Past Events

I will discuss a problem that appeared on MathOverflow and its solution by the user “Fedja”. The result we will demonstrate is that if T is subset of the reals with Hausdorff dimension exceeding ½, then there is a positive probability that a standard...

Previously we found certain convolution sums of divisor functions arising from physics yield Fourier coefficients of modular forms. In this talk we will discuss the limitations of the current proof of these formulas. We will also explore the...

A common theme in homotopy theory is to record not just whether two objects are equivalent, but also *how* they are equivalent. For instance, we can consider maps between spaces, homotopies between maps, homotopies between homotopies, and so on. An...

A fundamental challenge in infection biology is predicting the dynamics of within-host microbial growth and immune activation. However, data typically comes as static snapshots, limiting our ability to test theories. Therefore, we established live...

The Polya group Po(K) of a Galois number field K coincides with the subgroup of the ideal class group Cl(K) of K consisting of all strongly ambiguous ideal classes. We prove that there are only finitely many imaginary abelian number fields K whose...

Bregman proximal-type algorithms, such as mirror descent, are popular in optimization and data science for effectively exploiting problem structures and optimizing them under tailored geometries. However, most of existing convergence results rely on...

I will discuss a result with Bonatti and Crovisier from 2009 showing that the C^1 generic diffeomorphism f of a closed manifold has trivial centralizer; i.e. fg = gf implies that g is a power of f. I’ll discuss features of the C^1 topology that...

Measures provide valuable insights into long-term and global behaviors across a broad range of dynamical systems. In this talk, we present our recent research efforts that employ measure theory and optimal transport to tackle core challenges in...

In this talk, we consider a notion of stability for solutions of random optimization problems based on small perturbations of the input data and inspired by the technique for proving CLT using Stein's method as illustrated with examples by Chatterjee...

I will start by giving a broad overview of our seminar so far, outlining the way in which characteristic classes arise from the cohomology of classifying spaces. When the coefficients for cohomology are the real numbers, the characteristic classes...