Title: Normal Forms for Lattice Polarized K3 Surfaces and the Kuga-Satake-Hodge Conjecture
Charles Doran, University of Alberta
Abstract: We introduce a projective hypersurface "normal form" for a class of K3 surfaces which generalizes the classical Weierstrass normal form for complex elliptic curves. A geometric two-isogeny relates these K3 surfaces to the Kummer K3 surfaces of principally polarized abelian surfaces, with the normal form coefficients naturally identifying with the Igusa basis of Siegel modular forms of degree two. These results are reinterpreted through the lens of the Kuga-Satake Hodge Conjecture, and seen as a prediction coming from mirror symmetry. This is joint work with Adrian Clingher.


Title: Geometry and Syzygies of Line Bundles on an Algebraic Surface.
Krishna Hanumanthu, University of Kansas
Abstract: The syzygyies of a line bundle $L$  on a projective variety $X \subset \mathbb{P}(H^0(X,L))$  carry information about the geometry of the embedding. This interplay was studied in depth by M. Green and he defined the notion of $N_p$ property for $L$. While this situation is fairly well understood for curves, there is no completely satisfactory answer in higher dimensions. I will talk about some new results in this direction for surfaces. This is joint work with B. P. Purnaprajna

Title: Configurations of Lines in Del Pezzo Surfaces and Geometry of Gosset Polytopes.
Jaehyouk Lee, KIAS
Abstract: In this talk, we introduce the correspondences between the geometry of del Pezzo surfaces and the geometry of corresponding Gosset polytopes, and explain the study on the divisor classes of del Pezzo surfaces, which are written as the sum of distinct lines with fixed intersection according to the inscribed simplexes and crosspolytopes in Gosset polytopes.

Title: Kirwan Partial Desingularisation for Toric Varieties.
Yogesh More, University of Missouri - Columbia
Abstract: pdf

Title: Derived Equivalence and the Picard Variety.
Christian Schnell, University of Illinois - Chicago
Abstract: I will explain a result, joint with Mihnea Popa, saying that if two smooth projective varieties have equivalent derived categories of coherent sheaves, then their Picard varieties are isogeneous; in particular the number of independent holomorphic 1-forms is a derived invariant. A consequence of this is that derived equivalent threefolds have the same Hodge numbers.


Title: TBA.
Vasudevan Srinivas, Tata Institute of Fundamental Research
Abstract: TBA

Title:Classifying Symplectic Group Actions on K3 Surfaces.
Ursula Whitcher, Harvey Mudd College
Abstract: Let G be a finite group of automorphisms on a K3 surface X. If G acts symplectically, the minimal resolution Y of the quotient X/G will also be a K3 surface. We'll review the classification of finite groups which can act symplectically on a K3 surface, and describe a sublattice of the Picard group of X determined by G. Then we'll use the relationship between X and Y and the properties of our sublattice to investigate when the action of G is unique.