Tue, 05 Nov 2024
16:00
L6

Random growth models with half space geometry

Jimmy He
(Ohio State University)
Abstract
Random growth models in 1+1 dimension capture the behavior of interfaces evolving in the presence of noise. These models are expected to exhibit universal behavior including intriguing occurrences of random matrix distributions, but we are still far from proving such results even in relatively simple models. A key development which has led to recent progress is the discovery of exact formulas for certain models with a rich algebraic structure. I will discuss some of these results, with a focus on models where a single boundary wall is present, as well as applications to other areas of probability.



 

Tue, 03 Dec 2024
16:00
L6

Large deviations of Selberg’s CLT: upper and lower bounds

Emma Bailey
(University of Bristol)
Abstract

Selberg’s CLT informs us that the logarithm of the Riemann zeta function evaluated on the critical line behaves as a complex Gaussian. It is natural, therefore, to study how far this Gaussianity persists. This talk will present conditional and unconditional results on atypically large values, and concerns work joint with Louis-Pierre Arguin and Asher Roberts.

Tue, 05 Nov 2024
14:00
L6

Degenerate Representations of GL_n over a p-adic field

Johannes Girsch
(University of Sheffield)
Abstract

Smooth generic representations of $GL_n$ over a $p$-adic field $F$, i.e. representations admitting a nondegenerate Whittaker model, are an important class of representations, for example in the setting of Rankin-Selberg integrals. However, in recent years there has been an increased interest in non-generic representations and their degenerate Whittaker models. By the theory of Bernstein-Zelevinsky derivatives we can associate to each smooth irreducible representation of $GL_n(F)$ an integer partition of $n$, which encodes the "degeneracy" of the representation. By using these "highest derivative partitions" we can define a stratification of the category of smooth complex representations and prove the surprising fact that all of the strata categories are equivalent to module categories over commutative rings. This is joint work with David Helm.

Tue, 26 Nov 2024
16:00
L6

Level repulsion and the Floquet quantum Ising model beyond integrability

Felix von Oppen
(Freie Universität Berlin)
Abstract

Motivated by a recent experiment on a superconducting quantum
information processor, I will discuss the Floquet quantum Ising model in
the presence of integrability- and symmetry-breaking random fields. The
talk will focus on the relation between boundary spin correlations,
spectral pairings, and effects of the random fields. If time permits, I
will also touch upon self-similarity in the dynamic phase diagram of
Fibonacci-driven quantum Ising models.
 

Tue, 22 Oct 2024
16:00
L6

Simultaneous extreme values of zeta and L-functions

Winston Heap
(Max Planck Institute Bonn)
Abstract
I will discuss a recent joint work with Junxian Li which examines joint distributional properties of L-functions, in particular, their extreme values. Here, it is not clear if the analogy with random matrix theory persists, although I will discuss some speculations. Using a modification of the resonance method we demonstrate the simultaneous occurrence of extreme values of L-functions on the critical line. The method extends to other families and can be used to show both simultaneous large and small values.
 



 

Tue, 15 Oct 2024
16:00
L6

The third moment of the logarithm of the Riemann zeta function

Maxim Gerspach
(KTH Royal Institute of Technology)
Abstract

I will present joint work with Alessandro Fazzari in which we prove precise conditional estimates for the third (non-absolute) moment of the logarithm of the Riemann zeta function, beyond the Selberg central limit theorem, both for the real and imaginary part. These estimates match predictions made in work of Keating and Snaith. We require the Riemann Hypothesis, a conjecture for the triple correlation of Riemann zeros and another ``twisted'' pair correlation conjecture which captures the interaction of a prime power with Montgomery's pair correlation function. This conjecture can be proved on a certain subrange unconditionally, and on a larger range under the assumption of a variant of the Hardy-Littlewood conjecture with good uniformity.

Mon, 26 Aug 2024

14:00 - 15:00
L6

Analytic K-theory for bornological spaces

Devarshi Mukherjee
(University of Münster)
Abstract

We define a version of algebraic K-theory for bornological algebras, using the recently developed continuous K-theory by Efimov. In the commutative setting, we prove that this invariant satisfies descent for various topologies that arise in analytic geometry, generalising the results of Thomason-Trobaugh for schemes. Finally, we prove a version of the Grothendieck-Riemann-Roch Theorem for analytic spaces. Joint work with Jack Kelly and Federico Bambozzi. 

Tue, 29 Oct 2024

14:00 - 15:00
L6

Endomorphisms of Gelfand—Graev representations

Jack G Shotton
(University of Durham)
Abstract

Let G be a reductive group over a finite field F of characteristic p. I will present work with Tzu-Jan Li in which we determine the endomorphism algebra of the Gelfand-Graev representation of the finite group G(F) where the coefficients are taken to be l-adic integers, for l a good prime of G distinct from p. Our result can be viewed as a finite-field analogue of the local Langlands correspondence in families. 

Tue, 21 Jan 2025

14:00 - 15:00
L6

Proof of the Deligne—Milnor conjecture

Dario Beraldo
(UCL)
Abstract

Let X --> S be a family of algebraic varieties parametrized by an infinitesimal disk S, possibly of mixed characteristic. The Bloch conductor conjecture expresses the difference of the Euler characteristics of the special and generic fibers in algebraic and arithmetic terms. I'll describe a proof of some new cases of this conjecture, including the case of isolated singularities. The latter was a conjecture of Deligne generalizing Milnor's formula on vanishing cycles. 

This is joint work with Massimo Pippi; our methods use derived and non-commutative algebraic geometry. 

Tue, 22 Oct 2024

14:00 - 15:00
L6

A recursive formula for plethysm coefficients and some applications

Stacey Law
(University of Birmingham)
Abstract

Plethysms lie at the intersection of representation theory and algebraic combinatorics. We give a recursive formula for a family of plethysm coefficients encompassing those involved in Foulkes' Conjecture. We also describe some applications, such as to the stability of plethysm coefficients and Sylow branching coefficients for symmetric groups. This is joint work with Y. Okitani.

Subscribe to L6