M397S: Graduate Literature Class in Geometry


Announcements

Please note the schedule change and the addition of the mechanism to share commentaries.

Basic Information

Professor: Dan Freed, RLM 9.162

Class Meetings: TTh 2:00-3:30, RLM 11.176

Papers

Here is a list of suggested papers; you are free to choose papers which are not on the list. I in turn feel free to add and subtract papers, so the list may change over time.

Schedule

August 30: Aaron Royer N. Hitchin, Compact four-dimensional Einstein manifolds
September 1: Aaron Fenyes J. Moser, On the volume elements of a manifold
September 6: Hendrik Orem I. N. Bernstein, I. M. Gel'fand, V. A. Ponomarev, Coxeter functions and Gabriel's theorem
September 8: Pavel Safronov M. F. Atiyah, Complex analytic connections in fibre bundles
September 13: Matt Pancia J. Milnor, The Steenrod algebra and its dual
September 15: Rohit Jain S. S. Chern, A simple intrinsic proof of the Gauss-Bonnet formula
September 27: Cesar Garza K. Kodaira, On Kahler varieties of restricted type
October 4: Class Discussion
October 6: Aaron Royer M. Kontsevich, Deformation quantization of Poisson manifolds
October 11: Aaron Fenyes M. F. Atiyah and I. M. Singer, The index of elliptic operators: I
October 13: Hendrik Orem P. Deligne, La conjecture de Weil: I
October 18: Pavel Safronov P. Deligne and D. Mumford, On the irreducibility of the space of curves of given genus
October 20: Matt Pancia R. Bott, On the stable homotopy of the classical groups
October 25: Rohit Jain R. Schoen and S.-T. Yau, On the proof of the positive mass conjecture in general relativity
October 27: Cesar Garza S. Donaldson, An application of gauge theory to four-dimensional topology
November 1: Class Discussion
November 8: Aaron Royer G. Segal, The definition of conformal field theory
November 10: Aaron Fenyes E. Witten, Quantum field theory and the Jones polynomial
November 15: Hendrik Orem A. Beilinson and J. Bernstein, A proof of Jantzen conjectures
November 17: Pavel Safronov M Goresky and R. MacPherson, Intersection homology II
November 22: Matt Pancia D. Sullivan, Geometric topology: 1970 MIT notes
November 29: Rohit Jain R. Hamilton, Three-manifolds with positive Ricci curvature
December 1: Cesar Garza N. Hitchin, The self-duality equations on a Riemann surface

Commentaries

Please upload your commentaries on each of the papers at this link. You should also bring a hard copy to class. The commentaries are to be between a half page and a single page. Once you upload your commentary on a paper, you will have access to those of your classmates.

Additional Readings

Thurston on reading mathematics. (Forward to "The Best Writing on Mathematics 2010")

Various pieces of advice for young mathematicans. (From "The Princeton Companion to Mathematics")

More advice: Gian-Carlo Rota, Tom Korner, Jordan Ellenberg, Steven Weinberg