SCHEDULE of topics and reading
Date | Topics | Reading |
---|---|---|
Aug 27 | Introduction and Logistics | |
Sep 3 |
principal bundles, connections, gauge transformations, flat connections & representations, Chern-Simons functional, ASD equation |
[W-U] App.A (to A.4), [AB] Sec.1 |
Sep 10 |
Introduction to analytic results,
inhomogenous Neumann problem |
[W-U] Sec.3, Sec.4 |
Sep 17 | Hodge theory on manifolds with boundary | [W-U] Sec.5 |
Sep 24 | Sobolev estimates in gauge theory | [W-U] App.A (from A.4), App.B |
Oct 1 | Uhlenbeck gauge | [W-U] Sec.6 |
Oct 8 | Weak Uhlenbeck compactness | [W-U] Sec.7 |
Oct 15 | review session | |
Oct 22 | Local slice theorems | [W-U] Sec.8 |
Oct 29 | Yang-Mills regularity | [W-U] Sec.9 |
Nov 5 | Strong Uhlenbeck compactness | [W-U] Sec.10 |
Nov 12 | flat connections and introduction to instanton Floer theory | |
Nov 18 | Instanton Floer homology and a well defined part of the Atiyah-Floer conjecture | Topology seminar 2-3pm, 4-5pm |
Nov 19 | instanton Floer theory I | |
Nov 26 | no class - Thanksgiving | |
Dec 3 | instanton Floer theory II | |
Dec 10 | RRR - tbd |