Spring 2022
MATH GR8200 – Soliton Equations
Instructor: Igor Krichever
Day/Time: MW 02:40 – 3:55 PM
Title: Introductory course on algebraicgeomerical integration of nonlinear equations
Abstract: A selfcontained introduction to the theory of soliton equations with an emphasis on its applications to algebraicgeometry. Topics include:

 General features of the soliton systems. Lax representation. Zerocurvature equations. Integrals of motion. Hierarchies of commuting flows. Discrete and finitedimensional integrable systems.
 Algebraicgeometrical integration theory. Spectral curves. BakerAkhiezer functions. Thetafunctional formulae.
 Hamiltonian theory of soliton equations.
 Commuting differential operators and holomorphic vector bundles on the spectral curve. Hitchintype systems.
 Characterization of the Jacobians (RiemannSchottky problem) and Prym varieties via soliton equations.
 Perturbation theory of soliton equations and its applications.
MATH GR8210 – Partial Differential Equations
Instructor: Richard Hamilton
Day/Time: TR 02:40 – 3:55 PM
Title: TBD
Abstract: TBD
Math GR8675 – Topics In Number Theory
Instructor: Eric Urban
Day/Time: TR 11:40 – 12:55 PM
Title: Simplicial deformation of Galois representations and application
Abstract: The goal of this course is to introduce the theory of simplicial deformation rings in the style of GalasiusVenkatesh and apply it to the study of Selmer groups.
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