Previous Conferences & Workshops

The Conley conjecture, recently established by Nancy Hingston, asserts that every Hamiltonian diffeomorphism of a standard symplectic 2n-torus admits infinitely many periodic points. While this conjecture has been extended to more general closed...

This is a series of 3 talks on the topology of Stein manifolds, based on work of Eliashberg since the early 1990ies. More specifically, I wish to explain to what extent Stein structures are flexible, i.e. obey an h-principle. After providing some...

Consider the focusing semilinear wave equation in $R^3$ with energy-critical non-linearity \[ \partial_t^2 \psi - \Delta \psi - \psi^5 = 0,\ \psi(0) = \psi_0,\ \partial_t \psi(0) = \psi_1. \]

This equation admits stationary solutions of the form \[...

Andrei Rapinchuk and I have introduced a new notion of ``weak-commensurability’’ of subgroups of two semi-simple groups. We have shown that existence of weakly-commensurable Zariski-dense subgroups in semi-simple groups G_1 and G_2 lead to strong...

For a {0,1}-valued matrix M let CC(M) denote he deterministic communication complexity of the boolean function associated with M. The log-rank conjecture of Lovasz and Saks [FOCS 1988] states that CC(M) <= log^c(rank(M)) for some absolute constant c where rank(M) denotes the rank of M over the field of real numbers. We show that CC(M) <= c rank(M)/logrank(M) for some absolute constant c, assuming a well-known conjecture from additive combinatorics, known as the Polynomial Freiman-Ruzsa (PFR) conjecture. Our proof is based on the study of the "approximate duality conjecture" which was recently suggested by Ben-Sasson and Zewi [STOC 2011] and studied there in connection to the PFR conjecture. First we improve the bounds on approximate duality assuming the PFR conjecture. Then we use the approximate duality conjecture (with improved bounds) to get the aforementioned upper bound on the communication complexity of low-rank martices, and this part uses the methodology suggested by Nisan and Wigderson [Combinatorica 1995]. This is joint work with Eli Ben-Sasson and Shachar Lovett.

Modularity lifting theorems were introduced by Taylor and Wiles and formed a key part of the proof of Fermat's Last Theorem. Their method has been generalized successfully by a number of authors but always with the restriction that the Galois...

The talk will have 2 parts (between the parts we will have a break). In the first part, we will discuss two options for using groups to construct expander graphs (Cayley graphs and Schreier diagrams). Specifically, we will see how to construct...

I'll describe a physical implementation of zero knowledge proofs whose goal is to verify that two physical objects are identical, without revealing any information about them. Our motivation is the task of verifying that an about-to-be-dismantled...