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Equivariant homotopy theory learning seminar

This is the page for the Spring 2024 learning seminar on equivariant (stable) homotopy theory at UIUC.

Here is a syllabus for the topics we'll cover and the references we'll use for each topic. We will mostly draw from:

Blumberg, "The Burnside Category" notes (Blum),

Hill--Hopkins--Ravenel, On the non-existence of elements of Kervaire invariant one / Equivariant stable homotopy theory and the Kervaire invariant problem (HHR / HHRb),

among other references for each week.

Meeting information: Tuesday, 9:45-10:50am. Altgeld 141 (backup: Noyes 164).

Schedule of speakers

Week 0 (1/23). Yigal Kamel: Organization and overview.

Week 1 (1/30). Meng Guo: Equivariant homotopy theory of spaces.

Week 2 (2/6). Jiantong Liu: Equivariant cohomology. (notes)

Week 3 (2/13). Garrett Credi: G-spectra I. (notes)

Week 4 (2/20). Yigal Kamel: G-spectra II. (notes)

Week 5 (3/5). Gabrielle Li: Equivariant algebra for G-spectra. (notes)

Week 6 (3/19). Garrett Credi: Spectral sequences.

Week 7 (3/26). Doron Grossman-Naples: Multiplicative structures. (notes)

Week 8 (4/2). Langwen Hui: Examples of G-spectra.

Week 9 (4/9). Kiran Luecke: Real oriented homotopy theory.

Week 10 (4/16). Sam Hsu: Global homotopy theory.