# Penn 2014 Abstracts

**Donu Arapura**** (Purdue University) ****A new class of surfaces with maximal Picard number****.**

**Abstract: **I will talk about some joint work with Partha Solapurkar, where we construct a class

of surfaces with maximal Picard number (i.e. $\rho=h^{11}$). Although most of these examples have

general type, they are built from elliptic modular surfaces. If time permits, I will discuss some related things.

**Paolo Aluffi**** ****(Florida State University)**** **** ****Segre classes of monomial schemes.**

**Abstract: **Several invariants of singularities may be expressed in terms of

Segre classes, a key ingredient in Fulton-MacPherson intersection theory.

We will quickly review several applications of Segre classes, and

present a formula computing them for schemes that are `monomial' with

respect to a collection of possibly singular hypersurfaces meeting along

complete intersections. The formula is expressed as a formal integral

over a Newton polytope associated with the scheme.

**Ludmil Katzarkov**** (University of Miami and Universität Wien) ****Categorical base loci and applications****.**

**Abstract: **In this talk we will introduce the notion of categorical base loci.

Examples and applications will be considered**.**

**Video from the lecture, part 1**

**Video from the lecture, part 2**

**Chiu-Chu Melissa Liu**** (Columbia University) Gromov-Witten invariants of toric Calabi-Yau 3-orbifolds.**

**Abstract: **The remodeling conjecture proposed by Bouchard-Klemm-Marino-Pasquetti relates Gromov-Witten invariants of a toric Calabi-Yau 3-manifold/3-orbifold to Eynard-Orantin invariants of the mirror curve of the toric Calabi-Yau 3-fold. In this talk, I will describe results on this conjecture based on joint work with Bohan Fang and Zhengyu Zong.

**Video from the lecture, part 1**

**Video from the lecture, part 2**

**David R. Morrison**** (U C Santa Barbara) Some new tricks for good ol' SL(2,Z).**

**Video from the lecture, part 1**

**Video from the lecture, part 2**

**Madhav Nori (University of Chicago) Boundary behavior of the Teichmüller disc.**

**Abstract: **A translation surface is a pair (C,\omega) where \omega is a holomorphic differential form on a compact Riemann surface C. Every point of the moduli of translation surfaces gives rise to a Teichmuller disc: a holomorphic map from the open unit ball to this moduli space. We ask whether this disc exists on compactificationa of the moduli space.

**Video from the lecture, part 1**

**Video from the lecture, part 2**

**Rita Pardini**** (Università di Pisa) Bi/trielliptic curves of genus 2 and stable Godeaux surfaces.**

**Abstract: **We describe the stable bi/trielliptic curves of genus 2,

namely the stable curves $C$ of genus 2 such that there exist finite

maps $f:C\to E_1$ and $g:C\to E_2$ of degrees respectively 2 and 3. We

apply this result to describe one of the three possible types of

Gorenstein stable non-normal Godeaux surfaces (a stable Godeaux surface

is a stable surface with $K^2=\chi=1$).

This is joint work with M. Franciosi and S. Rollenske

**Giulia Saccà (Stony Brook University) Singularities of moduli spaces of sheaves on K3 surfaces and**

**Nakajima quivers varieties**

**Abstract: **The aim of this talk is to study a class of singularities of

moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver

varieties. The singularities in question arise from the choice of a

non generic polarization, with respect to which we consider stability,

and admit natural symplectic resolutions corresponding to choices of

general polarizations. By establishing the stability of the

Lazarsfeld-Mukai bundle for some class of rank zero sheaves on a K3

surface, we show that these moduli spaces are, locally around a

singular point, isomorphic to a quiver variety in the sense of

Nakajima and that, via this isomorphism, the natural symplectic

resolutions correspond to variations of GIT quotients of the quiver

varieties. This is joint work with E. Arbarello.