# Abstracts

I-70 Algebraic Geometry Symposium

## Invited Speakers

**Ana-Maria Castravet**, Northeastern University*Derived Categories of Moduli Spaces of Stable Rational **Curves*

The Grothendieck-Knudsen moduli space M0,n parametrized stable, rational curves with n markings. It is a question of Orlov whether the derived category of M0,n admits a full, strong, exceptional collection that is invariant under the action of the symmetric group Sn. I will present several approaches towards answering this question; in particular, I will explain a construction of an invariant full exceptional collection on the Losev-Manin space. This is joint work with Jenia Tevelev.

**Lawrence Ein**, University of Illinois, Chicago*Hilbert Scheme of Points for Singular Surfaces*

Let X be a singular surface and let Hilbn(X) be the Hilbert schemes of length n -closed subschemes of X. We would discuss joint work with Xudong Zheng on when Hilbn(X) is irreducible for all n.

**David Eisenbud**, Mathematical Sciences Research Institute*K3 Carpets and their Equations*

Some time ago Gallego and Purnaprajna proved the remarkable fact that there is a unique double structure X on each smooth rational normal 2-dimensional scroll that “looks like” a K3 surface — that is, ΩX = OX and h1OX = 0, or, in commutative algebra language, arithmetically Gorenstein with a-invariant 0. Frank Schreyer and I have been studying the equations of these and a family of related degenerate K3 surfaces. I will begin by describing the lovely old classification of scrolls, and their equations, and then describe the K3 carpets.

**Yifeng Liu**, Northwestern University*Non-Archimedean Dolbeault Cohomology and Superforms*

We will introduce a new cohomology theory for varieties over p-adic fields using analytic logarithmic differential forms, and study the corresponding cycle class map. We will see a close relation of this cohomology with superforms defined by Chambert-Loir and Ducros. If times permits, we will discuss how one can expect Hodge isomorphisms through so-called monodromy maps.

**Hsian-Hua Tseng**, Ohio State University*Gromov-Witten Theory of Hilbert Schemes of Points in the Plane.*

The Hilbert scheme HilbnC2 of n points on C2 parametrize 0-dimensional length-n subschemes of C2. HilbnC2 admits a natural T=(C*)2 action arising from the standard (C*)2-action on C2. About a decade ago, the T-equivariant quantum cohomology of HilbnC2 was completely determined by Okounkov-Pandharipande. In this talk we discuss some recent progress on higher genus Gromov-Witten theory of HilbnC2. This is based on a joint work with R. Pandharipande.

**Junwu Tu**, University of Missouri, Columbia*Gromov-Witten Invariants of Calabi-Yau A-infinity Categories*

Classical mirror symmetry relates Gromov-Witten invariants in symplectic geometry to Yukawa coupling invariants in algebraic geometry. Through non-commutative Hodge theory, one can define categorical Gromov-Witten invariants associated to (Calabi-Yau A-infinity) categories. Conjecturally, this construction should reproduce the Gromov-Witten invariants and Yukawa coupling invariants, when applied Fukaya categories and Derived categories, respectively. In this talk, I describe a first computation of categorical Gromov-Witten invariants at positive genus. This is a joint work with Andrei Caldararu.