COURSE DESCRIPTION
This course aims to build a knowledge base in gauge theory, starting with classical analytic results (Uhlenbeck compactness, Yang-Mills moduli spaces), and going into some applications (Seiberg-Witten / Donaldson-Yang-Mills / monopole and instanton Floer theories / connection to Heegard-Floer resp. Atiyah-Floer conjectures / ... ) according to participant's interests.
Prerequisites: Differential Geometry (manifolds, bundles, differential forms) and PDEs (Sobolev spaces, elliptic regularity).
Credit requires evidence of learning. Generic evidence would be regular participation in the reading discussions and giving two summary talks or one long talk. Alternative forms of evidence should be agreed upon with the instructor before drop date.
Talks will also be open to participants who wish to just sit in some or all meetings (without credit).
Format:
For the first 2/3 of the course, we will use an adaptation of the 'dice reading seminar' format: Reading for each week is posted in advance, should be done by all participants (at least for context and results - not necessarily all proof details), and should yield posts of questions/remarks in the online-pdf-annotation-tool. Those who feel prepared to give a 15-30min summary talk on the material volunteer by email - subject ''270 volunteer'' to wehrheimATberkeley.edu by Wednesday 10pm, and a speaker is randomly determined by Wednesday 11pm. The 80min class time will be used for the summary talk, interspersed with questions and discussions - in particular clarifying points that were raised online. As time allows, speaker and/or instructor will add further remarks and/or go into the details of proofs (again, as requested online).
In the last 1/3 of the course, participants and/or instructor will present applications of gauge theory in 60min talks with ample preparation time for speakers. We will always have at least 20min discussion, and some basic material for these talks will be posted as general reading for all to facilitate preparation and discussions.