Seminar: Topics in Topology, Sommersemester 2018

UPDATE: the topic has been decided and the regular meeting time and place have been changed (see below for details)

General information

Instructor: Prof. Chris Wendl (for contact information and office hours see my homepage)

Time and place: Thursdays 15:00-17:00 (c.t.) in room 3.007 (Rudower Chaussee 25) except in isolated special cases

Prerequisites: Knowledge of singular and cellular homology/cohomology as in Topologie II. Some knowledge of smooth manifolds (as in Differentialgeometrie I) will also be helpful.

Content: By a vaguely democratic process we have decided to focus the seminar on bordism theory, following approximately the first 12 chapters of the lecture notes from this course by Dan Freed. The seminar will be run in English.

Requirements: All (students and otherwise) are welcome to attend the seminar and may volunteer to give talks. For students to receive credit, the requirements are the following:

  1. Give at least one of the talks (normally this will mean one 90-minute session), with careful attention to fitting all necessary material within the given time constraints;
  2. Submit clearly readable notes for your talk (handwritten is fine), so that they can be scanned and uploaded to the website by the following day;
  3. Attend the seminar regularly (at most two absences in the semester).

Schedule of talks

Here is a detailed plan of talks with content recommendations.
UPDATE: I was not previously aware, but there is also a slightly revised version of Freed's notes available as a single file. Most of the typos observed in my document above appear to have been corrected in the revised version.
Wednesday April 18, 2018 Discussion of possible topics
Thursday April 26, 2018 Speaker: Chris Wendl
Topic: Introduction to bordism theory and background on fiber bundles
scanned notes
Thursday May 3, 2018 Speaker: Kangning Wei
Topic: Framed bordism and the Pontrjagin-Thom construction
scanned notes
Wednesday May 9, 2018
11:00 (c.t.) in Room 4.007
Speakers: Johannes Hauber and Jan Hesmert
Topic: Stabilization and the Freudenthal suspension theorem
scanned notes: part 1 (Hauber) and part 2 (Hesmert)
Thursday May 17, 2018 Speakers: Vera Baumgartner and Samuele Traviganti
Topic: The stable framed bordism ring
scanned notes: part 1 (Baumgartner) and part 2 (Traviganti)
Thursday May 24, 2018 Speaker: Davide Manini
Topic: Classifying spaces
scanned notes
Thursday May 31, 2018 no seminar this week
Thursday June 7, 2018 Speaker: Yoanna Kirilova and Evgeniya Lagoda
Topic: Characteristic classes 1
scanned notes: part 1 (Kirilova) and part 2 (Lagoda)
Thursday June 14, 2018 Speaker: Giuseppe Scriva
Topic: Characteristic classes 2
scanned notes
Thursday June 21, 2018 Speaker: Matthias Görg
Topic: A digression on intersection theory
scanned notes
Thursday June 28, 2018 Speaker: Tatiana Levinson
Topic: Tangential structures
scanned notes
Thursday July 5, 2018 Speaker: Agustin Moreno
Topic: Thom spectra and X-bordism
Thursday July 12, 2018 Speaker: Lucas Mann
Topic: Signature and the Hirzebruch theorem
Thursday July 19, 2018
(note change: usual time and place!)
Speaker: Youshua Kesting
Topic: The rational oriented bordism ring
Chris Wendl's homepage