Seminars Sorted by Series

We start by relating a result on the reducibility of induced representations of a reductive group through local Langlands correspondence to Artin L-functions. Such a result is of interest in the study of the arithmetic theory of intertwining...

A basic question in arithmetic statistics is:  what does the Selmer group of a random abelian variety look like?  This question is governed by the Poonen-Rains heuristics, later generalized by Bhargava-Kane-Lenstra-Poonen-Rains, which predict, for...

The braid group B_{2g+1} has a description in terms of the hyperelliptic mapping class group of a curve X of genus g.  This equips it with an action on V = H_1(X), and we may produce a wealth of new representations S^{\lambda}(V) by applying Schur...

Homological stability is now well established as an organizing principle and computational tool in algebraic topology and other areas. In many cases it is of interest to obtain homological stability with twisted coefficients, and the standard choice...

I will discuss infinite-dimensional linear programs producing bounds on the spectral gap in various settings. This includes new bounds on the spectral gap of hyperbolic manifolds as well as the Cohn+Elkies bound on the density of sphere packings...

In the study of some dynamical systems, the limsup set of a sequence of measurable sets is often of interest. The shrinking targets and recurrence are two of the most commonly studied problems that concern limsup sets. However, the zero-one laws for...

Diophantine approximation deals with quantitative and qualitative aspects of approximating numbers by rationals. A major breakthrough by Kleinbock and Margulis in 1998 was to study Diophantine approximations for manifolds using homogeneous dynamics...

Let $f: \mathbf C^2 \rightarrow \mathbf \C^2$ be a polynomial transformation. The dynamical degree of $f$ is defined as $\lim_n (\text{deg} f^n)^{1/n}$, where $\text{deg} f^n$ is the degree of the $n$-th iterate of $f$. In 2007, Favre and Jonsson...

Following Birkhoff's proof of the Pointwise Ergodic Theorem, it has been studied whether convergence still holds along various subsequences. In 2020, Bergelson and Richter showed that under the additional assumption of unique ergodicity, pointwise...

Ever since Furstenberg proved his multiple recurrence theorem, the limiting behaviour of multiple ergodic averages along various sequences has been an important area of investigation in ergodic theory. In this talk, I will discuss averages along...

We will discuss a version of the Green--Tao arithmetic regularity lemma and counting lemma which works in the generality of all linear forms. In this talk we will focus on the qualitative and algebraic aspects of the result.

In these two talks, I will discuss the structure of certain varieties that depend functorially on the choice of a finite-dimensional vector space. Examples include the variety of d-way tensors of "slice rank" at most k and the variety of degree-d...

In these two talks, I will discuss the structure of certain varieties that depend functorially on the choice of a finite-dimensional vector space. Examples include the variety of d-way tensors of "slice rank" at most k and the variety of degree-d...

In model theory Fraisse limits are certain highly homogeneous countable structures -- examples include the rational numbers as the unique dense linear order without endpoints, and the Rado graph as the "unique infinite random graph".  I will discuss...

The goal of this learning seminar is to explain some of the core model theoretic notions which are behind Tao’s algebraic regularity lemma about definable graphs in finite fields (Tao 2012).

We will assume minimal knowledge of model theory and...

We will survey general definitions and facts about ultrafilters, and how the algebraic operations on the integers extend to the space of ultrafilters. We will also discuss some applications in combinatorial number theory and ergodic theory.

The inverse theorem for the Gowers U^{s+1}-norms has a central place in modern additive combinatorics, but all known proofs of it are difficult and most do not give effective bounds.

Over this seminar and the next, I will give an outline of a proof...

The inverse theorem for the Gowers U^{s+1}-norms has a central place in modern additive combinatorics, but all known proofs of it are difficult and most do not give effective bounds.

Over this seminar and the next, I will give an outline of a proof...

The "intersectivity lemma" states that if a ∈ (0,1) and A_n, n ∈ N,  are measurable sets in a probability space (X,m) satisfying  m(A_n) ≥ a for all n, then there exist a subsequence n_k, k ∈ N, which has positive upper density and such that the...

The notion of strong stationarity was introduced by Furstenberg and Katznelson in the early 90's in order to facilitate the proof of the density Hales-Jewett theorem. It has recently surfaced that this strong statistical property is shared by...

A density theorem for L-functions is quantitative measure of the possible failure of the Riemann Hypothesis. In his 1990 ICM talk, Sarnak introduced the notion of density theorems for families of automorphic forms, measuring the possible failure of...

Sets of recurrence were introduced by Furstenberg in the context of ergodic theory and have an equivalent combinatorial characterization as intersective sets, an observation which has led to interesting connections between these areas.

Originally...

In 1976, Gérard Rauzy proved a characterization of deterministic numbers: y is deterministic iff for any normal number x, x+y is also normal. During my lecture I willdiscuss  how normal and deterministic numbers behave under arithmetic operations. ...