Past Events

A conjecture of Alon states that, for some absolute constant C, every finite group G possesses a Cayley graph with clique and independence number each at most C log |G|. Recently, Conlon, Fox, Pham, and Yepremyan have verified this conjecture for most abelian groups using mainly graph-theoretic…

The Langlands correspondence for real groups is a classification of irreducible admissible representations of a real reductive group in terms of Langlands parameters associated with the dual group. It was conjectured by Soergel (and proved in a restricted setting by Bezrukavnikov and Vilonen)…

Suppose you are given a sequence {a_n} of integers which obeys a linear recurrence relation. Can you decide whether this sequence has a zero? It turns out that this problem is hard. I will attempt to explain why. There might be p-adic analysis, transcendental number theory, and/or finite…

Suppose we are given a globally hyperbolic spacetime (M,g) solving the Einstein vacuum equations, and a timelike geodesic in M. I will explain how to construct, on any compact subset of M, a solution g_\epsilon of the Einstein vacuum equations which is approximately equal to g far from the…

We study the equilibrium temperature distribution in a model for strongly magnetized plasmas in dimension two and higher. Provided the magnetic field is sufficiently structured (integrable in the sense that it is fibered by co-dimension one invariant tori, on most of which the field lines…

Recently, 3&4 manifolds with finite group actions has become a popular topic. Real manifolds form the simplest class among them. Following the strategy of Manolescu, Kronheimer-Mrowka, respectively, Konno- Miyazawa-Taniguchi and Li introduced two versions of real Seiberg-Witten-Floer…

Suppose we are given a globally hyperbolic spacetime (M,g) solving the Einstein vacuum equations, and a timelike geodesic in M. I will explain how to construct, on any compact subset of M, a solution g_\epsilon of the Einstein vacuum equations which is approximately equal to g far from the…

The s-cobordism theorem uses simple homotopy equivalences, a refinement of homotopy equivalences detected by Whitehead torsion, to distinguish h-cobordant manifolds. More recently, it has appeared in symplectic geometry through the work of Abouzaid and Kragh, in connection with the topology of…

The Toda lattice is a particle system of classical mechanics, discovered by Toda in 1967. Due to its integrability, the Toda lattice with N particles possesses N independent conserved quantities. In this work, we show that under a certain class of random initial data with a constant particle…

The Toda lattice is a particle system of classical mechanics, discovered by Toda in 1967. Due to its integrability, the Toda lattice with N particles possesses N independent conserved quantities. In this work, we show that under a certain class of random initial data with a constant particle…