Math 248, Symplectic Geometry, Winter 2025

• Lectures: TTh 9:50 AM - 11:25 AM, McHenry Clrm 1279

• Instructor: Viktor Ginzburg; office: McHenry 4124
  email: ginzburg(at)ucsc.edu

• Office Hours: TBA or by appointment

• Text: There will be no "official" textbook in this course. Suggested reading:
  • Introduction to Symplectic Topology by Dusa McDuff and Dietmar Salamon
  • Lectures on Symplectic Geometry by Ana Canas da Silva

• Tentative Syllabus: Symplectic geometry is a relatively young field going back in its current form to the 70s and 80s. At this stage it encompasses several subfields such as symplectic topology, symplectic dynamics and Poisson geometry. The field is very active and intimately connected to a variety of other areas of mathematics and theoretical physics ranging from mathematical mechanics and dynamical systems to topology to representation theory to mirror symmetry, to mention just a few. In addition to deep results, symplectic geometry is also a mathematical language commonly used in many areas.

  This offering of Math 248 is intended to be a general interest introduction to the field. The course will cover the fundamentals from symplectic geometry and touch upon Morse theory. We will start with a discussion of basic concepts: symplectic and contact manifolds, Hamiltonian diffeomorphisms and flows, Lagrangian submanifolds, the least action principle, symplectic group actions and reduction, etc. Time permitting we will also discuss some more advanced topics. As a prerequisite, some familiarity with the material covered in Math 208 and 209 — manifolds and differential forms — will be essential.