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What's new!
o First class on Monday August 26! o Aug. 28: Last time we talked about Hamiltonian formulation of classical mechanics (Sec. 18.2) as motivation for studying symplectic geometry. We then discussed symplectic bilinear map, symplectomorphism on a symplectic vector space and symplectic manifold (Sec. 1.1, 1.2). o Aug. 28: We will spend a few lectures reviewing manifolds and differential forms. I mainly follow Arnold's "Mathematical methods in classical mechanics", Chapter 7 (Differential Forms). o Sep. 5: Posted the core topics to be covered in the course (see below). o No class on Friday the 13th! (September). I am away for a research talk. o Posted a link to Eckhard Meninrenk's Symplectic Geometry notes for extra reference material (see Course Information). o Oct. 12: So far we have discussed symplectic linear algebra, Hamiltonian mechanics, symplectic manifolds, Hamiltonian vector fields, symplectic structure on cotangent bundle, Lagrangian submanifolds and integrable systems, local forms and Moser-Darboux-Weinstein theorems. o Oct. 12: We just started with Kaehler manifolds. Our discussion will be relatively brief and less comprehensive as da Silva's. o Oct. 23: We have started with Hamiltonian group actions and moment maps. We will review standard material about Lie groups, their Lie algebras and Lie group actions. As usual we follow Meinrenken (Chapter 6 Symplectic group actions and moment maps) and da Silva (Chapter VIII Moment Maps). o Nov. 10: We are starting with symplectic reduction. o Dec. 4: We discussed Atiyah's convexity theorem. o Dec. 6: We discussed proof of BKK theorem (Bernstein-Khovanskii-Kushnirenko). o Final exam is take-home. Starts on Sunday Dec. 8. Find the exam below! Weekly homework and other online material o Homework 1 o Homework 2 o Homework 3 o Final exam Course Information Text: "Topics in Symplectic Geometry" by De Silva, which is available in her website: click here Other references: Meinrenken's Symplectic Geometry notes Arnold's Mathematical Methods in Classical Mechanics Time of lectures: Monday-Wednesday-Friday 10:00AM - 10:50AM Location of lectures: 427 Thackeray Hall Prerequisite: familiarity with differentiable manifolds There will be 3-4 homeworks and a final exam. Topics to be discussed: Symplectic Linear Algebra Symplectic Form on Cotangent Bundle Lagrangian Submanifolds and Integrable Systems Local Forms Kaehler Manifolds Hamiltonian Mechanics Moment Maps and Hamiltonian Group Actions Symplectic Reduction Symplectic Toric Manifolds (if time permits) Instructor's Information Email: kavehk AT pitt.edu Office: Thackeray #424 Office hours: 11:00AM-12:00PM Tuesdays or by appointment. You can drop by I am usually in. Office phone: 412-624-8331 |