Events and Activities

Sponsored by Dr. John P. Hempel 

Organizer: Jacob Tsimerman

We will focus 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 will...

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 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...

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...

Abstract: We will discuss a proof that the integral Hodge conjecture is false for a very general abelian variety of dimension ≥ 4. Associated to any regular matroid is a degeneration of principally polarized abelian varieties. We introduce a new...