Mini-school on Abelian and Symplectic Varieties

University of North Carolina at Chapel Hill
Monday 17th to Wednesday 19th April, 2017



UNC Chapel Hill
2017


About the mini-school

We are very pleased to welcome Olivier Debarre (École normale supérieure/Duke University) and Benjamin Bakker (University of Georgia - Athens) to speak at UNC in our graduate mini-school, whose broad theme is algebraic varieties with trivial canonical bundles (or vanishing first Chern classes). Such varieties are important in a wide range of areas in algebraic geometry, differential geometry, number theory, and mathematical physics. Prof Debarre will give a series of four lectures on abelian varieties. Prof Bakker will give a pair of lectures on holomorphic symplectic varieties. All lectures will be at an introductory level, aimed at graduate students with a limited background in algebraic geometry.

The mini-school is organized by Justin Sawon and generously supported by the National Science Foundation, award DMS-1555206. If you have any questions, please send us an e-mail.


Local information

The mini-school will be held at the University of North Carolina at Chapel Hill, in the Department of Mathematics, located in Phillips Hall. Lectures will take place in Phillips 332 and breaks will take place in Phillips 330.

Click here for a campus map. Phillips Hall is on East Cameron Ave.

If you are coming by car, the closest visitor parking lot to Phillips Hall is the Morehead Lot.


Schedule
Monday 17th April
Tuesday 18th April
Wednesday 19th April
Time
Place
Activity
3:30-4:20 Phillips 332
Talk: Debarre I
4:20-4:40
Phillips 330
Break
4:40-5:30
Phillips 332
Talk: Debarre II
Time
Place
Activity
3:30-4:20 Phillips 332
Talk: Bakker I
4:20-4:40
Phillips 330
Break
4:40-5:30
Phillips 332
Talk: Bakker II
Time
Place
Activity
3:30-4:20 Phillips 332
Talk: Debarre III
4:20-4:40
Phillips 330
Break
4:40-5:30
Phillips 332
Talk: Debarre IV


Titles and abstracts

"Two or three things I know about abelian varieties" - Olivier Debarre (École normale supérieure/Duke University)
I will try to present some fact about abelian varieties over an algebraically closed field. This series of four lectures is designed for students who want to get an idea of the results and problems in the field and the style will be very informal; reactions and questions from the audience are expected. I will probably do very few proofs. I will cover the general theory of abelian varieties (over an algebraically closed field), Jacobian of curves, Prym varieties, intermediate Jacobians, rationality problems.

"A global Torelli theorem for singular symplectic varieties" - Benjamin Bakker (University of Georgia - Athens)
The local and global deformation theories of holomorphic symplectic manifolds enjoy many beautiful properties. By work of Namikawa, some of the local results generalize to singular symplectic varieties, but the moduli theory is badly behaved. In joint work with C. Lehn we show that for locally trivial deformations the entire picture is exactly analogous to the smooth case. In particular, we prove a global Torelli theorem and deduce some applications to birational contractions of moduli spaces of vector bundles on K3 surfaces. In place of twistor lines, the crucial global input is Verbitsky's work on ergodic complex structures using Ratner's theorems.


University
		 of North Carolina

Department of Mathematics