Soothampton) Applied Mathematics Colloquium 14:00 Hicks, LT 9 Mar 8 Thu David Spencer (Sheffield) Number Theory seminar 14:00 F35 TBA Mar 13 Tue TBA Magnitude Homology 13:00 J11 Mar 14 Wed Igor Sikora (Sheffield) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks Mar 15 Thu Matthew Bisatt (King's College) Number Theory seminar 14:00 LT A TBA Mar 19 Mon Cameline Orlendo (Glasgow) Mathematical Biology Seminar Series 14:00 Hicks F41 Mar 21 Wed Evgeny Shinder (Sheffield) Pure Maths Colloquium 14:00 J11 Mar 21 Wed Sam Morgan (Sheffield) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks Mar 22 Thu Netan Dogra (Imperial) Number Theory seminar 14:00 F35 TBA Apr 16 Mon Natasha Savage (Liverpool) Mathematical Biology Seminar Series 14:00 Hicks LT6 Apr 16 Mon Evgeny Ferapontov (Loughborough) Differential geometry seminar 15:00 J11 Dispersionless integrable systems in 3D/4D and Einstein-Weyl/self-dual geometry. Apr 17 Tue Algebra / Algebraic Geometry seminar 14:00 J11 Apr 18 Wed Ilke Canakci (University of Newcastle) Pure Maths Colloquium 14:00 J11 Apr 18 Wed Elena Marensi (Sheffield) Applied Mathematics Colloquium 14:00 Hicks, LT 9 Apr 18 Wed David Spencer (Sheffield) ShEAF: postgraduate pure maths seminar 16:00 J11 Hicks Apr 19 Thu Martine Barrons (Warwick) Statistics Seminar 14:00 LT3 Apr 19 Thu Gary McConnell (Imperial) Number Theory seminar 14:00 J11 TBA May 2 Wed David O'Sullivan (Sheffield Hallam University) Pure Maths Colloquium 14:00 J11 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 Andrew Granville (University College London) Pure Maths Colloquium 14:00 J11 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 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