Past Events

The notions of Hausdorff and Fourier dimensions are ubiquitous in harmonic analysis and geometric measure theory. It is known that any hypersurface in ℝd+1 has Hausdorff dimension d. However, the Fourier dimension depends on the finer geometric...

I will discuss the fourth moment of quadratic Dirichlet L-functions where we prove an asymptotic formula with four main terms unconditionally. Previously, the asymptotic formula was established with the leading main term under generalized Riemann...

Single-cell omics data play a pivotal role in identifying cell-to-cell heterogeneity, understanding cell differentiation, unveiling cell population structures, and ultimately deciphering disease pathogenesis. Due to inherent high-dimensionality...

I will describe some connections between arithmetic geometry of abelian varieties, non-archimedean/tropical geometry, and combinatorics. For a principally polarized abelian variety, we show an identity relating the Faltings height and the Néron--Tate...

In this talk, I will introduce the restricted Euler and hypodissipative Navier-Stokes equations. These equations are analogous to the Euler and hypodissipative Navier-Stokes equations, respectively, but with the Helmholtz projection replaced by a...

The topic of this talk is on Blackbox optimization (BBO), the study of applications, attributes, and solutions of optimization problems in which the values of one or more of the functions defining the problem are provided through blackboxes. The Mesh...

We will discuss conjectures and results regarding the Hilbert Property, a generalization of Hilbert's irreducibility theorem to arbitrary algebraic varieties. In particular, we will explain how to use conic fibrations to prove the Hilbert Property...

Turán-type problems for hypergraphs have been an intriguing area of research. Despite significant efforts, the Turán density of F is known for only a few three-uniform hypergraphs F. This talk concerns Turán-type problems for 3-uniform tight cycles C...

An orthogonal array with parameters \((N,n,q,t)\) (\(OA(N,n,q,t)\) for short) is an \(N\times n\) matrix with entries from the alphabet \(\{1,2,...,q\}\) such that in any of its \(t\) columns, all possible row vectors of length \(t\) occur equally...

A basic aim of homological algebra is to establish invariants for various algebraic objects. This is achieved by constructing resolutions for these objects. These resolutions can be intractable, however for quadratic algebras one obtains a simpler...