July 21, 2024

Thematic Program on Geometric Applications of Homotopy Theory

January 9-13, 2007
Higher categories and their applications

Organizers: J. Baez (Univ. of California, Riverside), E. Cheng (Chicago), P. May (Chicago)

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SPEAKERS (Tentative):

John Baez (University of California) Aaron Lauda (University of Cambridge)
Julie Bergner (Kansas State University) Tom Leinster (University of Glasgow)
Eugenia Cheng (The University of Chicago) Peter May (University of Chicago)
Alissa Crans (Loyola Marymount University) Joshua Nichols-Barrer (Massachusetts Institute of Technology)
Nick Gurski (Yale University) Simona Paoli (Macquarie University)
Andre Henriques (Westfaelische Wilhelms-Universitaet) Urs Schreiber (Universität Hamburg)
Andre Joyal (UQAM) Mike Shulman (The University of Chicago)
Steve Lack (University of Western Sydney) Danny Stevenson (University of California)

SCHEDULE (Tentative):

Tuesday January 9 "Low dimensions"
9:00-9:30 Coffee and registration,
Welcoming remarks
9:30-10:30 Tom Leinster
A survey of the theory of bicategories
10:30 - 11:00 Coffee Break
11:00 - 12:00 Steve Lack
A survey of the theory of Gray-categories
12:00 - 3:00 Lunch
3pm Russian seminar Nick Gurski
7:00 - 8:00 Reception
8pm Informal talk

Mike Shulman
Model categories for beginners

Wednesday January 10 "n-categories and Homotopy Theory"
9:00-9:30 Morning Coffee
9:30-10:30 John Baez
The Homotopy Hypothesis
10:30 - 11:00 Coffee Break
11:00 - 12:00

Simona Paoli
Semistrict Tamsamani's n-groupoids and connected n-types

12:00 - 3:00 Lunch
3pm Russian seminar Eugenia Cheng
Batanin omega-groupoids and the homotopy hypothesis
8pm Peter May
Applications of bicategories to algebraic topology
Thursday January 11 "Quasicategories"
9:00-9:30 Morning Coffee
9:30 - 10:30 Michael Shulman
Introduction to quasicategories
10:30 - 11:00 Coffee Break
11:00 - 12:00 Julie Bergner
Model categories Quillen equivalent to the quasi-category model structure
12:00 - 2:30 Lunch
2:30 - 3:30 Joshua Nichols-Barrer
Fibred Quasi-Categories and Stacks
3:30 - 4:00 Coffee Break
4pm Andre Joyal
From quasi-categories to higher categories
(Audio and slide are not available)
Friday January 12 "Higher Gauge Theory"
9:00-9:30 Morning Coffee
9:30 - 10:30 Alissa Crans
A Survey of Higher Lie Theory
10:30 - 11:00 Coffee Break
11:00 - 12:00 Danny Stevenson
Lie 2-algebras and Higher Gauge Theory
12:00 - 3:00 Lunch
3pm Russian Seminar Urs Schreiber
Parallel transport in low dimensions
8pm Igor Bakovic
Bigroupoid principal 2-bundles
Saturday January 13 "QFT and TQFT"
9:00-9:30 Morning Coffee
9:30 - 10:30 Aaron Lauda
Frobenius algebras, quantum topology and higher categories
10:30 - 11:00 Coffee Break
11:00 - 12:00 Urs Schreiber
On 2-dimensional QFT: from arrows to disks


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