Past Events

Hillel Furstenberg conjectured in the 1960s that the intersections of closed ×2 and ×3-invariant Cantor sets have “small” Hausdorff dimension. This conjecture was proved independently by Meng Wu and by myself; recently, Tim Austin found a simple...

An emerging mechanism for intracellular organization is liquid-liquid phase separation (LLPS). Found in both the nucleus and the cytoplasm, liquidlike droplets condense to create compartments that are thought to localize factors, such as RNAs and...

Given a Galois extension of number fields L/K, the Chebotarev Density Theorem asserts that, away from ramified primes, Frobenius automorphisms equidistribute in the set of conjugacy classes of Gal(L/K). In this talk we report on joint work with D...

Non--isomorphic graphs with isomorphic canonical double cover (CDC) have the same number of walks of arbitrary length from corresponding vertices of the same degree. The total number of walks, for a specific length, depends only on the main...

Principal bundles arise in different areas of matematics with different definitions. However, they all have in common some kind of local triviality. Here I will present some work in progress on generalizing these in terms of join restriction...

Any tangent category has a notion of connection for its differential bundles (the analog of vector bundles). In this talk, we’ll explore what this definition gives us in the tangent category of affine schemes. The talk will be roughly divided into...

Modern machine learning methods, in particular deep learning approaches, have enjoyed unparalleled success in a variety of challenging application fields like image recognition, medical image reconstruction, and natural language processing. While a...

In this project, we discuss some fine properties and the existence of variational solutions to the Total Variation Flow. Instead of the classical Euclidean setting, we intend to work mostly in the general setting of metric measure spaces. During the...

In the preface of its Lectures on Noncommutative Geometry [Gin05], Ginzburg writes: “Each of the mathematical worlds that we study is governed by an appropriate operad. Commutative geometry is governed by the operad of commutative (associative)...

From the work on Bernoulli convolutions by P. Erd\H{o}s in 1939 and up to the recent advances on self-similar measures by M. Hochman, P. Shmerkin, P. Varj\'u, and others, questions on absolute continuity and singularity remain to be a challenge. They...