Gradate Analysis Seminar
18.199 -- Spring 2024

Lecture topics:

See the Loop2024 notes for more commentary.

6 February: Brief overview
8 February: Compression onto Hardy space
13 February: Bogus snow day!
15 February: Omar on manifolds. Parse the statement that the tangent bundle of the loop space of a manifold is the loop space of the tangent bundle. As time permits, more on the Bott-Virasoro group.
22 February (20 February is an MIT Monday): Alain on Riemann metric and exponential map. The direct application here is that we can find coordinate patches on the loop space this way.
27 February: Dain on Lie groups Notes
29 February: Isaac on Clifford algebra
5 March: Kevin on principal bundles
7 March: Spin and loop-orientation
12 March: Isaac on spin structures
14 March: Alain on Cech cohomology Notes
19 March: Dain on holonomy and circle bundles
21 March: Kevin on K-theory
2 April: Isaac on spin Dirac Notes
4 April: Loop-spin structures - central extension of LSpin
9 April: Eclipse vacation day for me! Mike on SpinC canceled Notes
11 April: The central extension of LSpin is fusive
16 April: Dain on the index of the spin Dirac operator
18 April: Dain continues
23 April: Mike on SpinC
25 April: Loop-spin structures - overview
30 April: Torus, Fock and Bargmann
2 May: Dirac-Ramond for the torus
7 May: Last lecture on Dirac operators

Updated 7 May, 2024.