Rennes, from May 12th to May 23rd, 2014
Contact: C. Mourougane
Scientific board: X. Caruso, F. Charles, M. Gros, C. Mourougane
We organize a spring school on complex and p-adic aspects of the Hodge theory with a view towards deformation theory.
The first week is devoted to constructions of complex and p-adic Hodge theories, for a single smooth variety or for a smooth family of smooth varieties. In the complex setting, construction of moduli spaces thanks to Torelli type theorems will be the main target. In the p-adic setting, the first aim will be the constructions of cohomological tools and the second aim the statement and the proof in a special case of comparison theorems between p-adic cohomologies.
Hodge theories of deformations with singular fibers will be the topic of the second week. In the complex setting, one leading theme will be the use of Hodge theory in the description of properties of moduli spaces like hyperbolicity. Similarly, some properties of étale cohomologies and more surprisingly complex cohomologies will be derived from p-adic Hodge theory.
Each course will be given in English and divided into three lectures of 90 minutes.
Conference - Moduli spaces of real and complex varieties
Moduli spaces of real and complex varieties
Angers (France), from June 2nd to June 6th, 2014
Contact: F. Mangolte
Organisation board: Frédéric Mangolte, Jean-Philippe Monnier, Daniel Naie
Scientific board: Fabrizio Catanese, Viatcheslav Kharlamov
The goal of this meeting is to bring together mathematicians interested in various aspects of the geometry of moduli spaces --surfaces, compactifications, real moduli...
There will be three mini-courses -given by Fabrizio Catanese, Viktor Kulikov and Radu Laza- and about 15 talks.
This summer school will be mainly devoted to three courses by Ivan Corwin and Martin Hairer on Khardar-Parisi-Zhang (KPZ) equation and Peter Friz on rough paths. Several others talks will present the most recent advances on these topics.
Guiding principle in the courses will be to present the theory of rough paths and recent work by Martin Hairer who managed to solve rigorously the KPZ equation using this theory among other ones. In conjunction with recent breakthroughs on the exact statistics of the KPZ equation (the topic of Ivan Corwin's mini-course), these results will likely validate a number of predictions in the physics literature in which this equation is often seen as a universal limit. The method developed by Martin Hairer will also allow progresses on other very singular equations.
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