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2024-03-28T14:48:54Z
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https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=17134
K3 Seminar Spring 2019
2019-03-11T16:36:42Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck B135<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E$, and <br />
<br />
2. the abelian category of coherent torsion sheaves on $E$. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto<br />
'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=17133
K3 Seminar Spring 2019
2019-03-11T16:35:35Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck B135<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E$, and <br />
<br />
2. the abelian category of coherent torsion sheaves on $E$. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto<br />
'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=17013
K3 Seminar Spring 2019
2019-02-21T17:15:41Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck B135<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E$, and <br />
<br />
2. the abelian category of coherent torsion sheaves on $E$. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16887
K3 Seminar Spring 2019
2019-02-08T23:09:22Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E$, and <br />
<br />
2. the abelian category of coherent torsion sheaves on $E$. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16861
K3 Seminar Spring 2019
2019-02-06T21:44:00Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E$, and <br />
<br />
2. the abelian category of coherent torsion sheaves on $E$. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16860
K3 Seminar Spring 2019
2019-02-06T21:43:42Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E$, and <br />
<br />
2. the abelian category of coherent torsion sheaves on &E$. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16859
K3 Seminar Spring 2019
2019-02-06T21:42:58Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E&, and <br />
<br />
2. the abelian category of coherent torsion sheaves on &E&. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16858
K3 Seminar Spring 2019
2019-02-06T21:42:02Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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 dual of a homogeneous line bundles on $A$. For an elliptic curve $E$, we will establish the equivalence between<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E&, and <br />
<br />
2. the abelian category of coherent torsion sheaves on &E&. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16857
K3 Seminar Spring 2019
2019-02-06T21:40:27Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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 dual of a unipotent vector bundle on $A$. For an elliptic curve $E$, we will establish the equivalence between<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E&, and <br />
<br />
2. the abelian category of coherent torsion sheaves on &E&. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16856
K3 Seminar Spring 2019
2019-02-06T21:39:38Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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 dual of a unipotent vector bundle on $A$. For an elliptic curve $E$, we will establish the equivalence between<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E&, and <br />
<br />
2. the abelian category of coherent torsion sheaves on &E&. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16855
K3 Seminar Spring 2019
2019-02-06T21:36:39Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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 dual of a unipotent vector bundle on an abelian variety. For an elliptic curve E, we will establish the equivalence between<br />
<br />
1. the abelian category of semistable bundles of slope 0 on E, and <br />
<br />
2. the abelian category of coherent torsion sheaves on E. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16854
K3 Seminar Spring 2019
2019-02-06T21:33:09Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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 $A \times \hat{A}$. 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<br />
<br />
1. the abelian category of semistable bundles of slope 0 on E, and <br />
<br />
2. the abelian category of coherent torsion sheaves on E. <br />
<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16853
K3 Seminar Spring 2019
2019-02-06T21:32:13Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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 $A \times \hat{A}$. 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 \\<br />
1. the abelian category of semistable bundles of slope 0 on E, and \\<br />
2. the abelian category of coherent torsion sheaves on E. \\<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16852
K3 Seminar Spring 2019
2019-02-06T21:30:18Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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 Ax$\widehat{A}$^. The K-theoretic Fourier Mukai transform on elliptic curves will be computed. We will look at the integral transform from D(A) to D(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<br />
1. the abelian category of semistable bundles of slope 0 on E, and <br />
2. the abelian category of coherent torsion sheaves on E.<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi
https://wiki.math.wisc.edu/index.php?title=K3_Seminar_Spring_2019&diff=16851
K3 Seminar Spring 2019
2019-02-06T21:28:07Z
<p>Cirimagzi: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5-7 pm<br />
<br />
'''Where:''' Van Vleck TBA<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Mao Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| Elliptic K3 Surfaces]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Zheng Lu<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 28| Moduli of Stable Sheaves on a K3 Surface]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Canberk Irimagzi<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| Fourier-Mukai Transforms]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBA<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| Derived Categories of K3 Surfaces]]<br />
|}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Mao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Basics of K3 Surfaces and the Grothendieck-Riemann-Roch theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Elliptic K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zheng Lu'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Moduli of Stable Sheaves on a K3 Surface<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Canberk Irimagzi'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Fourier-Mukai Transforms<br />
|-<br />
| 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 AxA^. The K-theoretic Fourier Mukai transform on elliptic curves will be computed. We will look at the integral transform from D(A) to D(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<br />
1. the abelian category of semistable bundles of slope 0 on E, and <br />
2. the abelian category of coherent torsion sheaves on E.<br />
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.<br />
<br />
|} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Derived Categories of K3 Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>
Cirimagzi