Pure Mathematics Seminars
All seminars will take place on Wednesday at 2 pm in Horton LT1, unless stated otherwise. Here is a campus plan.Tea will be served after the seminar at 3pm in Room 237 of the McCrea Building. All are welcome!
Autumn Term 2017
September 27: Alex Fink (Queen Mary) "Tutte characters for combinatorial bialgebras"
Abstract: In the forty years since Rota introduced it, the perspectiveon combinatorial objects through Hopf algebras has continued to growin productivity. For one, Krajewski, Moffatt, and Tanasa found thatmany famous Tutte-like graph polynomials arise in a uniform fashionfrom the Hopf algebras formulated from various classes of topologicalgraph or their associated matroid-like structures. With ClémentDupont and Luca Moci, we tried to understand _arithmetic matroids_ andthe convolution formula of Backman and Lenz for their Tutte polynomialin this fashion. We found an obstruction in the lack of a(convincingly canonical) antipode, but managed to extend the theory tothe bialgebra case. I'll explain.
October 4: !!At 4pm in Horton LT1!! Anitha Thillaisundaram (Lincoln) "On branch groups"
Abstract: Stemming from the Burnside problem, branch groups have delivered lots of exotic examples over the past 30 years. Among them are easily describable finitely generated torsion groups, as well as the first example of a finitely generated group with intermediate word growth. We will investigate a generalisation of the Grigorchuk-Gupta-Sidki branch groups and talk about their maximal subgroups and about their profinite completion. Additionally, we demonstrate a link to a conjecture of Passman on group rings.
October 11: Sibylle Schroll (Leicester) "New varieties of algebras"
Abstract: In this talk I will report on joint work with Ed Green and Lutz Hille introducing new varieties whose points are in bijections with algebras. Each variety has a distinguished point corresponding to a monomial algebras and all algebras in a variety have a properties that are governed by those of the monomial algebra.
October 18: Rachel Newton (Reading) "Counting failures of a local-global principle"
Abstract: The search for rational solutions to polynomial equations is ongoing for more than 4000 years. Modern approaches try to piece together 'local' information to decide whether a polynomial equation has a 'global' (i.e. rational) solution. I will describe this approach and its limitations, with the aim of quantifying how often the local-global method fails within families of polynomial equations arising from the norm map between fields, as seen in Galois theory. This is joint work with Tim Browning.
October 25: Karin Bauer (Graz) "Dimers with boundary, associated algebras and module categories"
Abstract: Dimer models with boundary were introduced in joint work with King and Marsh as a natural generalisation of dimers. We use these to derive certain infinite dimensional algebras and consider idempotent subalgebras w.r.t. the boundary.The dimer models can be embedded in a surface with boundary. In the disk case, themaximal CM modules over the boundary algebra are a Frobenius category which categorifies the cluster structure of the Grassmannian.
November 1: !!Starting at 13.50 in ABLT1!! Aurelien Galateau (Besancon) "Explicit versions of the Manin-Mumford conjecture".
Abstract: The Manin-Mumford conjecture describes the distribution of torsion points in subvarieties of abelian varieties. It was proven by Raynaud thirty years ago, and some explicit versions were later given by Coleman, Buium or Hrushovski. I will discribe these classical results as well as a recent joint work with César Martinez, in which we give uniform bounds for the distribution of torsion points with essentially sharp dependence on the geometry of the subvariety.
November 8: Gareth Jones (Manchester) "Pfaffian functions and elliptic functions"
Abstract: I will discuss work with Harry Schmidt in which we give a definition of Weierstrass elliptic functions in terms of pfaffian functions, refining a result due to Macintyre. I'll also mention an application in which we give an effective version of a result of Corvaja, Masser and Zannier on a sharpening of the Manin-Mumford conjecture for non-split extensions of elliptic curves by the additive group.
November 15: Alison Parker (Leeds) "Some central idempotents for the Brauer algebra"
Abstract: The Brauer algebra is an important algebra in representation theory, partly because it includes the representation theory of the symmetric group as a special case.I will introduce this algebra and give some background as well as explain why it is so important. I will then describe a method for constructing central idempotents in the Brauer algebra that is more efficient and computational tractable than previous methods. This is joint work with Oliver King and Paul Martin.
November 22: Tim Browning (Bristol) "Diophantine equations: use and misuse"
Abstract: Integer solutions to polynomial equations have been studied since the dawn of time. In this talk I will discuss some of the surprising contexts that these equations arise, such as in quantum computing, before describing some recent work specific to cubic equations.
November 29: Simon Smith (Lincoln)
December 6: Xiaolei Wu (Bonn)