Lorentz Center - Geometric Invariants and Spectral Curves from 1 Jun 2015 through 5 Jun 2015
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    Geometric Invariants and Spectral Curves
    from 1 Jun 2015 through 5 Jun 2015


Scientific Report

Geometric invariants and quantum spectral curves

Lorentz Center, 1-5 June 2015

organized by L. Chekhov (Moscow), B.

Eynard (Gif-sur-Yvette), and S. Shadrin (Amsterdam)


The workshop was devoted to the core problems of the theory of topological recursion and quantum spectral curves and its interaction with combinatorics, geometry of moduli spaces, and integrable systems. The key topics were: Givental and Frobenius structures; quantum spectral curves and topological recursion; discretizations of moduli spaces; Hurwitz numbers and related generating functions; quantum Riemann surfaces and knot invariants.


The workshop attracted a big amount of experts specializing in the theory of topological recursion as well as prominent scholars working in the are of interaction of geometry of the moduli spaces of curves and integrable hierarchies. We also had a huge number of PhD students.


Though there is no obvious breakthroughs or "aha" moments that we can report so far, the discussions were really very fruitful. It is sufficient to mentions, for instance, the discussions that we had on global spectral curves in singularity theory, where two different groups have not only completely different approaches but also literally completely different curves as an outcome.


The format of the workshop was absolutely standard, which is the best for scientific discussions (a few lectures in the morning and the afternoon, with an ample time for discussions in small groups). A special focus was on the introduction and discussions with PhD students, we had special sessions for that, and they were very well received. Also the morning lectures were requested to be more focus on general exposition, and this was really a great benefit even for senior participants, since we managed to gather people with completely different points of view on the subject.


Though a very small time has passed since the workshop, there is already a number of papers where the authors acknowledge it, for instance:

         Relations in the tautological ring, a PhD thesis by Felix Janda, http://webusers.imj-prg.fr/ felix.janda/thesis.pdf

         Lectures on the topological recursion for Higgs bundles and quantum curves, by M. Mulase and O. Dimitrescu, arXiv 1509.09007v1

         Edge-contraction on dual ribbon graphs, 2D TQFT, and the mirror of orbifold Hurwitz numbers, by M. Mulase and O. Dimitrescu, arXiv 1508.05922v1