Friday 7  Saturday 8 
Sunday 9 
Monday 10 
Tuesday 11 
10:0012:00 MacLane Memorial 
9:3010:30 Johnstone 11:0012:00 Lawvere 
9:3010:30 Stevenson 11:0012:00 Fiedorowicz 
9:3010:30 Gurski 11:0012:00 Bergner 
9:3010:30 Fiore 11:0012:00 Shulman 
2:003:30 Reminiscences 
2:003:00 Crans 
2:003:00 Moerdijk 
2:003:00 Awodey 
1:302:30 Freyd 3:004:00 May 
4:005:00 Baez/Namb. 
4:005:00 Joyal 
4:005:00 Cheng 
4:005:00 Baez/Namb. 
4:305:30 Baez/Namb. 
Details
morning and afternoon coffee breaks will
take
place in the Eckhart Tea Room
Friday April 7 

9:0010:00 
Coffee and donuts 
Eckhart Tea Room 

10:0012:00 
Mac Lane Memorial 
Bond Chapel 

Reception 
Quadrangle Club 

2:003:30 
Reminiscences 
Ry 352 (Barn) 

Coffee 
Eckhart Tea Room 

4:005:00 
John Baez, Namboodiri I 
Higher categories, higher gauge theory 
Ry 251 
Saturday April 8 

9:3010:30 11:0012:00 
Peter Johnstone William Lawvere 
Potential invertibility and presheaf toposes Smooth and simplicial toposes 
Ry 251 
2:003:00 4:005:00 
Alissa Crans André Joyal 
Lie 2groups, Lie 2algebras, and Loop groups The theory of quasicategories 
Ry 251 
Sunday April 9 

9:3010:30 11:0012:00 
Danny Stevenson Zig Fiedorowicz 
Lie 2algebras and the geometry of gerbes Tensor products of E_n operads 
Ry 251 
2:003:00 4:005:00 
Ieke Moerdijk Eugenia Cheng 
Quasicategories and quasioperads The periodic table of ncategories 
Ry 251 
Monday April 10 

9:3010:30 11:0012:00 
Tom Fiore Julie Bergner 
Double categories and pseudo algebras Model categories, dg categories, and derived Hall algebras 
Ry 352 (Barn) 
2:003:00 4:005:00 
Steve Awodey John Baez, Namboodiri II 
Topology and modality Higher categories, higher gauge theory 
Ry 352 (Barn) Ry 251 
Tuesday April 11 

9:3010:30 11:0012:00 
Nick Gurski Mike Shulman 
From bicategories to tricategories Anchored bicategories 
Ry 352 (Barn) 
1:302:30 3:004:00 4:305:30 
Peter Freyd Peter May John Baez, Namboodiri III 
New structures on old categories Duality in bicategories and topological applications Higher categories, higher gauge theory 
Eck 206 
Abstract:
The work of Eilenberg and Mac Lane marks the beginning of a trend in which mathematics based on sets is generalized to mathematics based on categories and then higher categories. We illustrate this trend towards "categorification" by a detailed introduction to "higher gauge theory".
Gauge theory describes the parallel transport of point particles using the formalism of connections on bundles. In both string theory and loop quantum gravity, point particles are replaced by 1dimensional extended objects: paths or loops in space. This suggests that we seek some kind of "higher gauge theory" that describes the parallel transport as we move a path through space, tracing out a surface. Surprisingly, this requires that we "categorify" concepts from differential geometry, replacing smooth manifolds by smooth categories, Lie groups by Lie 2groups, Lie algebras by Lie 2algebras, bundles by 2bundles, sheaves by stacks or gerbes, and so on. The basic tool used here is Ehresmann's notion of "internalization".
To explain how higher gauge theory fits into mathematics as a whole, we begin with a lecture reviewing the basic principle of Galois theory and its relation to Klein's Erlangen program, covering spaces and the fundamental group, EilenbergMac Lane spaces, and Grothendieck's ideas on fibrations.
The second lecture treats connections on trivial bundles and 2connections on trivial 2bundles, explaining how they can be described either in terms of their holonomies or in terms of Liealgebravalued differential forms. For a clean treatment of these concepts, we recall Chen's theory of "smooth spaces", which generalize smooth finitedimensional manifolds.
The third lecture explains connections on general bundles and 2connections on general 2bundles, explaining how they can be described either in terms of holonomies or local data involving differential forms. We also explain how 2bundles are classified using nonabelian Cech 2cocycles, and how the theory of 2connections relates to Breen and Messing's theory of "connections on nonabelian gerbes".
Name 
Affiliation 
Steve Awodey 
Carnegie Mellon University 
John Baez 
University of California at Riverside 
Julie Bergner 
Kansas State University 
Jeff Caruso 

Eugenia Cheng 
University of Chicago 
Alissa Crans 
Ohio State University 
Geoff Cruttwell 
Dalhousie University 
Robert Dawson 
St Mary's University 
Thomas Drucker 
University of WisconsinWhitewater 
Tony Elmendorf 
Purdue University at Calumet 
Zbigniew Fiedorowicz 
Ohio State University 
Thomas Fiore 
University of Chicago 
Brandon Fogel 
University of Notre Dame 
Peter Freyd 
University of Pennsylvania 
Carl Futia 

Megan Guichard 
University of Chicago 
Bertrand Guillou 
University of Chicago 
Nick Gurski 
University of Chicago 
Michele Intermont 
Kalamazoo College 
Samuel Isaacson 
Harvard University 
Rick Jardine 
University of Western Ontario 
Niles Johnson 
University of Chicago 
Peter Johnstone 
Cambridge University 
André Joyal 
Université du Québec à
Montréal 
Noah Kieserman 
University of WisconsinMadison 
Joachim Kock 
Universitat Autònoma de Barcelona 
Sanjeevi Krishnan 
University of Chicago 
Aaron Lauda 
University of Cambridge 
William Lawvere 
SUNY at Buffalo 
Dean Leonardi 
University of Illinois at Chicago 
Michael Lieberman 
University of Michigan 
John Macdonald 
University of British Columbia 
Michael Mandell 
Indiana University 
Howard Marcum 
The Ohio State University at Newark 
Martin Markl 
Academy of Sciences of the Czech Republic 
Peter May 
University of Chicago 
Ieke Moerdijk 
University of Utrecht 
Justin Noel 
University of Chicago 
Son Nguyen 
Wayne State University 
Zaza Omiadze 
A.Razmadze Mathematical Institute, Tbilisi 
Bob Paré 
Dalhousie University 
Hendryk Pfeiffer 
Max Planck Institute for Gravitational Physics 
Kate Ponto 
University of Chicago 
Dorette Pronk 
Dalhousie University 
Laura Scull 
University of British Columbia 
Brooke Shipley 
University of Illinois at Chicago 
Armira Shkembi 
Wayne State University 
Michael Shulman 
University of Chicago 
Jim Stasheff 
University of Pennsylvania 
Danny Stevenson 
University of Adelaide 
Lawrence Stout 
Illinois Wesleyan University 
This site is maintained by Eugenia Cheng. You can email me at: eugenia at math.uchicago.edu
Last updated April 6 2006, 21:31