Seminars Sorted by Series

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...

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...

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...

Abstract: Which complex analytic spaces can arise as the universal cover of a complex algebraic variety? Motivated by this question, Shafarevich asked whether the universal cover of a smooth projective variety X is always holomorphically convex —...

Abstract:  Applications of o-minimality to unlikely intersection problems usually begin with the observation that the relevant analytic covering maps are definable.  However, this observation is almost never literally true in that the maps are...

Abstract: In this talk, we construct a Zariski open dense locus in $M_g$ on which the Beilinson-Bloch height of the Gross-Schoen and Ceresa cycles is a Weil height, i.e. it has a lower bound and satisfies the Northcott property. This implies a...

Abstract: Since Langlands's earliest paper on his now famous program, canonical integral models of Shimura varieties have occupied a central role in modern number theory. Steady progress has been made in the intervening 50 years toward the correct...

Abstract: In 2019, Dimitrov proved the Schinzel-Zassenhaus Conjecture. Harry Schmidt and I extended his general strategy to cover some dynamical variants of this conjecture. One common tool in both results is Dubinin's Theorem on the transfinite...

Abstract: We study a non-commutative counterpart $C_n(X)$ of the symmetric product $Sym^n X$ of a space $X$, defined as the space of nxn-matrix valued points on $X$. Our main result will be a precise formula for the cohomology of this space in great...

Abstract: 
I'll start by discussing some work with Binyamini, Schmidt, and Thomas in which we prove a uniform Manin-Mumford result for products of CM elliptic curves. I'll show how we apply this to obtain an effective Andre-Oort result for fibre...

Abstract: Given a family $X \rightarrow S$, one may consider the corresponding fiber-wise (quasi-) period integrals as (multi)-functions on S. Built out of these using a flag variety, one obtains variation of (mixed) hodge structures giving period...

Abstract: The anabelian phenomenon may be viewed as an arithmetic analogue of Mostow rigidity: it predicts that certain varieties can be reconstructed from their arithmetic fundamental groups. A celebrated result of S. Mochizuki shows that...

Abstract: Constructing completions of period mappings with significant geometric and Hodge-theoretical meaning is an important topic in Hodge theory and its applications. There are rich theories for the classical case in which the period domain is...

Abstract: I will talk about a joint work with Antoine Sedillot. We study sup-norms of sections of metrized line bundles for families of arithmetic varieties. Using Riemann-Zariski spaces we obtain formulas that imply new definability results in the...

Abstract: Joint project with Pavao Mardesic, Laura Ortiz-Bobadilla, and Jessie Pontigo-Herrera.

Hibert's 16th problem asks for an upper bound on the number of limit cycles of planar polynomial vector fields. For polynomial perturbations $\dH+\epsilon...

Abstract: I will give a review of recent progress on finite-time singularity formation in incompressible fluid models.

Abstract: The quadratic Monge optimal transportation problem can be revisited in Euler's language of Hydrodynamics as was explained by Jean-David Benamou and the speaker about 20 years ago. It turns out that Einstein's theory of gravitation, at...

Abstract. I will describe a new geometric approach for the shock formation problem for the Euler equations.   A complete description of the solution along the hypersurface of first singularities or preshocks will be given.

Abstract:   I will discuss the construction of continuous solutions to the incompressible Euler equations that exhibit local dissipation of energy and the surrounding motivations.  A significant open question, which represents a strong form of the...

Abstract: The incompressible porous media (IPM) equation describes the evolution of density transported by an incompressible velocity field given by Darcy’s law. Here the velocity field is related to the density via a singular integral operator...

Abstract: We consider the density properties of divergence-free vector fields $b \in L^1([0,1],\BV([0,1]^2))$ which are ergodic/weakly mixing/strongly mixing: this means that their Regular Lagrangian Flow $X_t$ is an ergodic/weakly mixing/strongly...