Towards Quantum Primitive Form Theory

8 Oct 2014, 10:30 → 10 Oct 2014, 17:45 Asia/Tokyo

Seminar Room B (Kavli IPMU, The University of Tokyo (Kashiwa campus))

Towards  Quantum Primitive Form Theory
A mini-workshop (Towards quantum primitive form theory) will be held on October 8-10, 2014 at IPMU Seminar Room B, which is organized jointly by Kavli IPMU and FMSP Program.             (see  http://ipmu.ac.jp  and  http://fmsp.ms.u-tokyo.ac.jp). 
We cordially invite anyone who is interested in the subjects.

Organizers:
Kyoji Saito     (Kavli-IPMU)
Toshitake Kohno (FMSP Program)

Dates:  October 8-10, 2014

Venue: Seminar Room B, Kavli IPMU, The University of Tokyo (Kashiwa campus)

Language : English

Speakers : 
Mikhail Kapranov:   IPMU, univ. of Tokyo
Kohei Iwaki:   RIMS, Kyoto university
Akishi Ikeda:   Graduate school of mathematics, Univ. of Tokyo

Schedule :

Oct. 8 (Wed) 
10:00-11:30     Kapranov  1  
13:30-15:00    Iwaki   1
15:30-17:00     Ikeda   1

Oct. 9 (Thu)
10:00-11:30     Ikeda 2  
13:30-15:00    Kapranov  2
15:30-17:00     Iwaki 2

Oct. 10 (Fri) 
10:00-11:30     Iwaki 3 
13:30-15:00    Ikeda 3
15:30-17:00     Kapranov 3 

Title and Abstracts of lectures:

Kapranov 1. Background on secondary polytopes, Newton polytopes and exponential sums.
Kapranov 2. Homotopy Lie algebras from secondary polytopes.
Kapranov 3. Secondary polytopes and Hochschild complexes.
Abstract: TBA

Iwaki  1.  Introduction to exact WKB analysis 1.
Iwaki  2.  Introduction to exact WKB analysis 2.
Iwaki  3.  Exact WKB analysis and cluster algebras.
Abstract: TBA

Ikeda  1. Derived categories of Ginzburg dg algebras and Bridgeland stability conditions
Ikeda  2. Geometry of surfaces, derived categories and quadratic differentials
Ikeda  3. Construction of stability conditions from quadratic differentials

Abstract: Recently, Bridgeland and Smith constructed stability
conditions on some $3$-Calabi-Yau categories from meromorphic quadratic
differentials with simple zeros. In this talk, generalizing their results to higher 
dimensional Calabi-Yau categories, we describe the space of stability conditions 
on $N$-Calabi-Yau categories associated to $A_n$-quivers as the universal 
cover of the space of polynomials of degree n+1 with simple zeros. In particular, 
central charges of stability conditions on $N$-Calabi-Yau categories are 
constructed as the periods of quadratic differentials.