K3 Seminar Spring 2019
From UWMath Wiki
When: Thursday 57 pm
Where: Van Vleck B135
Schedule
Date  Speaker  Title 
March 7  Mao Li  Basics of K3 Surfaces and the GrothendieckRiemannRoch theorem 
March 14  Shengyuan Huang  Elliptic K3 Surfaces 
March 28  Zheng Lu  Moduli of Stable Sheaves on a K3 Surface 
April 4  Canberk Irimagzi  FourierMukai 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 GrothendieckRiemannRoch 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: FourierMukai 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 FourierMukai transform on elliptic curves. With the help of the base change theorem, we will describe the FourierMukai 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
David Wagner 
Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem 
Abstract: 
April 25
Moisés Herradón Cueto

Title: Derived Categories of K3 Surfaces 
Abstract: 
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