K3 Seminar Spring 2019

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When: Thursday 5-7 pm

Where: Van Vleck TBA


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 David Wagner Cohomology of Complex K3 Surfaces and the Global Torelli Theorem
April 25 TBA 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 $A \times \hat{A}$. The K-theoretic Fourier Mukai transform on elliptic curves will be computed. We will look at the integral transform from $D(A)$ to $D(\hat{A})$ induced by the Poincaré bundle. Cohomology of the Poincaré bundle and the base change theorem will be stated and used to describe the Fourier-Mukai dual of a unipotent vector bundle on an abelian variety. 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 deduce Atiyah’s classification of the indecomposable vector bundles of degree 0.

April 11

David Wagner
Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem
Abstract:

April 25

TBA
Title: Derived Categories of K3 Surfaces
Abstract:

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Canberk Irimagzi