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Justin Lynd (Aberdeen) "Fusion systems and classifying spaces"
Abstract: The Martino-Priddy conjecture asserts that two finite groups have equivalent p-completed classifying spaces if and only if their associated fusion systems at the prime p are isomorphic. This was first proved by Bob Oliver in 2004 and 2006. Andrew Chermak generalized this in 2013 by showing that each saturated fusion system over a finite p-group has a unique classifying space attached to it. The proofs of these results depend on the classification of the finite simple groups (CFSG). The focus for this talk will be on the group theoretic aspects of joint work with George Glauberman that helped us remove the dependence of these results on the CFSG. These results concern the question: given a finite group G acting on a finite abelian p-group, when can one find a p-local subgroup H (i.e., a normalizer of a nonidentity p-subgroup) having the same fixed points on the module as does G itself?
Located in Academic Departments / Mathematics / Research
"Elliptic curves and the conjecture of Birch--Swinnerton-Dyer", Sarah Zerbes (UCL)
An important problem in number theory is to understand the rational solutions to algebraic equations. One of the first non-trivial examples, cubics in two variables, leads to the theory of so-called elliptic curves. The famous Birch—Swinnerton-Dyer conjecture, one of the Clay Millennium Problems, predicts a relation between the rational points on an elliptic curve and a certain complex-analytic function, the L-function on an elliptic curve. In my talk, I will give an overview of the conjecture and of some new results establishing the conjecture in certain cases.
Located in Academic Departments / Mathematics / Research
Pure Maths Seminar Archive
Located in Academic Departments / Mathematics / Research
Sebastian del Baño (Queen Mary, London) "Gaussian distributions on affine spaces"
Abstract: We present intrinsic variants of some classical results on real and p-adic Gaussian distributions. Results such as the Isserles/Wick formula for higher moments are considerably simplified by using an intrinsic tensorial approach.
Located in Academic Departments / Mathematics / Research
Greg Stevenson (Glasgow) "In search of greener pastures"
There is an instructive and (miraculously) faithful analogy between commutative rings and tensor triangulated categories. One can speak of prime ideals, the Zariski topology, localization, and the resulting spectra in both contexts and these concepts relate to one another in a way that far exceeds what one would naively, and perhaps reasonably, expect. However, there is trouble in paradise: there is no existing analogue of closed subschemes for tensor triangulated categories and, in particular, residue fields are a problematic concept. I'll discuss joint work with Paul Balmer and Henning Krause which is aimed toward elucidating these elusive residue fields.
Located in Academic Departments / Mathematics / Research

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