Past Events

Finitely generated groups can be treated as geometric objects by considering their Cayley graphs with respect to finite generating sets. All such graphs are quasi-isometrically equivalent. In the 80s, Gromov proposed studying finitely generated...

In mathematics, a proof not only demonstrates that a statement is true; it also allows others to confirm its correctness by verifying the argument. This talk highlights two places where the same “prove and verify” principle is applied to build...

Famously, the adjacency matrix of a graph can be used to enumerate walks in graphs. This makes the adjacency spectrum important to understanding graph structure. I will talk about the non-backtracking matrix, which is used to enumerate walks that are...

This talk will focus on the embedding problem: given two subshifts, under what conditions can one be embeded into the other? We will start with the classical Krieger embedding theorem which give criteria for embedding a subshift into a mixing SFT. We...

How many lines can lie on a smooth surface of degree d? This classical question in algebraic geometry has been studied since at least the mid 1800s, when Clebsch gave an upper bound of d(11d-24) for the number of lines on a smooth surface of degree d...

A 1935 problem of Erdos and Szekeres asks for the smallest number, r(n), such that given any collection of r(n) points in the plane there exist n points no 3 of which are the vertices of a right triangle. It is known that r(4) = 8, 9, or 10, and in...

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through...

A common theme in mathematics is to discern properties of a mathematical structure by making certain mathematical "measurements" of that structure. In operator theory, this theme often translates to the problem of studying operators on high- or...

The Jacobian of a very general curve of genus at least 3 contains an algebraic cycle called the Ceresa cycle that is homologically trivial but algebraically nontrivial. It is straightforward to show that hyperelliptic curves have trivial Ceresa cycle...

The main task of causal discovery is to learn direct causal relationships among observed random variables. These relationships are usually depicted via a directed graph whose vertices are the variables of interest and whose edges represent direct...