Previous Conferences & Workshops

Shimura Curves over Q parameterize abelian surfaces with quaternionic multiplication. However the universal families exist only when considerable level structure is added. This makes it difficult to write eqautions for these families, or...

We will present combinatorial approaches to property (T), spectra of graphs and Kazhdan constants.

Coding theory emerged in the late 1940's, thanks to the works of Shannon and Hamming, as the theory supporting "reliable transmission of information (in the presence (fear?) of noise)". More than fifty years since, enormous progress has been made...

We prove a general result bridging the fields of Secure Protocols and Game Theory. We show that ANY mediated game with incomplete information can be perfectly simulated by the players alone, essentially by means of an extensive-form game in which...

Ideal classes in (totally real) number fields give naturally rise to compact orbits inside SL(n,Z)\SL(n,R) for the diagonal subgroup. We will discuss their (equi-)distribution properties as the field varies, and the two main ideas in our approach...

For a discrete group G and a finite subset X of G, let K(G, X) denote the Kazhdan constant of G associated to X. We define the uniform Kazhdan constant of G by K(G) = min { K(G,X) | X is finite and generates G }. Obviously K(G)>0 for any finite...

We give three different analytic interpretations of Szemeredi's famous Regularity Lemma. The first one is a general statement about Hilbert spaces. The second one presents the Regularity Lemma as the compactness of a certain metric space. The third...

Classical Teichmueller space parametrizes complex structures on a Riemann surface of genus g>1. Recently several generalized Teichmueller spaces have been defined and studied by very different approaches. Nevertheless, some of the results are...

Let E be an elliptic curve over the rationals and p a fixed prime. A (very hard) question of Kolyvagin asks if there exists a quadratic discriminant d such that the Tate-Shafarevich group of the quadratic twist E_d has order prime to p. I will...

A code is said to be locally testable if an algorithm can distinguish between a codeword and a vector being essentially far from the code using a number of queries that is independent of the code's length. The question of characterizing codes that...