Seminars Sorted by Series

The Bowen-Ruelle conjecture predicts that geodesic flows on negatively curved manifolds are exponentially mixing with respect to all their equilibrium states. In a breakthrough in '98, Dolgopyat pioneered a method rooted in the thermodynamic...

We discuss some recent progress on the model-theoretic problem of classifying the reducts of the complex field (with named parameters and up to interdefinability). The tools we use include Castle’s recent solution of the Restricted Trichotomy...

The Chowla conjecture from 1965 predicts that all autocorrelations of the Liouville function vanish. In fact, after an adaptation, the Chowla conjecture was expected to hold for all aperiodic multiplicative functions with values in the unit disc (cf...

Finding the smallest integer N=ES_d(n) such that in every configuration of N points in R^d in general position there exist n points in convex position is one of the most classical problems in extremal combinatorics, known as the Erdős-Szekeres...

Horospherical group actions on homogeneous spaces are famously known to be extremely rigid. In finite volume homogeneous spaces, it is a special case of Ratner’s theorems that all horospherical orbit closures are homogeneous. Rigidity further...

It is an open question as to whether the prime numbers contain the sum A+B of two infinite sets of natural numbers A, B (although results of this type are known assuming the Hardy-Littlewood prime tuples conjecture).  Using the Maynard sieve and the...

Incidence bound for points and spheres in higher dimensions generally becomes trivial in higher dimensions due to the existence of the Lenz example consisting of two orthogonal circles in ${\Bbb R}^4$, and the corresponding construction in higher...

The last decade has witnessed a revolution in the circle of problems concerned with proving sharp moment inequalities for exponential sums on tori. This has in turn led to a better understanding of pointwise estimates, but this topic remains...

We show that for every positive integer k there are positive constants C and c such that if A is a subset of {1, 2, ..., n} of size at least C n^{1/k}, then, for some d \leq k-1, the set of subset sums of A contains a homogeneous d-dimensional...

The Gowers uniformity k-norm on a finite abelian group measures the averages of complex functions on such groups over k-dimensional arithmetic cubes. The inverse question about these norms asks if a large norm implies correlation with a function of...

The Mackey-Zimmer representation theorem is a key structural result from ergodic theory: Every compact extension between ergodic measure-preserving systems can be written as a skew-product by a homogeneous space of a compact group. This is used, e.g...

Complex dynamics explores the evolution of points under iteration of functions of complex variables. In this talk I will introduce into the context of complex dynamics, a new approximation tool allowing us to construct new examples of entire...

Given $n\in\mathbb{N}$ and $\xi\in\mathbb{R}$, let $\tau(n;\xi)=\sum_{d|n}d^{i\xi}$. Hall and Tenenbaum asked in their book \textit{Divisors} what is the value of $\max_{\xi\in[1,2]} |\tau(n;\xi)|$ for a ``typical'' integer $n$. I will present work...

Erdős-style geometry is concerned with combinatorial questions about simple geometric objects, such as counting incidences between finite sets of points, lines, etc. These questions can be typically viewed as asking for the possible number of...

The goal of this talk is to present new results dealing with the asymptotic joint independence properties of commuting strongly mixing transformations along polynomials. These results form natural strongly mixing counterparts to various weakly and...

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In 1996 Manjul Barghava introduced a notion of P-orderings for arbitrary sets S of a Dedekind domain, with respect to a prime ideal P, which defined associated invariants called P-sequences. He combined these invariants to define generalized...

In its dynamical formulation, the Furstenberg—Sárközy theorem states that for any invertible measure-preserving system $(X, \mu, T)$, any set $A \subseteq X$ with $\mu(A) > 0$, and any integer polynomial $P$ with $P(0) = 0$,
$$c(A) = \lim_{N-M \to...

I will discuss pointwise ergodic theory as it developed out of Bourgain's work in the 80s, leading up to my work with Mirek and Tao on bilinear ergodic averages.

Ruzsa asked whether there exist Fourier-uniform subsets of $\mathbb{Z}/N\mathbb{Z}$ with very few 4-term arithmetic progressions (4-AP). The standard pedagogical example of a Fourier uniform set with a "wrong" density of 4-APs actually has 4-AP...

This talk is based on a joint work with Steve Lester.

We review the Gauss circle problem, and Hardy's conjecture regarding the order of magnitude of the remainder term. It is attempted to rigorously formulate the folklore heuristics behind Hardy's...

Let SO(3,R) be the 3D-rotation group equipped with the real-manifold topology and the normalized Haar measure \mu. Confirming a conjecture by Breuillard and Green, we show that if A is an open subset of SO(3,R) with sufficiently small measure, then...

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This is the organizational meeting for a learning seminar during the fall term on topics related to non-abelian p-adic Hodge theory. 

With every bounded prism Bhatt and Scholze associated a cohomology theory of formal p-adic schemes. The prismatic cohomology comes equipped with the Nygaard filtration and the Frobenius endomorphism. The Bhatt-Scholze construction has been advanced...

Multiplier ideals in characteristic zero and test ideals in positive characteristic are fundamental objects in the study of commutative algebra and birational geometry in equal characteristic.  We introduced a mixed characteristic version of the...

This talk will introduce background, achievements and challenges in the quest to find non-Archimedean versions of the celebrated Corlette-Simpson correspondence, which on Kähler manifolds relates representations of the fundamental group to certain...

I will discuss the following conjecture: an irreducible $\bar{Q}$$_{\ell}$-local system L on a smooth complex algebraic variety S arises in cohomology of a family of varieties over S if and only if L can be extended to an etale local system over...

In this talk, we introduce the analytic de Rham stack for rigid varieties over $Q_p$ (and more general analytic stacks). This object is an analytic incarnation of the (algebraic) de Rham stack of Simpson, and encodes a theory of analytic D-modules...

Cohomology of classifying space/stack of a group G is the home which resides all characteristic classes of G-bundles/torsors. In this talk, we will try to explain some results on Hodge/de Rham cohomology of BG where G is a $p$-power order...

Etale cohomology of $F_p$-local systems does not behave nicely on general smooth p-adic rigid-analytic spaces; e.g., the $F_p$-cohomology of the 1-dimensional closed unit ball is infinite. 

However, it turns out that the situation is much better if...

The notion of $p$-adic shtukas are introduced by Scholze in his Berkeley lectures on $p$-adic geometry. They are closely related to $p$-divisible groups when their ``legs" are bounded by some minuscule cocharacter. But compared to $p$-divisible...

In this talk, I will first describe how classical Dieudonne module of finite flat group schemes and $p$-divisible groups can be recovered from crystalline cohomology of classifying stacks. Then, I will explain how in mixed characteristics, using...

I will present a new theory of motivic cohomology for general (qcqs) schemes. It is related to non-connective algebraic K-theory via an Atiyah-Hirzebruch spectral sequence. In particular, it is non-$A^1$-invariant in general, but it recovers...

I will present two settings where $q$-De Rham and prismatic vector bundles can be described in terms of modules over an appropriate ring of $q$-twisted differential operators and also the relation with former results. 

This is a joint work with...

Motivated by the desire to express in terms of de Rham data the pro-étale cohomology with non-trivial $\mathbb{Q}_p$-coefficients of rigid spaces $X$, defined over $\mathbb{Q}_p$ or $\mathbb{C}_p$, I will explain how to define D-modules on the...

Topological Hochschild homology is an important invariant, closely related to algebraic K-theory, and can be seen as a noncommutative analogue of de Rham chains.

In this talk, I will describe various computations of the ring/monoid of endomorphisms...

In this talk, I will present a computation of the image of the Hodge-Tate logarithm map (defined by Heuer) in the case of smooth Stein varieties. When the variety is the affine space, Heuer has proved that this image is equal to the group of closed...

A few years ago, Bhatt-Morrow-Scholze introduced an invariant of $p$-adic formal schemes called syntomic cohomology, which has a close relationship to (étale-localized) algebraic $K$-theory. In a recent paper, Antieau-Mathew-Morrow-Nikolaus showed...

In the first talk, I will give a broad survey of classical inequalities that arise in enumerative and algebraic combinatorics.  I will discuss how these inequalities lead to questions about combinatorial interpretations, and how these questions...

In the second talk, I will concentrate on polynomial inequalities and whether the defect (the difference of two sides) has a combinatorial interpretation.  For example, does the inequality  $x^2+y^2 \geq 2xy$  have a combinatorial proof and what...

Chapter 14 of the classic text "Computational Complexity" by Arora and Barak is titled "Circuit lower bounds: complexity theory's Waterloo". I will discuss the lower bound problem in the context of algebraic complexity where there are barriers...

A class of tensors, called "concise (m,m,m)-tensors  of minimal border rank", play an important role in proving upper bounds for the complexity of matrix multiplication. For that reason Problem 15.2 of "Algebraic Complexity Theory" by Bürgisser...

The theme of the lecture is the notion of points over F1, the field with one element. Several heuristic computations led to certain expectations on the set of F1-points: for example the Euler characteristic of a smooth projective complex variety X...

This will be an expository talk on the structure and classification of equivariant vector bundles on toric varieties. I will emphasize Klyachko's classification results from the 1980s and 1990s and discuss more recent re-formulations of this...

The Kronecker coefficients of the Symmetric group $S_n$ are the multiplicities of an irreducible $S_n$ representation in the tensor product of two other irreducibles. They were introduced in 1938 by Murnaghan and generalize the beloved Littlewood...