Integrable Systems/Quantum Groups Learning Seminar Fall 2020

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Time and location information

Time: Wednesday at 5:00 - 6:15 pm
Organizer: Sam DeHority
Zoom info: The zoom link is https://columbiauniversity.zoom.us/j/93215728593. Please email me at samdehority@math.columbia.edu to be added to the mailing list and for the zoom password.

References and topics

The goal of the seminar is to understand specific examples of integrable systems with a view towards their relationship with supersymmetric gauge theories and enumerative geometry. More specifically:

  1. Spin chains, lattice models, Bethe ansatz. There are many resources for this. A few good ones are https://arxiv.org/abs/1010.5031, and the introduction to Jimbo, Miwa Algebraic Analysis of Solvable Lattice Models.
  2. Relationship with supersymmetric vacua/topological theories/enumerative geometry. Key papers are Nekrasov-Shatashvilli https://arxiv.org/abs/0901.4748, https://arxiv.org/abs/0901.4744 from a physical perspective and the mathematical papers by Aganagic-Okounkov https://arxiv.org/abs/1704.08746 and Pushkar, Smirnov, Zeitlin https://arxiv.org/abs/1612.08723
  3. At some point it would be good to see talks on the KdV, KP, and Toda lattice hierarchies. E.g. from Date, Jimbo, Miwa Soltions: Differential Equations, Symmetries and Infinite Dimensional Algebras.
  4. Other approaches including the sequence Costello-Witten-Yamazaki https://arxiv.org/abs/1709.09993 https://arxiv.org/abs/1802.01579 and Costello-Yamazaki https://arxiv.org/abs/1908.02289.

List of talks

Date Talk Info
Wednesday
Oct. 21
Speaker: Davis Lazowski
Title: Bethe Ansatz for the XXZ Spin Chain
Abstract: I will explain what a spin chain is, then I will introduce the algebraic Bethe ansatz via the example of the XXZ spin chain.
Wednesday
Oct. 28
TBD