Fall 2021 MATH 242 001 LEC

Prerequisites 214 (Differential manifolds, Lie groups and algebras, De Rham complex) 

Description Unlike Riemannian geometry, whose purpose is to classify Riemannian metrics (according to Felix Klein's "Erlangen program" of characterizing various geometries), symplectic geometry should not be viewed as yet another branch. It is rather a language, or a common landscape for classical mechanics, quantization, PDEs, representations of Lie groups, and probably much else. As any language, it is elegant and powerful but not particularly deep. In the contrary, symplectic topology is a deep theory studying intricate rigidity properties of phase spaces of hamiltonian mechanics. It is not our goal to sink into symplectic topology, but time permitting, we'll have an informal primer of it as well.

For the most of the course, we will loosely follow the article Symplectic Geometry by Vladimir Arnold and myself, found on pages 1--135 in the volume Dynamical Systems IV of Springer's Encyclopaedia of Mathematical Sciences. Officially it is a survey paper, and as such is not required to contain proofs. In reality the exposition of the most essential material was organized as if a detailed textbook was first written, and then all trivial proofs removed and left as exercises to the reader, while all non-trivial ones left as outlines. This makes the text suitable for a graduate-level course, and testing this conjecture is a part of the plan.

Office 

Office Hours 

Required Text Symplectic Geometry and its Applications, V. Arnold and S. Novikov (eds.) (Encyclopaedia of Mathematical Science.  Dynamical Systems IV ) freely available in the electronic PDF format for patrons of the UC Berkeley library

Recommended Reading 

Grading Letter grade.

Homework weekly

Course Webpagehttps://math.berkeley.edu/~giventh/24221.html