Previous Conferences & Workshops

Abstract: I will discuss the general strategy of studying arithmetic objects, such as p-adic Galois representations, L-values, and automorphic forms, as members of (p-adic) families and explain how this can make certain questions more accessible. In...

We revisit the question of whether it is possible to build succinct non-interactive arguments (SNARGs) for all of NP under standard cryptographic assumptions. In particular, we give a candidate non-adaptive SNARG for NP and prove its soundness under...

Sponsored by Dr. John P. Hempel 

Organizer: Jacob Tsimerman

The workshop focused on recent developments in Hodge theory, which has emerged as both a unifying framework and powerful tool for problems in arithmetic and unlikely intersections. The goal...

Abstract: A result of Simpson characterizes subspaces that are (irreducible) algebraic varieties on both sides of the rank one Riemann-Hilbert correspondence. This result suggests an underlying Ax-Schanuel statement. In joint work with Jacob...

We prove that in any dimension n there exists an origin-symmetric ellipsoid of volume c n^2 that contains no points of Z^n other than the origin. Here c > 0 is a universal constant. Equivalently, there exists a lattice sphere packing in R^n whose...

Ellenberg-Jain-Venkatesh (2011) proposed a p-adic version of the Katz-Sarnak philosophy for usual L-functions: the statistics of zeroes of p-adic L-functions, averaged over families, should agree with the limiting eigenvalue statistics of p-adic...

Usually, papers and talks present only a polished final product, and ignore the wrong turns we took along the way. I will do the opposite, and explain how a problem about counting points on moduli spaces led us (myself, Samir Canning, and Olivier...

In this talk, we show that the pair correlation of the Laplacian eigenvalues on 3-dimensional rectangular flat tori follows Poissonian statistics. Similar to the earlier work of Eskin, Margulis, and Mozes on 2D flat tori, these eigenvalues are...