Lectures on Symplectic Geometry

by Ana Cannas da Silva

These notes approximately transcribe a 15-week course on symplectic geometry I taught at UC Berkeley in the Fall of 1997. The course at Berkeley was greatly inspired in content and style by Victor Guillemin, whose masterly teaching of beautiful courses on topics related to s- plectic geometry at MIT, I was lucky enough to experience as a graduate student. I am very thankful to him! That course also borrowed from the 1997 Park City summer courses on symplectic geometry and topology, and from many talks and discussions of the symplectic geometry group at MIT. Among the regular participants in the MIT - formal symplectic seminar 93–96, I would like to acknowledge the contributions of Allen Knutson, Chris Woodward, David Metzler, Eckhard Meinrenken, Elisa Prato, Eugene Lerman, Jonathan Weitsman, Lisa Jeffrey, Reyer Sjamaar, Shaun Martin, Stephanie Singer, Sue Tolman and, last but not least, Yael Karshon. Thanks to everyone sitting in Math 242 in the Fall of 1997 for all the c- ments they made, and especially to those who wrote notes on the basis of which I was better able to reconstruct what went Alexandru Scorpan, Ben Davis, David Martinez,DonBarkauskas,EzraMiller,HenriqueBursztyn,John-PeterLund,Laura De Marco, Olga Radko, Peter P? rib´ ?k, Pieter Collins, Sarah Packman, Stephen Bigelow, Susan Harrington, Tolga Etgu ¨ and Yi Ma.

Genres: Mathematics

232 pages, Paperback

First published July 17, 2001

Reviews

[Juke · Rating 5 out of 5]

Brillant introduction to symplectic geometry. Certainly one of the greatest reference.

[Lucas Chen · Rating 3 out of 5]

halfway-through review:

da Silva is certainly more intuitive and elementary on this subject than any other expositor except maybe Arnold, whose reference can't even really be argued to cover what people think of as symplectic geometry when they say it today.

I think I (and most other people who think this subject is cool) probably nonetheless should not have started by reading it (unless your goal is something specific like to understand Gromov's paper), since symplectic structures occur a lot more widely than I'd thought and are probably better understood in context. This is probably why I found these lectures so sparse and disconnected, but I feel like the relative beauty in the subject really doesn't lend itself to a self-contained textbook anyway.

(will update when I have any authority to make real points on symplectic geometry)