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...

The relationship between $p$-adic (pro)-etale cohomology and de Rham cohomologies is well understood now for algebraic varieties over local fields of mixed characteristic. For analytic varieties it remains largely conjectural though much progress...

Abstract: Given an algebraic variety over a number field F, one can attach to it its etale cohomology groups, etale fundamental group, and higher etale homotopy groups, all equipped with an action of the absolute Galois group of F. The Galois action...