Past Events

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

In how many ways can an m x n chessboard be tiled using 2 x 1 tiles? The solution is given by the number of perfect matchings in a related graph. Although computationally difficult in general, in this circumstance we are able to efficiently count...

An unweighted graph is conformally rigid if allowing nonnegative edge weights will not increase the second eigenvalue, or decrease the largest eigenvalue, of its Laplacian matrix. There are natural motivations for finding weights on a graph that...

In this talk, we will introduce the Weak and the Strong Lefschetz Properties (WLP and SLP) focusing on Artinian complete intersections. A famous result of Stanley shows that every Artinian monomial complete intersection over a field of characteristic...

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...