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:

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Canberk Irimagzi