eCHT Research Seminar Reading Group

The reading group is organized by Hassan Abdallah (Wayne State University), Scotty Tilton (UCSD), and Dan Isaksen (Wayne State University).

Meeting information

Link: wayne-edu.zoom.us/j/9486065385?pwd=UU1tTno5c0FvaGZvVm1lTjVtWU41UT09

Meeting ID: 948 606 5385

Passcode: eCHT

Schedule

In preparation for Liz Tatum’s talk on 10 October, the suggested readings are:

• Sections 2 and 3.1 of Behrens-Ormsby-Stapleton-Stojanoska, On the ring of cooperations for 2-primary connective topological modular forms
• Pages 1-3 of Mahowald, bo-resolutions
• Section 1 of Gonzalez, A vanishing line in the BP<1>-Adams Spectral Sequence

In preparation for Lennart Meier’s talk on 12 September, the suggested readings are:

• Dan Edidin, What is a stack?
• Section 1.3 of Jacob Lurie, A survey of elliptic cohomology
• Section 2 of Chi-Kwong Fok, A stroll in equivariant K-theory

In preparation for Ben Antieau’s talk on 25 April, the suggested readings are:

• The introduction to Mandell, E_\infty-algebras and p-adic homotopy theory
• The theorems and definitions (avoiding proofs to just get the main ideas) of Sections 4.1 and 4.2 in Raksit, Hochschild cohomology and the derived de Rham complex revisiited
• Section 2.1 of Mondal-Reinecke, Unipotent homotopy theory of schemes

In preparation for Andrew Senger’s talk on 28 March, the suggested readings are:

• Hesselholt-Nikolaus: Topological cyclic homology . Beginning through section 1.1.2 in the arXiv version. (General background on trace methods, syntomic cohomology.)
• Antieau-Krause-Nikolaus: On the K-theory of Z/p^n — announcement Sections 1-3. (Background on the problem) Take a look at the tables!

In preparation for Mark Behrens’s talk on 29 February, the suggested readings are:

• Section 2 of Behrens, Ormsby, Stapleton, Stojanoska, On the ring of cooperations for 2-primary connective topological modular forms
• Sections 1 and 5 of Mark Mahowald, bo-resolutions

In preparation for Morgan Opie’s talk on 1 February, the suggested readings are:

• The introduction of Morgan Opie, A classification of rank 3 bundles on complex projective 4-space (about vector bundle classification problems)
• Sections 1 and 2 of Yang Hu, Metastable complex vector bundles over complex projective spaces (about applications of Weiss calculus to enumerating bundles with vanishing Chern data)
• The introduction of Prasit Bhattacharya and Hood Chatham, On the EO-orientability of vector bundles (about higher real K-theories EO_{p-1} at the prime p and EO_{p-1}-orientability of bundles on projective spaces)
• The introduction of Hood Chatham, An orientation map for height p-1 real E-theory (also about higher real K-theories EO_{p-1} at the prime p and EO_{p-1}-orientability of bundles on projective spaces)

In preparation for Christian Carrick’s November 2 research seminar talk, participants will read material that gives relevant background to the talk and have an opportunity to meet and discuss the material over Zoom. The suggested readings are:

• Chapters 2 and 6 of Carrick’s thesis: Stacks and Real-Oriented Homotopy Theory
• (If time permits) Mahowald and Rezk, Brown-Comenetz duality and the Adams spectral sequence