Kan Seminar 2019-2020 Semester A

This is a seminar on classical results in Algebraic Topology. The seminar is modeled on the seminar organized by Dan Kan in MIT.
Each week, one of the participants will give a talk about a classical paper in Algebraic Topology (most of the papers are from the 50's-70's).
We will try to reinterpret and simplify (some of) the papers using the modern language of ∞-categories and higher algebra.

The meetings take place on Sundays at 10:00-12:00 (note the time change!), in Sprinzak 27.

If you are going to participate, please let me know by email at shay.benmoshe@mail.huji.ac.il.
Also, look at the papers suggestion, and try to pick one.
Feel free to talk to me, e.g. by email.

Talks Schedule

The first two talks will be introductory, and serve as a background for many of the other talks.
Everyone is encouraged to give a talk some time at the semester.

• 27/10/2019 - Shay Ben Moshe - ∞-Categories and Spectra (intro)
• 03/11/2019 - Shachar Carmeli - Steenrod Algebra (intro)
• 10/11/2019 - Shauly Ragimov - Milnor, On Manifolds Homeomorphic to the 7-Sphere
• 17/11/2019 - Danil Akhtiamov - Strom, A simple homotopy-theoretical proof of the Sullivan conjecture
• 24/11/2019 - Danil Akhtiamov cont., Ariel Davis - Adams, On the groups J(X)—IV
• 01/12/2019 - Ariel Davis cont.
• 08/12/2019 - Daniel Kaner - Harris, Bott Periodicity via Simplicial Spaces
• 15/12/2019 - Segev Cohen - Kan, A Combinatorial Definition of Homotopy Groups
• 22/12/2020 - Elhanan Nafha - Sullivan, Infinitesimal computations in topology (rational homotopy theory)
• 29/12/2019 - no meeting (Hanukkah)
• 05/01/2020 - Shaul Barkan - Mandell, E_∞ algebras and p-adic homotopy theory
• 12/01/2020 - no meeting (Abel in Jerusalem)
• 19/01/2020 - Kesha - Wall, Finiteness Conditions for CW-Complexes
• 26/01/2020 - Arye Deutsch - Frobenius algebras and 2D topological quantum field theories (following Kock)

Papers Suggestions

There are many great classical papers in Algebraic Topology.
A handful of papers are listed below, just give you some ideas. There are a lot more wonderful papers, many of them listed in the lists linked below.

• Brown, Cohomology Theories
• Quillen, Rational Homotopy Theory
• Miller, The Sullivan Conjecture on Maps from Classifying Spaces (or other proofs)
• Milnor, On Manifolds Homeomorphic to the 7-Sphere
• Wall, Finiteness Conditions for CW-Complexes
• Adams, On the groups J(X)—IV
• Harris, Bott Periodicity via Simplicial Spaces

Lists

• List in MIT
• List by Bohmann and Francis
• List by Lurie
• List by Behrens
• List by Isaksen, Klein, Salch