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DTSTART;TZID=America/New_York:20221014T093000
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DTSTAMP:20260408T034400
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SUMMARY:Singularities of the quantum connection on a Fano variety
DESCRIPTION:Algebraic Geometry in String Theory Seminar \n\n\n\n\n\nSpeaker: Daniel Pomerleano\, UMass Boston \nTitle: Singularities of the quantum connection on a Fano variety \nAbstract: The small quantum connection on a Fano variety is one of the simplest objects in enumerative geometry. Nevertheless\, it is the subject of far-reaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally\, these conjectures are made for manifolds with semi-simple quantum cohomology or more generally for Fano manifolds whose quantum connection is of unramified exponential type at q=\infty. \nI will explain a program\, joint with Paul Seidel\, to show that this unramified exponential type property holds for all Fano manifolds M carrying a smooth anticanonical divisor D. The basic idea of our argument is to view these structures through the lens of a noncommutative Landau-Ginzburg model intrinsically attached to (M\, D).
URL:https://cmsa.fas.harvard.edu/event/agst-102122/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-10.14.2022.png
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DTSTART;TZID=America/New_York:20221014T110000
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CREATED:20240214T103536Z
LAST-MODIFIED:20240301T081027Z
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SUMMARY:Quantum magnet chains and Kashiwara crystals
DESCRIPTION:Speaker: Leonid Rybnikov\, Harvard CMSA/National Research University Higher School of Economics \nTitle: Quantum magnet chains and Kashiwara crystals \nAbstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are\, generally\, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely\, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves\, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals — i.e. combinatorial objects modeling the tensor category of finite-dimensional representations of a semisimple Lie algebra g. More specifically\, this monodromy action is naturally equivalent to the action of the same group by commutors (i.e. combinatorial analog of a braiding) on a tensor product of Kashiwara crystals. This is joint work with Iva Halacheva\, Joel Kamnitzer\, and Alex Weekes.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101422/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.14.22.png
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