One might say that there exist zeta functions of three kinds: the very well-known ones (whose stock example is Riemann's zeta function); some less familiar ones; and at least one type which has been totally forgotten for decades. We intend to mention instances of all three types. The first type is important, if not predominant, in algebraic number theory, as we will try to illustrate by (very few) examples. As examples of the second type we will discuss zeta functions of finite groups.

Analysis of Boolean functions aims at "hearing the shape" of functions on the discrete cube {-1,1}^n — namely, at understanding what the structure of the (discrete) Fourier transform tells us about the function. 
In this talk, we focus on the structure of "low-degree" functions on the discrete cube, namely, on functions whose Fourier coefficients are concentrated on "low" frequencies. While such functions look very simple, we are surprisingly far from understanding them well, even in the most basic first-degree case. 

A common observation in data-driven applications is that data has a low intrinsic dimension, at least locally.
Thus, when one wishes to work with data that is not governed by a clear set of equations, but still wishes to perform statistical or other scientific analysis, an optional model is the assumption of an underlying manifold from which the data was sampled.
This manifold, however, is not given explicitly but we can obtain samples of it (i.e., the individual data points).

Whenever departing from a pure reversibility in models that are relevant to macroscopic solid behavior, one is most often confronted with 
coupled PDE-ODE systems that behave very badly and for which classical PDE methods fail. A modicum of order can be restored with the introduction of
a notion of unilateral stability. However the resulting energetic framework still displays marginal or severe loss of convexity resulting in non-smoothness and/or 
non-uniqueness.

Rigidity of horospherical group actions, and more generally unipotent group actions, is a well established phenomenon in homogeneous dynamics. Whereas all finite ergodic horospherically invariant measures are algebraic (due to Furstenberg, Dani and Ratner), the category of locally finite measures, particularly in the context of geometrically infinite quotients, is known to be much richer (following works by Babillot, Ledrappier and Sarig). The rigidity of such locally finite measures is manifested in them having large and exhaustive stabilizer groups.

Erdős and Hajnal showed that graphs satisfying any fixed hereditary property contain much larger cliques or independent sets than what is guaranteed by (the quantitative form of) Ramsey's theorem. We start with a whirlwind tour of the history of this observation, and then we present some new results for ordered graphs, that is, for graphs with a linear ordering on their vertex sets.

The talk will introduce, hopefully at a basic level, the meaning and analysis of spaces with Ricci curvature bounds.  We will discuss the process of limiting spaces with such bounds, and studying the singularities on these limits.  The singularities come with a variety of natural structure which have been proven in the last few years, from dimension bounds to rectifiable structure, which is (measure-theoretically) a manifold structure on the singular set.  If time permits we will discuss some recent work involving the topological structure of boundaries of such spaces.

Motivated by questions in p-adic Fourier theory, we study invariant norms on the p-adic Schrödinger representations of Heisenberg groups. These Heisenberg groups are p-adic, and the Schrödinger representations are explicit irreducible smooth representations that play an important role in their representation theory.

A power series f is said to satisfy a p-Mahler equation (p>1 a natural number) if it satisfies a functional equation of the form
                   a_n(x).f(x^{p^n}) + ... + a_1(x).f(x^p) + a_0(x).f(x) = 0
where the coefficients a_i(x) are polynomials. These functional equations were studied by Kurt Mahler with relation to transcendence theory.

Meeting ID: 934 5637 9511
Password: 5l113u




Title: Hypertrees

I will discuss some recent advances in combinatorics, among them the disproof of Hedetniemi conjecture by Shitov, the proof of the sensitivity conjecture by Huang, the progress on the Erdos-Rado sunflower conjecture by Alweiss, Lovett, Wu, and Zhang, and the progress on the expectation threshold conjecture by Frankston, Kahn, Narayanan, and Park.