Algebraic Geometry

The goal of this talk is to explore what symmetries can say about an object. We will then focus on the case of algebraic varieties, where the symmetries are birational self-maps. This is joint work with L. Esser, A. Regeta, C. Urech, and I. van Santen.

The tautological ring for the moduli of Shtukas

Abstract: Many well-known moduli spaces have tautological classes, and it is an important question to study the structure of the subring they generate in cohomology. In this talk, we examine the tautological ring for the moduli of Shtukas,…

Abstract:  We will explain the phenomena in the title in various number field and function field scenarios. 

In 1870 Jordan explained how Galois theory can be applied to problems from enumerative geometry, with the group encoding intrinsic structure of the problem. Earlier Hermite showed the equivalence of Galois groups with geometric monodromy groups, and in 1979 Harris initiated the modern study of…

Given a projective variety $X$, it is always covered by curves obtained by taking the intersection with a linear subspace. We study whether there exist curves on $X$ that have smaller numerical invariants than those of the linear slices. If $X$ is a general complete intersection of large degrees…

In this talk we will introduce new birational invariants.Many examples of obstruction to rationality and G rationality will beconsidered.

Using tropical geometry, Block-Göttsche defined polynomials with the remarkable property to interpolate between Gromov-Witten counts of complex curves and Welschinger counts of real curves in toric del Pezzo surfaces. I will describe a generalization of Block-Göttsche polynomials to…

The local volume of a Kawamata log terminal (klt) singularity is an invariant that plays a central role in the local theory of K-stability. By the stable degeneration theorem, every klt singularity has a volume preserving degeneration to a K-semistable Fano cone singularity. I will talk about a…

The main theme of the talk is the combinatorics of lattice polygons and its relationship to the geometry of the associated toric surfaces. Our point of view is to measure the complexity of lattice polygons via the complexity of geometric objects to which they give rise. For the latter, we will…

The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau…