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Séminaire de géométrie algébrique

Horaires : Le jeudi 25 septembre 2014, 14h

Double ramification cycles and integrable systems

Alexandr Buryak (ETH Zürich)

Double ramification cycles are certain homology classes in the moduli space of stable curves. They have proved to be very useful in the study of the geometry of the moduli space. A cohomological field theory is a system of cohomology classes in the moduli space of curves that satisfy certain natural properties. The theory of integrable systems of partial differential equations provides an efficient tool for a description of the correlators of cohomological field theories. In my talk I will present a new construction of an integrable system of PDEs associated to a cohomological field theory. The construction is based on the integration over the double ramification cycles and is motivated by Symplectic Field Theory. The constructed integrable system has a lot of nice properties that immediately follow from the geometry of the double ramification cycles. If the time permits, I will present a construction of a quantization of our new integrable system.


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