Second Chicago Summer School in Geometry and Topology

This is the second in a series of NSF funded summer schools in geometry and topology at the University of Chicago. Over several years it intends to introduce advanced undergraduates and beginning graduate students to a broad range of topics that are important to topology. This year the focus is on algebraic topology and should be accessible to undergraduate and graduate students with a solid background in the fundamental group, covering spaces, and the basics of homology and cohomology.

Organizers: Ben Antieau, Agnes Beaudry, Peter May, Dylan Wilson, Inna Zakharevich.

Speakers: Ben Antieau, Agnes Beaudry, Mark Behrens, Henry Chan, Peter May, Dylan Wilson, Jesse Wolfson, Zhouli Xu, Inna Zakharevich.

For questions, write to chicagotopology2@math.uchicago.edu.

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Application/Registration for this summer school is at the AMS mathprograms website: https://www.mathprograms.org/db/login/ja.

The deadline is March 31, 2016. You will need the following application material:

• A cover letter describing your background and why you want to participate to the program
• A curriculum vitae
• Transcripts
• A letter of recommendation

Registered students will be contacted by email in due course.

Financial support will be available for some qualified applicants. Because of funding restrictions, funding is only available to US citizens and permanent residents.

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Schedule

The schedule for the summer school is available here.

Resources

Glossary A collection of concepts and definitions

Stable Algebraic Topology, 1945-1966 Peter May's historical survey

A Concise Course in Algebraic Topology Peter May's book on algebraic topology

Algebraic Topology Allen Hatcher's book on algebraic topology

Vector Bundles and K-Theory Allen Hatcher's book on vector bundle

Characteristic Classes John W. Milnor and James D. Stasheff's book on characteristic classes

Categories for the Working Mathematician Saunders Mac Lane's book on category theory

K-Theory Notes on lectures by Atiyah by Anderson.

Algebraic and Geometric Surgery Andrew Ranicki

Notes on Cobordism Robert E. Stong

Topological Library Novikov and Taimnanov, contains Thom's paper "Some General Properties of Differentiable Manfiolds"

Lectures

Video recordings of the lectures can will be available soon at this link (filmed and edited by Michael Jehlik).

Problem sets

Day 1

Day 2

Day 3

Day 4

Notes: Day 1

Talk 1: Introduction (Peter May)

Talk 3: The homotopy category of spaces (Inna Zakharevich)

Talk 4: Algebraic structure on cohomology (Agnes Beaudry)

Notes: Day 2

Talk 1 and 2: Vector Bundles 1 and 2 (Jess Wolfson) [outline]

Talk 3: Vector Bundles 3 (Agnes Beaudry)

Talk 4: Cobordism 1 (Inna Zakharevich)

Notes: Day 3

Talk 1: Cobordism 2 (Inna Zakharevich)

Talk 3: Cobordism 4 (Agnes Beaudry)

Talk 4: Cobordism 5/K-theory (Dylan Wilson)

Notes: Day 4

Talk 1: K-theory 2 (Peter May)

Talk 2: K-Theory 3 (Ben Antieau)

Talk 3: K-Theory 4 (Ben Antieau)

Talk 4: Onwards-Upwards (Mark Behrens)

Notes: Day 5

Talk 1: Equivariant Generalizations 1 (Dylan Wilson)

Talk 2: Onwards-Upwards (Ben Antieau)

Talk 4: Onwards-Upwards (Peter May)

Participants

List

Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).