Seminars

Given a hypergraph with edges of size at most $3$, the $3$-set cover problem asks to determine the minimum size of a family of edges that covers the vertex set. As the problem is NP-hard, it is natural to consider its fractional (linear programming)...

The recent flurry of AI-generated mathematical activity has brought an avalanche of new results. Among them are the resolution of some conjectures that I made more than a quarter of a century ago, as a graduate student. In this talk I’ll give the...

I will discuss the wonderful theory of intersection homology, introduced by Goresky and MacPherson, and its connections to the combinatorics of convex polytopes and cellular spaces. I will mention results and questions about "toric g-vectors"...

Random walks on a graph, and Markov chains in general, provide endless fascination and myriad applications (for example, in sampling and approximation algorithms.)  A nearly trivial but endlessly useful tool in this theory is the "harmonic lemma for...

A cornerstone result in complexity theory is that O(1)-depth circuits with unbounded fan-in AND/OR gates computing the parity of an n bit string must have exp(n) size. Two completely different proofs of this are known, both dating back to the 1980's...