K3 Seminar Spring 2019: Difference between revisions

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'''When:''' Thursday 5-7 pm
'''When:''' Thursday 5-7 pm


'''Where:''' Van Vleck TBA
'''Where:''' Van Vleck B135


'''
'''
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| bgcolor="#E0E0E0"| March 7
| bgcolor="#E0E0E0"| March 7
| bgcolor="#C6D46E"| Mao Li
| bgcolor="#C6D46E"| Mao Li
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 6| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]
| bgcolor="#BCE2FE"|[[#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]
|-
|-
| bgcolor="#E0E0E0"| March 14
| bgcolor="#E0E0E0"| March 14
| bgcolor="#C6D46E"| Shengyuan Huang
| bgcolor="#C6D46E"| Shengyuan Huang
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 13| Elliptic K3 Surfaces]]
| bgcolor="#BCE2FE"|[[#March 14| Elliptic K3 Surfaces]]
|-
|-
| bgcolor="#E0E0E0"| March 28
| bgcolor="#E0E0E0"| March 28
| bgcolor="#C6D46E"| Zheng Lu
| bgcolor="#C6D46E"| Zheng Lu
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 20| Moduli of Stable Sheaves on a K3 Surface]]
| bgcolor="#BCE2FE"|[[#March 28| Moduli of Stable Sheaves on a K3 Surface]]
|-
|-
| bgcolor="#E0E0E0"| April 4
| bgcolor="#E0E0E0"| April 4
| bgcolor="#C6D46E"| Canberk Irimagzi
| bgcolor="#C6D46E"| Canberk Irimagzi
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 27| Fourier-Mukai Transforms]]
| bgcolor="#BCE2FE"|[[#April 4| Fourier-Mukai Transforms]]
|-
|-
| bgcolor="#E0E0E0"| April 11
| bgcolor="#E0E0E0"| April 11
| bgcolor="#C6D46E"| Moisés Herradón Cueto
| bgcolor="#BCE2FE"|[[#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]
|-
| bgcolor="#E0E0E0"| April 23
| bgcolor="#C6D46E"| David Wagner
| bgcolor="#C6D46E"| David Wagner
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 6| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]
| bgcolor="#BCE2FE"|[[#April 23| Derived Categories of K3 Surfaces]]
|-
| bgcolor="#E0E0E0"| April 25
| bgcolor="#C6D46E"| TBA
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 13| Derived Categories of K3 Surfaces]]
|}
|}
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''
|-
|-
| bgcolor="#BCD2EE" | Title: Heisenberg Groups and the Fourier Transform
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem
|-
|-
| bgcolor="#BCD2EE"  |   
| bgcolor="#BCD2EE"  |  Abstract:  
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.
|}
|}
</center>
</center>


== March 14 ==
== March 14 ==
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''
|-
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces
|-
| bgcolor="#BCD2EE"  |  Abstract:
|}                                                                   
</center>
== March 28 ==
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''
|-
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface
|-
| bgcolor="#BCD2EE"  |  Abstract:
|}                                                                   
</center>
== April 4 ==
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''
|-
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms
|-
| bgcolor="#BCD2EE"  |  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.
|}                                                                   
</center>
</center>
== April 11 ==
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''
|-
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem
|-
| bgcolor="#BCD2EE"  |  Abstract:
|}                                                                   
</center>
== April 23 ==
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''
|-
|-
| bgcolor="#BCD2EE" |  
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces
|-
|-
| bgcolor="#BCD2EE"  |   
| bgcolor="#BCD2EE"  |  Abstract:  
Abstract:  
|}                                                                     
|}                                                                     
</center>
</center>

Latest revision as of 13:29, 22 April 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:

Contact Info

To get on our mailing list, please contact

Canberk Irimagzi

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