Seminars Sorted by Series

I will explain the construction of an action of the Hecke category on the principal block of representations of a connected reductive algebraic group over an algebraically closed field of positive characteristic, obtained in joint work with Roman...

Using the arithmetics of quantum numbers we construct some “approximations” of tilting modules for reductive algebraic groups that might be useful for understanding the generational patterns of tilting characters conjectured by Lusztig and...

Let $G$ be a complex reductive group, $G^*$ its dual Poisson-Lie group, and $g$ the Lie algebra of $G$. $G$-valued Stokes phenomena were exploited by P. Boalch to linearise the Poisson structure on $G^*$. I will explain how $Ug$-valued Stokes...

The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the local Langlands program is...

In joint work with Andy Manion, we required a generalization of the tensor product of 2-representations in order to reconstruct the 2-dimensional part of Lipshitz-Oszvath-Szabo’s bordered Heegaard-Floer theory. I will discuss this and possible...

Given a maximal torus $T$ of a connected reductive group $G$ over a local field $F$, there does not exist a canonical embedding of the L-group of $T$ into the L-group of $G$. Generalizing work of Adams and Vogan in the case $F=R$, we will construct...

In an ongoing project of D. Ben-Zvi, Y. Sakellaridis and A. Venkatesh, the authors propose a conjectural generalization of the derived Satake equivalence for complex reductive groups to spherical varieties. I will describe a program aimed at...

The study of totally positive matrices, i.e., matrices with positive minors, dates back to 1930s. The theory was generalised by Lusztig to arbitrary split reductive groups using canonical bases, and has significant impacts on the theory of cluster...

Let $g$ be a semisimple Lie algebra. The affine W-algebra associated to $g$ is a topological algebra which quantizes the algebraic loop space of the Kostant slice. It is constructed as a quantum Hamiltonian (alias quantum Drinfeld--Sokolov)...

Sponsored by Dr. John P. Hempel 

Organizer: Jacob Tsimerman

The goal of the workshop was to investigate recent progress on special cycles from various perspectives, and the connection between geometric and arithmetic methods. 

Speakers:
Yves Andre...

Abstract: Building on previous work of Satake and Baily, Baily and Borel proved in 1966 that arithmetic locally symmetric varieties admit canonical projective compactifications whose graded rings of functions are given by automorphic forms. Such...

Abstract: The cohomology of a family of algebraic varieties carries a number of interrelated structures, of both Hodge-theoretic and arithmetic flavors. I’ll explain joint work with Josh Lam developing analogues of some of these structures and...

Abstract: Let $k$ be a field and $X$ a geometrically connected variety over $k$. The Tate or degeneracy locus of a $l$-adic local system on $X$ is the etale counterpart of the Hodge locus of a VHS. While in the last decade tremendous progresses have...

Abstract: I’ll describe recent work for approaching certain functional transcendence problems through a combination of model theory and differential Galois theory. This is based on joint work with Blazquez-Sanz, Casale, and Nagloo.

Abstract: We prove that an algebraic flat connection has $ {\mathbb R}_{\rm{ an, \  exp}}$-definable flat sections if and only if it is regular singular with unitary monodromy eigenvalues at infinity, refining previous work of Bakker–Mullane. This...

Abstract: We will survey various recent results around the distribution of the Hodge locus of a (mixed) variation of Hodge structures. Various concrete applications to moduli spaces will also be presented.

Abstract: I will discuss work in progress with M. Orr (Manchester) and G. Papas (Weizmann) on the Zilber-Pink conjecture for $Y(1)^3$. This is known for so-called asymmetric curves by the 2012 work of Habegger-Pila. More recently, an approach known...

Abstract: I will talk about mod p versions of the Mumford—Tate and André—Oort conjectures. Via a notion of formal linearity, the two conjectures, together with a third one ($mod p $Ax—Lindemann), are closely entangled with each other — much closer...

Abstract: A classical theorem due to Borel states that every holomorphic map from a poly-punctured disk into a Shimura variety (with torsion-free level structure) extends holomorphically across the punctures to the minimal compactification. As a...

Abstract: Abstract: Let $C$ be a curve defined over a finite field, and let $X/C$ be a non-isotrivial family of K3 surfaces. In joint work with Maulik-Tang, under a compactness assumption (an assumption removed in later work by Tayou), we prove that...

Abstract: From the outset, topology has played an important role in the study of o-minimal structures. The central focus has been on developing the theory of o-minimality as a framework for 'tame topology', built upon the natural and well-behaved...

Abstract: The classical Rees construction (of common use in commutative algebra and Hodge theory) interpolates between filtrations, viewed as $G_m$-equivariant vector bundles on the affine line, and their associated gradings. Various non-abelian...

Abstract: The Zilber-Pink conjecture is a far reaching and widely open conjecture in the area of "unlikely intersections" generalizing many previous results in the area, such as the recently established André-Oort conjecture. Recently the ``G...

Abstract: To show that the Gamma function, restricted to the positive real half-axis, generates an o-minimal structure over the real field, we had to show (in collaboration with Lou van den Dries) that the expansion of the real field by all...

Abstract: : Let $g$:$X \rightarrow S$ be a smooth proper family over algebraic varieties over a number field $K$. Consider the statement $W(g,p)$: the weight-monodromy conjectures hold for all fibres of g defined over a finite extension $L/Q_p$. We...

Abstract: Given a local system on a complex algebraic variety, what are the subvarieties on which the monodromy drops? The talk will discuss these monodromy special loci, a natural generalisation of (the positive period dimension components of) the...

Abstract: I'll talk about some classical problems around orthogonal polynomials and harmonic analysis that fall into the "unlikely intersection" paradigm: they can be reformulated as questions about counting integers in definable sets whose...

Let $I= (f_t)_{t \in [0,1]}$ be an identity isotopy on an oriented surface $M$ and denote by $Cont(I)$ the set of points $z \in M$ whose trajectory $I(z)$ is a contractible loop of $M$. A recent result of Olivier Jaulent asserts that there exists an...

This is a joint work with Renato Iturriaga.

We consider a Hamiltonian $H: \mathbf R^n \times \mathbf R \to \mathbf R, \ (x,p) \mapsto H(x,p)$ that is $Z^n$ periodic in the first variable $x$, and convex superlinear in the second variable $p$.

For $...