# Difference between revisions of "K3 Seminar Spring 2019"

When: Thursday 5-7 pm

Where: Van Vleck B135

## Schedule

 Date Speaker Title March 7 Mao Li Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem March 14 Shengyuan Huang Elliptic K3 Surfaces March 28 Zheng Lu Moduli of Stable Sheaves on a K3 Surface April 4 Canberk Irimagzi Fourier-Mukai Transforms April 11 Moisés Herradón Cueto Cohomology of Complex K3 Surfaces and the Global Torelli Theorem April 23 David Wagner Derived Categories of K3 Surfaces

## March 7

 Mao Li Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem Abstract:

## March 14

 Shengyuan Huang Title: Elliptic K3 Surfaces Abstract:

## March 28

 Zheng Lu Title: Moduli of Stable Sheaves on a K3 Surface Abstract:

## April 4

 Canberk Irimagzi Title: Fourier-Mukai Transforms Abstract: I will describe Chow theoretic correspondences as a motivation to derived correspondences. We will then define integral functors on derived categories. The dual abelian variety will be given as a moduli space in terms of its functor of points, leading us to a definition of the universal Poincaré bundle on $A \times \hat{A}$. We will look at the integral transform from $D(A)$ to $D(\hat{A})$ induced by the Poincaré bundle. Cohomology of the Poincaré bundle will be stated and used for the computation of the $K$-theoretic Fourier-Mukai transform on elliptic curves. With the help of the base change theorem, we will describe the Fourier-Mukai duals of homogeneous line bundles on $A$. For an elliptic curve $E$, we will establish the equivalence between 1. the abelian category of semistable bundles of slope 0 on $E$, and 2. the abelian category of coherent torsion sheaves on $E$. Simple and indecomposable objects of these categories will be described (with the help of the structure theorem of PIDs) and we will relate this picture to Atiyah’s classification of the indecomposable vector bundles of degree 0.

## April 11

 Moisés Herradón Cueto Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem Abstract:

## April 23

 David Wagner Title: Derived Categories of K3 Surfaces Abstract: