COGENT Summer School 2022
The Institut Fourier held a summer school on Cohomology, Geometry, and Explicit Number Theory June 13-30, 2022. Jennifer Wilson and I gave a lecture series on "High dimensional cohomology of SL_n(Z) and its principal congruence subgroups" during the second week. Below you can find our lecture notes and links to videos.
- Jennifer Wilson's Background on Group Cohomology
- Our Lecture notes (including an appendix on the maps of poset spectral sequence)
- Lecture 1 (Peter Patzt): Borel-Serre Duality [video]
- Lecture 2 (Jennifer Wilson): The top-degree cohomology of SL_n(R) for R Euclidean [video]
- Lecture 3 (Jennifer Wilson): The Steinberg module and (integral) apartment classes [video]
- Lecture 4 (Jennifer Wilson): The complex of partial bases is Cohen-Macaulay [video]
- Lecture 5 (Peter Patzt): The codimension-1 cohomology of SL_n(Z) [video]
- Lecture 6 (Peter Patzt): The top-degree cohomology of congruent subgroups of SL_n(Z) [video]
- Lecture 7 (Peter Patzt): Open problems and future directions [video]
MSRI Summer School 2019
The Mathematical Science Research Institute hosted a summer school on Representation Stability June 24-July 5, 2019. I gave a lecture series on "The second homology of the Torelli groups". Below you can find my lecture notes and links to videos.
- Lecture notes
- Spectral sequence cheat sheet
- Lecture 1: Free groups and their automorphisms [video]
- Lecture 2: VIC-modules [video]
- Lecture 3: The homology of IA_n [video]
- Lecture 4: Central stability homology [video]
- Lecture 5: Highly connected simplicial complexes [video]
- Lecture 6: Quillen’s spectral sequence argument for homological stability [video]
- Lecture 7: Polynomial functors [video]
- Lecture 8: Central stability homology for polynomial VIC(Z)–module [video]