Seminars Sorted by Series

Twenty years ago, a link was discovered between the neurotransmitter dopamine and the computational framework of reinforcement learning. Since then, it has become well established that dopamine release reflects a reward prediction error, a surprise...

This talk presents evidence that humans learn complex functions by harnessing compositionality: complex structure is decomposed into simpler building blocks. I formalize this idea in the framework of Bayesian nonparametric regression using a grammar...

People learn in fast and flexible ways that elude the best artificial neural networks. Once a person learns how to “dax,” they can effortlessly understand how to “dax twice” or “dax vigorously” thanks to their compositional skills. In this talk, we...

(Joint work with Richard Thomas) I will discuss K-stability and its relation to constant scalar curvature metrics. This leads to a notion of slope stability for manifolds in terms of its subschemes, which gives an obstruction to finding constant...

An incomplete metric, the Weil-Petersson metric, has played a significant role in the study of the geometry of Teichmuller space. We will mainly discuss the asymptotics of the curvatures of this metric in this talk. Some aspects of another metric...

According to the conjecture of Bondal, the derived category of coherent sheaves on any smooth projective variety can be embedded as a semiorthogonal component into the derived category of a Fano variety of higher dimension. I will explain how this...

Searching literature you will find the following statement (I'm paraphrasing): "If $X_1,X_2$ are nonsingular schemes proper over a complete DVR $R$ with residue characteristic 0, and $\phi: X_1 \to X_2$ is birational, then $\phi$ can be factored as...

In the mid 1980s, Mark Green and I conjectured that one could read off the gonality of an algebraic curve $C$ from the syzygies among the equations defining any one sufficiently positive embedding of $C$. Ein and I recently noticed that a small...

In the course of constructing the Langlands correspondence for GL(2) over a function field, Drinfeld discovered a surprising fact about the interaction between étale fundamental groups and products of schemes in characteristic p. We state this...

The Sato–Tate conjecture, originally stated for elliptic curves on 1963, predicts the equidistribution of the normalized Frobenius traces with respect to the Sato–Tate measure, given by the pushforward of the Haar measure on SU(2). We would like to...

Does a smooth proper variety in positive characteristic know the Hodge number of its liftings? The answer is "of course not". However, it's not that easy to come up with a counter-example. In this talk, I will first introduce the background of this...

This talk will focus on geometric realizations of vertex algebras. The Virasoro uniformization provides an incarnation of the Virasoro algebra in the tangent space of the Hodge line bundle on moduli of curves with marked points and local coordinates...

Computing volumes of moduli spaces has significance in many fields. For instance, Witten's conjecture regarding intersection numbers on the Deligne–Mumford moduli space of stable Riemann surfaces has a fascinating connection to the Weil–Petersson...

A significant step in the Pila–Zannier approach to the André–Oort conjecture is a geometric transcendence result for the uniformization map of modular curves. I will discuss joint work with François Loeser. We prove an analogue of this result in non...

Kazhdan–Lusztig (KL) polynomials for Coxeter groups were introduced in the 1970s, providing deep relationships among representation theory, geometry, and combinatorics. In 2016, Elias, Proudfoot, and Wakefield defined analogous polynomials in the...

The Grothendieck group of varieties over a field k is the quotient of the free abelian group of isomorphism classes of varieties over k by the so-called cut-and-paste relations. It moreover has a ring structure coming from the product of varieties...

To reduce to resolving Cohen–Macaulay singularities, Faltings initiated the program of "Macaulayfying" a given Noetherian scheme X. Under various assumptions Faltings, Brodmann, and Kawasaki built the sought Cohen–Macaulay modifications without...

The p-curvature conjecture is an analogue of the Hasse principle for arithmetic differential equations. I will discuss this conjecture in the context of families of algebraic varieties, and among other things, demonstrate a proof of the p-curvature...

The Langlands and Fontaine–Mazur conjectures in number theory describe when an automorphic representation f arises geometrically, meaning that there is a smooth projective variety X, or more generally a Chow motive M in the cohomology of X, such...

Achar recently introduced a "nearby cycles formalism" in the framework of chain complexes of parity sheaves. In this talk, I'll explain joint work with Achar in which we compute the output of this functor in two related settings. The first is affine...

Motivation. Isogenies with a given polarized abelian variety give moduli points in a Hecke orbit. In characteristic zero any Hecke orbit is dense in this moduli space. What can be said about the Zariski closure of a Hecke orbit in positive...

Motivic homotopy theory is a powerful framework for understanding algebraic varieties and the associated algebraic objects. Moreover, computations in the motivic stable homotopy category can also assist in the computation of stable homotopy groups...

P-adic non abelian Hodge theory, also known as the p-adic Simpson correspondence, aims at describing p-adic local systems on a smooth rigid analytic variety in terms of Higgs bundles. I will explain in this talk why the « Hodge-Tate stacks »...