Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Past events in this series


Tue, 27 Feb 2024

14:00 - 15:00
L5

Modular Reduction of Nilpotent Orbits

Jay Taylor
(University of Manchester)
Abstract

Suppose πΊπ•œ is a connected reductive algebraic π•œ-group where π•œ is an algebraically closed field. If π‘‰π•œ is a πΊπ•œ-module then, using geometric invariant theory, Kempf has defined the nullcone π’©(π‘‰π•œ) of π‘‰π•œ. For the Lie algebra π”€π•œ = Lie(πΊπ•œ), viewed as a πΊπ•œ-module via the adjoint action, we have π’©(π”€π•œ) is precisely the set of nilpotent elements.

We may assume that our group πΊπ•œ = πΊ Γ—β„€ π•œ is obtained by base-change from a suitable β„€-form πΊ. Suppose π‘‰ is π”€ = Lie(G) or its dual π”€* = Hom(𝔀, β„€) which are both modules for πΊ, that are free of finite rank as β„€-modules. Then π‘‰ β¨‚β„€ π•œ, as a module for πΊπ•œ, is π”€π•œ or π”€π•œ* respectively.

It is known that each πΊβ„‚ -orbit π’ͺ βŠ† π’©(𝑉ℂ) contains a representative ΞΎ βˆˆ π‘‰ in the β„€-form. Reducing ΞΎ one gets an element ΞΎπ•œ βˆˆ π‘‰π•œ for any algebraically closed π•œ. In this talk, we will explain two ways in which we might want ΞΎ to have β€œgood reduction” and how one can find elements with these properties. We will also discuss the relationship to Lusztig’s special orbits.

This is on-going joint work with Adam Thomas (Warwick).

Tue, 05 Mar 2024

14:00 - 15:00
L5

TBC

Oleg Chalykh
(University of Leeds)
Abstract

to follow

Tue, 12 Mar 2024

14:00 - 15:00
L3

A potpourri of pretty identities involving Catalan, Fibonacci and trigonometric numbers

Enoch Suleiman
(Federal University Gashua)
Abstract

Apart from the binomial coefficients which are ubiquitous in many counting problems, the Catalan and Fibonacci sequences seem to appear almost as frequently. There are also well-known interpretations of the Catalan numbers as lattice paths, or as the number of ways of connecting 2n points on a circle via non-intersecting lines. We start by obtaining some identities for sums involving the Catalan sequence. In addition, we use the beautiful binomial transform which allows us to obtain several pretty identities involving Fibonacci numbers, Catalan numbers, and trigonometric sums.

Tue, 23 Apr 2024

14:00 - 15:00
L5

TBC

Dimitriy Rumynin
(University of Warwick)
Abstract

to follow

Tue, 30 Apr 2024

14:00 - 15:00
tbc

TBC

Lucas Mason-Brown
((Oxford University))
Abstract

to follow