Previous Conferences & Workshops

An epsilon-biased set X in {0,1}^n is a set so that for every non-empty set T in [n] the following holds. The random bit B(T) obtained by selecting at random a vector x in X, and computing the mod-2 sum of its T-coordinates, has bias at most epsilon...

In joint work with Barry Mazur, we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions for an elliptic curve to have twists of arbitrary 2-Selmer rank, and we...

Sparse recovery problems arise in many applications. Suppose v is an unknown N-dimensional signal with at most k nonzero components. We call such signals k-sparse. Suppose we are able to collect n \ll N linear measurements of v , and wish to...

I will present a recent joint work with Paul Bourgade (Paris) about the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices and matrices from the Gaussian...

The motivating open question for this talk is to find for a given prime p all local Z_p-algebras which can occur as the deformation ring of some linear representation over F_p of some finite group G. We will show for every p that not all of them are...

The theory of Hitchin systems and their moduli spaces of solutions has important connections to N=2 gauge theory in four dimensions. Exploring this connection, we have conjectured the existence of certain integral invariants which encode the...

We consider the problem of approximately solving a system of homogeneous linear equations over reals, where each equation contains at most three variables. Since the all-zero assignment always satisfies all the equations exactly, we restrict the...