MATH 6630

MATH 6630

Course information provided by the Courses of Study 2020-2021.

Symplectic geometry is a branch of differential geometry which studies manifolds endowed with a nondegenerate closed 2-form. The field originated as the mathematics of classical (Hamiltonian) mechanics and it has connections to (at least!) complex geometry, algebraic geometry, representation theory, and mathematical physics. In this introduction to symplectic geometry, the class will begin with linear symplectic geometry, discuss canonical local forms (Darboux-type theorems), and examine related geometric structures including almost complex structures and Kähler metrics. Further topics may include symplectic and Hamiltonian group actions, the orbit method, the topology and geometry of momentum maps, toric symplectic manifolds, Hamiltonian dynamics, symplectomorphism groups, and symplectic embedding problems.

When Offered Fall.

Prerequisites/Corequisites Prerequisite: MATH 6510 and MATH 6520, or permission of instructor.

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Enrollment Information
Syllabi: none
  •   Regular Academic Session. 

  • 4 Credits Stdnt Opt

  • 16609MATH 6630  LEC 001

    • TROnline Meeting
    • Sep 2 - Dec 16, 2020
    • Holm, T

  • Instruction Mode: Online