Tue, 21 Jun 2022

14:00 - 15:00
L6

### The orbit method and normality of closures of nilpotent orbits

Dan Barbasch
(Cornell University, USA)
Abstract

The work of Kraft-Procesi classifies closures of nilpotent orbits that are normal in the cases of classical complex Lie algebras. Subsequent work of Ranee Brylinsky combines this work with the Theta correspondence as defined by Howe to attach a representation of the corresponding complex group. It provides a quantization of the closure of a nilpotent orbit. In joint work with Daniel Wong, we carry out a detailed analysis of these representations viewed as (\g,K)-modules of the complex group viewed as a real group. One consequence is a "representation theoretic" proof of the classification of Kraft-Procesi.

Thu, 26 May 2022

14:00 - 15:30
L6

### BV Formalism

Sujar Nair
((Oxford University))
Abstract
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.
Fri, 27 May 2022

14:00 - 15:00
L6

### Coping with mechanical stress: tissue dynamics in development and repair

Prof Yanlan Mao
(Laboratory for Molecular Cell Biology UCL)
Abstract

During growth and development, tissue dynamics, such as tissue folding, cell intercalations and oriented cell divisions, are critical for shaping tissues and organs. However, less is known about how tissues regulate their dynamics during tissue homeostasis and repair, to maintain their shape after development. In this talk, we will discuss how differential growth rates can generate precise folds in tissues. We will also discuss how tissues respond to mechanical perturbations, such as stretching or wounding, by altering their actomyosin contractile structures, to change tissue dynamics, and thus preserve tissue shape and patterning. We combine genetics, biophysics and computational modelling to study these processes.

Thu, 02 Jun 2022

14:00 - 15:30
L6

### S-Folds

Horia Magureanu
((Oxford University))
Abstract
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.
Tue, 16 Jun 2020

11:30 - 12:45
L6

### (Postponed)

Angus Macintyre
(Queen Mary University of London)
Abstract

TBA

Thu, 26 May 2022

11:30 - 12:45
L6

### Axiomatizing the existential theory of $F_p((t))$

Arno Fehm
(TU Dresden)
Abstract

From a model theoretic point of view, local fields of positive characteristic, i.e. fields of Laurent series over finite fields, are much less well understood than their characteristic zero counterparts - the fields of real, complex and p-adic numbers. I will discuss different approaches to axiomatize and decide at least their existential theory in various languages and under various forms of resolution of singularities. This includes new joint work with Sylvy Anscombe and Philip Dittmann.

Thu, 05 May 2022

11:30 - 12:45
L6

### Defining valuations in ordered fields

Franziska Jahnke
(University of Münster)
Abstract

We study the definability of valuation rings in ordered fields (in the language of ordered rings). We show that any henselian valuation ring that is definable in the language of ordered rings is already definable in the language of rings. However, this does not hold when we drop the assumption of henselianity.

This is joint work with Philip Dittmann, Sebastian Krapp and Salma Kuhlmann.

Tue, 07 Jun 2022

14:00 - 15:00
L6

### How to restrict representations from a complex reductive group to a real form

Lucas Mason-Brown
((Oxford University))
Abstract

Let G(R) be the real points of a complex reductive algebraic group G. There are many difficult questions about admissible representations of real reductive groups which have (relatively) easy answers in the case of complex groups. Thus, it is natural to look for a relationship between representations of G and representations of G(R). In this talk, I will introduce a functor from admissible representations of G to admissible representations of G(R). This functor interacts nicely with many natural invariants, including infinitesimal character, associated variety, and restriction to a maximal compact subgroup, and it takes unipotent representations of G to unipotent representations of G(R).

Tue, 14 Jun 2022

14:00 - 15:00
L6

### Invariable generation and totally deranged elements of simple groups

Scott Harper
(Bristol)
Abstract

By a classical theorem of Jordan, every faithful transitive action of a nontrivial finite group admits a derangement (an element with no fixed points). More recently, the existence of derangements with additional properties has attracted much attention, especially for primitive actions of almost simple groups. Surprisingly, there exist almost simple groups with elements that are derangements in every faithful primitive action; we say that these elements are totally deranged. I'll talk about ongoing work to classify the totally deranged elements of almost simple groups, and I'll mention how this solves a question of Garzoni about invariable generating sets for simple groups.

Tue, 24 May 2022

15:30 - 16:30
L6

### On centralizers in Azumaya domains

Thomas Bitoun
(University of Calgary)
Abstract

We prove a positive characteristic analogue of the classical result that the centralizer of a nonconstant differential operator in one variable is commutative. This leads to a new, short proof of that classical characteristic zero result, by reduction modulo p. This is joint work with Justin Desrochers available at https://arxiv.org/abs/2201.04606.

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