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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.

Video from the lecture

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).

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

Audio from the lecture

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.

Video from the lecture