Arithmetic of connections
Summer school 15-19 July 2019
The summer school will revolve around arithmetic aspects of the theory of differential equations. This topic, which can be traced back at least to Gauss's study of hypergeometric functions, was a major driving force of mathematical research in the 19th century. It witnessed a spectacular revival during the next century thanks to the interaction with several seemingly unrelated areas of mathematics, in particular algebraic geometry (Higgs bundles and Simpson’s conjecture), and number theory (Siegel-Shidlovskii Theorem and transcendence theory).
Organizers
external pageJavier Fresáncall_made (École polytechnique), external pageDimitar Jetchevcall_made (EPF Lausanne), Peter Jossen (ETH Zurich), Emmanuel Kowalski (ETH Zurich)
Speakers
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Minicourses
- Jean-Benoît Bost, Université Paris Sud (Orsay)
Transcendence techniques and modules with integrable connections over number fields
- Nicholas Katz, Princeton University
Connections and Monodromy: the finite field version
Talks
- Yves André, Université de Jussieu
Parallel transport, transcendence, and the category of "bivector spaces"
- Yohan Brunebarbe, Institut de Mathématiques de Bordeaux
o-minimal geometry and algebraicity of period maps
- Hélène Esnault, FU Berlin
l-arithmetic subloci of the moduli space of local systems - Mircea Mustaƫă, University of Michigan
Hodge filtration, minimal exponent, and local vanishing
- Fernando Rodriguez Villegas, ICTP Trieste
Mixed Hodge numbers of hypergeometric motives
- Claude Sabbah, École Polytechnique
Hodge structures and rigid local systems
- Masha Vlasenko, Polish Academy of Sciences
Dwork crystals