Previous Conferences & Workshops

I will report on joint work with Aurel Page on a number/representation theoretic approach to the question "Can you hear the shape of a drum". We use quaternion algebras over number fields to construct pairs of manifolds that "sound the same", but...

We give a lower bound on the codimension of a component of the non-abelian Hodge locus within a leaf of the isomonodromy foliation on the relative de Rham moduli space of flat vector bundles on an algebraic curve. The bound follows from a more...

I will talk very briefly about what number theorists call special values of $zeta$ and L-functions. I will start with some familiar, classical equalities and will attempt to touch upon some less familiar (mostly conjectural and very far reaching)...

A Hodge structure is a certain linear algebraic datum.  Importantly, the cohomology groups of any smooth projective algebraic variety come equipped with Hodge structures which encode the integrals of algebraic differential forms over topological...

I will discuss random walks on manifolds and pose questions of stiffness and rigidity of stationary measures.  In the case of conservative random walks, I will discuss criteria that guarantee stiffness of stationary measures and certain rigidity...

Can we encode data in a way that it is recoverable even when 1) most data becomes corrupted, and 2) we can only read a sub-constant fraction of the database? This is the central question of local list decoding, a powerful tool from coding theory...

$p$-adic character varieties are rigid analytic moduli spaces of $p$-adic representations of fundamental groups. For curves, I will explain how these varieties lead to a non-abelian generalisation of the $p$-adic Hodge-Tate decomposition, by way of...

Langlands, inspired by his work on classification of representations of real groups, initiated a program of classifying representations of certain topological groups associated to reductive groups in terms of Langlands parameters. In the recent...

A conjecture of Komlós states that the discrepancy of any collection of unit vectors is $O(1)$, i.e., for any matrix A with unit columns, there is a vector x with -1,1 entries such that $|Ax|_\infty = O(1)$. The related Beck-Fiala conjecture states...