This is a seminar class on the Langlands program understood in a broad sense, with topics selected from subjects ranging from number theory to quantum field theory, including, but not limited to, the following:
In the first few lectures, the instructor explains how some of these topics fit into a big picture. For the remainder of the term, each participant gives a few talks on topics chosen in discussion with the instructor. One aim is to learn how to give a good expository talk. The instructor will also give a series of talks on topics of interest for the audience.
Disclaimer: The instructor is not an expert on most of the suggested topics!
Class notes (none of us are experts, so use at your own risk!)
1/23: Phil  Introduction
1/25, 1/30: Phil  Langlands Reciprocity
2/1, 2/6: Phil  Geometric Langlands2/15: Andrew  Geometric Class Field Theory
2/20: Phil  LocalGlobal Compatibility of Geometric Langlands I
2/22: Matt  Tate's Thesis
2/27: Phil  LocalGlobal Compatibility of Geometric Langlands II
3/1: Elad  Local Langlands Correspondence I (Local Class Field Theory)
3/6: Alex  Intro to QFT: Path Integrals and Observables
3/8: Yau Wing  Global Class Field Theory I (KroneckerWeber Theorem)
3/27, 3/29: Phil  Modular Forms and Modular Curves
4/3: Yau Wing  Global Class Field Theory II (Complex Multiplication)
4/5: Andrew  Geometric Satake I (Perverse Sheaves and Affine Grassmannians)
4/10: Matt  Heegner Points and the BSD Conjecture
4/12: Daping  Geometric Satake II (Statement and Examples)
4/17: Phil  EicherShimura Relation
4/19: Alex  Geometric Satake III (QFT Perspective)
4/24: Elad  Local Langlands Correspondence II
4/26: Daping  Geometric Satake IV (Convolution Product)

Teaching >