Graduate Course Notes
Notes from Graduate Courses
- Topics Course on Chromatic homotopy theory, Spring 2024.
This course was an introduction to chromatic homotopy theory.
- Course notes
- Worksheets: zip file
- Topics Course on Equivariant homotopy and cohomology, Fall 2020.
This course is in two parts. The first part, on Equivariance in Algebra, covers constructions on group representations, discusses Mackey functors, and group (co)homology. The second part, on Equivariance in Topology, focuses on equivariant homotopy theory and introduces Bredon and Borel cohomology.
- Course notes
- Homework: HW1, HW2, and HW3.
- Worksheets: zip file
- Topics Course on Vector Bundles, Fall 2018.
This was an introductory course on vector bundles, discussing K-theory and characteristic classes as well.
- Course notes
- Homework: HW1 and HW2.
- Worksheets: zip file
-
Topics Course on Hopf Algebras, Spring 2017.
The course starts with a general discussion of Hopf algebras before specializing to the Steenrod algebra. The Cartan-Eilenberg spectral sequence is introduced as a tool for computing the cohomology of Hopf algebras. The course ends with a brief introduction to the May and Adams spectral sequences.
-
Topics Course on Homotopy Theory, Spring 2015.
The main focus of the course was fiber bundles and the Serre spectral sequence.
- Course notes for Homotopy Theory (Spring 2011). Fibrations, cofibrations, homotopy excision.
- University of Illinois Suminar 2010 and 2011.
Proseminar talk notes (from graduate school):
- Algebraic K-theory: Intro (11/11/04).
- Unstable A^1-homotopy theory (3/2/05).
- Stable A^1-homotopy theory (3/4/05).
- Algebraic K-theory: +=Q (11/15/05-11/22/05).
- Kan's Ex^\infty Functor (10/11/06).
- Models for Equivariant Homotopy Theory (11/16/06).
- The Bousfield-Kan Spectral Sequence (1/25/07-1/30/07).
- The Equivariant Dold-Thom Theorem (5/06/07).
