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Title:
Spectral curves for KP tau functions of hypergeometric type
Speaker:
Abstract:
KP tau functions of hypergeometric type (also known as Orlov--Scherbin tau functions) are very simple objects which, however, cover enormous amount of enumerative geometric and combinatorial problems (Gromov-Witten invariants, various Hurwitz numbers, topological vertex, colored HOMFLY-PT polynomials, enumeration of (hyper)maps and constellations, etc.)I want to present a closed algebraic formula for the corresponding $n$-point functions that conceptually explains how the spectral curve formula of Alexandrov--Chapuy--Eynard--Harnad naturally emerges and why it universally covers all cases studied in the literature.This formula appears to be a very powerful tool for the further analysis of KP tau functions of hypergeometric type, and it leads through the theory of topological recursion to remarkable applications resolving a number of open conjectures in algebraic geometry and integrable systems.The talk will be partly based on a joint work with Bychkov, Dunin-Barkowski, and Kazarian, and Carlet, van de Leur, and Posthuma.
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