Arithmetic and Geometry of Picard-Fuchs Differential Equations


Picard-Fuchs differential equations are particular linear differential equations which arise from the variation of algebraic varieties. In the particular case of Calabi-Yau varieties they have many applications in Physics, mirror symmetry and in particular the calculation of Gromov-Witten invariants and partition functions. 
The principal goal of the workshop is to introduce new development and give directions to future researches in geometric, arithmetic, group theory and Physics applications of Picard-Fuchs equations. The following topics will be covered: 
1. Calabi-Yau Picard-Fuchs equations
2. Period and monodromy calculations
3. Middle convolution of linear differential equations
4. Partition functions and modular forms attached to Calabi-Yau varieties

Monday 20.08.2012

Hossein Movasati - Modular-type functions attached to Calabi-Yau equations I - download
Michael Bogner - Differential operators of Calabi-Yau type -  download
Khosro Monsef Shokri Automorphic forms for triangle groupsdownload
Joerg HofmannGlobal Monodromy and Zeta(3)download
Benjamin CollasGrothendieck-Teichmüller groups: Galois and Hodge aspects Idownload


Tuesday 21.08.2012

Michael Bogner
- Construction of differential operators of Calabi-Yau type - download
Hossein Movasati Modular-type functions attached to Calabi-Yau equations, II download
Stefan Reiter - Orthogonally rigid local systems - download
Khosro Monsel Shokri - The asymptotic expansion of a hypergeometric series coming from mirror symmetry download
Benjamin Collas - Grothendieck-Teichmüller groups: Galois and Hodge aspects II - download