AG seminar

Utrecht University

This is the webpage of the Algebraic / Arithmetic Geometry Seminar at Utrecht University. The seminar features both research talks, as well as preprint talks presenting papers that appeared recently on arXiv. If you wish to participate and or be added to the mailing list, contact me at w.lim@uu.nl. See here for the previous talks at AG seminar. 

In Block 4 (Spring 2024), the seminar will usually take place on Wednesday at 1-2pm. For the seminar lunch, we meet at 11:50 on the ground floor of the HFG. 


Ruijie Yang (Berlin) -- Minimal exponent of a hypersurface

Abstract: Recently, the minimal exponent of a hypersurface over complex numbers has been understood as a quite useful refined invariant of the log canonical threshold. It has found many new applications including deformation of Calabi-Yau 3-folds (Friedman-Laza), higher rational and higher du Bois singularities (Mustata-Popa) and geometric Schottky problem (Schnell-Yang). However, some properties of this invariant remain mysterious. In this talk I will discuss the conjecture of Mustata and Popa on birational characterization of the minimal exponent via log resolutions, which is the main obstruction for the computation in practice. I will explain the heuristic of the Mustata-Popa conjecture from Igusa's work on counting integer solutions of congruence equations and the monodromy conjecture. Then I will discuss how several ideas from Hodge theory and geometry representation theory can lead to a better understanding of the minimal exponent (birationally). This is based on the joint work with Christian Schnell on higher multiplier ideals and the joint work in progress with Dougal Davis on a new description of the Kashiwara-Malgrange V-filtration of mixed Hodge modules.


Felix Wierstra (Utrecht) -- The Mumford conjecture

Abstract: The Mumford conjecture is an important result that computes the cohomology of the moduli space of curves in the stable range and was originally proved by Madsen and Weiss about 20 years ago. Recently, a new alternative proof of the Mumford conjecture was given by Bianchi. In this talk, I will discuss a version of Bianchi's proof which was further streamlined by Das and Petersen.



Bianca Gouthier (University of  Bordeaux) -- Infinitesimal rational actions

Abstract: For any finite $k$-group scheme $G$ acting rationally on a $k$-variety $X$, if the action is generically free then the dimension of $Lie (G)$ is upper bounded by the dimension of the variety. This inequality turns out to be also a sufficient condition for the existence of such actions, when $k$ is a perfect field of positive characteristic and $G$ is infinitesimal commutative trigonalizable. These group schemes are non-reduced and arise only in positive characteristic. After presenting the main objects involved and overviewing the motivation for this problem, we willl explain the result in the case of actions of the $p$-torsion of a supersingular elliptic curve.


Rahul Pandharipande (ETH Zurich) -- Higher genus GW theory of the Hilbert scheme of points of the plane

Abstract: The quantum cohomology of the Hilb(C2,n) is determined by the operator of quantum multiplication by the divisor class (and was computed 20 years ago in work with Okounkov). I will explain how to think about the higher genus theory from several perspectives: CohFT, MNOP, and, in the case of genus 1, the intersection theory of the moduli space A_g of PPAVs. The talk is connected to recent joint and disjoint work of several mathematicians: S. Canning, F. Greer, A. Iribar Lopez, C. Lian, S. Molcho, D. Oprea, A. Pixton,and  H.-H. Tseng.


Young-hoon Kiem (KIAS) -- Shifted Lagrange multipliers method

Abstract: Lagrange multipliers method relates critical points on a submanifold with those on the ambient manifold. In derived algebraic geometry, we are allowed to consider a more general type of functions called shifted functions and their critical loci. In this talk, I will discuss how Lagrange multipliers method adapted to derived algebraic geometry naturally produces quantum Lefschetz principle of Chang-Li and more. 


Thibault Poiret (University of St Andrews) -- Moduli of roots of universal line bundles

Abstract: Let L be a line bundle on the universal curve over M_{g,n}. The moduli space S^0 of r-th roots of L admits a natural compactification S over the Deligne-mumford compactification of M_{g,n}. When r is 2 and L is the canonical bundle, S^0 is the well-studied moduli space of spin curves, which is known to have two connected components: one parametrizing even spin curves, and one parametrizing odd spin curves. I will describe a natural partition of S into connected locally closed subspaces for arbitrary r and L. This partition is compatible with the partition of the Deligne-Mumford compactification indexed by stable graphs. This is joint work in progress with Margarida Melo.


Raju Krishnamoorthy (Humboldt Universität Berlin) -- tbd

Abstract: tbd


Katharina Hübner (Goethe-Universität Frankfurt) -- tbd

Abstract: tbd


Lucien Hennecart (University of Edinburgh) -- tbd

Abstract: tbd