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Events – Upcoming
Rubenstein Commons Meeting Room 5
Wednesday, September 30, 2026 - Friday, October 2,
2026
Organizers: Andreas Blommaert, Beatrix Muehlmann
This workshop will bring together mathematicians and physicists
that have made important contributions to Liouville theory.
Drop-ins are welcome...
Straighten up and fly right: Lessons from the cockpit of a fly
Michael Dickinson
10:30am|Bloomberg Hall, Lecture Hall (First Floor)
Flies represent nearly 10% of all species described by science
and are arguably unmatched among flying organisms in their aerial
agility. The flight trajectory of flies often consists of straight
flight segments interspersed with rapid changes in...
12:30pm|Room 1-N-5, Green Hall or Zoom
Events - Previous
10:30am|Simonyi Hall 101 and Remote Access
Since their inception, random graphs have been a central topic
in probability and combinatorics, offering a remarkably rich
landscape for studying how complex structures emerge from
randomness. We will discuss the following fundamental
questions...
Three-color van der Waerden Numbers Grow Super-exponentially
Jacob Fox
11:00am|Simonyi 101 and Remote Access
The van der Waerden number w(k;r) is the minimum positive
integer N such that every r-coloring of the positive integers up to
N contains a monochromatic k-term arithmetic progression.
Estimating these numbers has remained a challenging open
problem...
A Probabilistic Construction of Bipartite Ramanujan Graphs
10:30am|West Lecture Hall and Remote Access
The first construction of Ramanujan graphs is due to Lubotzky,
Phillips, and Sarnak (STOC 1986, Combinatorica 1987). Their
construction and analysis were deeply algebraic, and at the time it
seemed that only algebraic methods were strong enough to...
Upcoming Talk
Speaker:
Eli Berger, University of Haifa
When:
Monday, October 5, 2026 | 11:00 AM EDT
Where: Simonyi 101 and Remote Access
Abstract
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) relaxation, which is the most common tool for providing a lower bound on the value of the optimal solution. The ratio between the actual value and that of the fractional relaxation is called the integrality gap. A classic bound of Lovász implies that the integrality gap in this problem is at most $11/6$. This has been improved to $5/3$ by Fujito and Okumura. In this talk, we prove that the integrality gap is at most $3/2$, which is best possible. A corollary of this result is that the vertex set of any $3$-uniform, regular hypergraph on $n$ vertices can be covered by $n/2$ (or fewer) edges. This solves the $k=3$ case of a problem of de~A.~Moreira and Kohayakawa. As another application, we derive a certain variant of the Gale-Shapley stable marriage theorem for triples.
Upcoming Schedule
Wednesday, Oct 07, 2026 | 3:30pm
Gil Kalai, Reichman University and The Hebrew University of Jerusalem
Intersection Homology and Combinatorics
Abstract
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", important invariants of polytopes, with particular emphasis on the combinatorially motivated search for a suitable ring structure—or a substitute.
I will then turn to the search for traces of intersection homology in Stanley–Reisner rings and exterior face rings of triangulated spaces. Inspired by the many algebraic manifestations of ordinary Betti numbers for manifolds, we seek descriptions of intersection homology that do not require a chosen stratification.
Finally, I will discuss possible extensions of intersection homology to multiperversities and the prospect of obtaining new topological invariants for singular spaces.
This lecture continues discussions from the pleasant informal 1995 seminar here at the IAS with Bob MacPherson, Mark Goresky, Tom Braden, and a few others. I will try to make it self-contained and easygoing.
Monday, Oct 12, 2026 | 11:00am
Peter Winkler, Dartmouth College
Random Walk and Paint Blending
Abstract
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 graphs". We show that the role of averaging in this lemma can be played by paint blending about which we know nothing.
Joint work with Tejo Madhavarapu and Kyle Petersen.
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