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(2+1)-dimensional integrable systems and moduli spaces of curves

Paolo Rossi
University of Padova
Wednesday, October 21, 2020 - 16:00
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Integrable systems of (1+1)-dimensional PDEs lurk in the intersection theory of moduli spaces of stable algebraic curves, describing the intricate relations among intersection numbers. There are at least two methods to uncover them: the Dubrovin-Zhang method and the double ramification hierarchy construction, the latter due to Buryak and myself. The power of our approach consists in requiring weaker assumptions and in leading to a quantum integrable system, whose classical limit conjecturally recovers the Dubrovin-Zhang result (we have proven this conjecture in a wide class of examples). In this talk, after a brief general introduction, I will use a third advantage of the DR construction (that, at the classical level, it works for infinite rank CohFTs as well) to apply it to the intersection theory of the moduli space meromorphic functions and of meromorphic differentials, producing two (2+1)-dimensional integrable systems: a version of the KdV equation on the Moyal torus and the celebrated KP equation.

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