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Graduate Topics Courses

Fall 2022

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Spring 2022

MATH GR8200 – Soliton Equations

Instructor: Igor Krichever
Day/Time: W 02:40 – 5 PM
Title: Introductory course on algebraic-geomerical integration of non-linear equations
Abstract: A self-contained introduction to the theory of soliton equations with an emphasis on its applications to algebraic-geometry. Topics include:

    1. General features of the soliton systems. Lax representation. Zero-curvature equations. Integrals of motion. Hierarchies of commuting flows. Discrete and finite-dimensional integrable systems.
    2. Algebraic-geometrical integration theory. Spectral curves. Baker-Akhiezer functions. Theta-functional formulae.
    3. Hamiltonian theory of soliton equations.
    4. Commuting differential operators and holomorphic vector bundles on the spectral curve. Hitchin-type systems.
    5. Characterization of the Jacobians (Riemann-Schottky problem) and Prym varieties via soliton equations.
    6. 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: Geometric Flows and the Ricci Flow


Math GR8675 – Topics In Number Theory

Instructor: Eric Urban
Day/Time: TR 4:10 – 5:25 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 Galasius-Venkatesh and apply it to the study of Selmer groups.





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