SCIENTIFIC PROGRAMS AND ACTIVITIES

November 22, 2014

October 14-16, 2011
Workshop on Category Theoretic Methods in Representation Theory
University of Ottawa

All talks will take place in room B005 of KED 585, located at 585 King Edward Avenue.

Organizers:
Alexander Hoffnung, Alistair Savage
Department of Mathematics and Statistics, University of Ottawa


OVERVIEW

The term 'categorification' refers to replacing algebraic objects such as sets, rings, and algebras, with categories. The original algebraic structure is then recovered by passing to isomorphism classes. Interesting categorifications provide new structure and interesting connections between apparently disparate mathematical concepts.

While many developments in the history of mathematics can be interpreted in terms of categorification, community consensus traces the initiation of a formal program of study to the 1994 paper of Crane and Frenkel proposing the existence of categorified quantum groups as fundamental objects in the study of 4-dimensional topological quantum field theories. Since then, researchers have enjoyed great success and a wide array of applications from the study of categorified structures.

Recently, building on geometric results, category theory has offered its own transformative results to the study of representation theory. For example, the application of the diagramatic theory of monoidal categories and adjoint functors to the study of quantum groups by Khovanov and Lauda has produced the conjectured categorified quantum groups of Crane and Frenkel (also obtained by Rouquier algebraically). Other fundamental representation theoretic objects such as Weyl groups, Hecke algebras, and the Heisenberg algebra have also been categorified. The applications of this work have had immediate impact across representation theory and mathematical physics.

INVITED SPEAKERS

Sabin Cautis (Columbia)
James Dolan (UC Riverside)
Ben Elias (MIT)
Joel Kamnitzer (Toronto)
Aaron Lauda (Southern California)
Anthony Licata (Institute for Advanced Study)
Marco Mackaay (Universidade do Algarve)
Volodymyr Mazorchuk (Uppsala)
Kevin McGerty (Oxford)
Scott Morrison (UC Berkeley)
Raphaël Rouquier (Oxford)
Pedro Vaz (University of Zurich and IST Lisbon)
Ben Webster (Northeastern)
Oded Yacobi (Toronto)
Geordie Williamson (Oxford)

 

FINANCIAL SUPPORT

There is some funding available for graduate students and postdoctoral fellows. Those interested should complete the funding application by clicking on the link above. The deadline for applying for support is September 1, 2011.

SCHEDULE:

All talks will take place in room B005 of KED 585, located at 585 King Edward Avenue. Registration and coffee breaks will take place in room 104.

Friday, October 14
9:00-9:30 Registration and Coffee
9:30-10:20

Kevin McGerty
A geometric construction of the quantum Frobenius morphism

10:20-10:35 Coffee Break
10:35-11:25

Pedro Vaz
A diagrammatic categorification of the q-Schur algebra

11:25-11:40 Coffee Break
11:40-12:30 Marco Mackaay
The extended Khovanov-Lauda calculus and the colored Rouquier complex
12:30-2:00 LUNCH BREAK
2:00-2:50 Oded Yacobi
Polynomial functors and categorification
2:50-3:20 Coffee Break
3:20-4:10 Anthony Licata
Heisenberg categorification and Affine Lie algebras
4:10-4:40 Coffee Break
4:40-5:30 Sabin Cautis
Categorification of vertex operators
Saturday, October 15
9:00 - 9:30 Coffee
9:30-10:20

Ben Webster
Categorification of Reshetikhin-Turaev invariants

10:20-10:35 Coffee Break
10:35-11:25 Ben Elias
Soergel bimodules and Kazhdan-Lusztig theory I
11:25-11:40 Coffee Break
11:40-12:30

Geordie Williamson
Soergel bimodules and Kazhdan-Lusztig theory II

12:30-2:00 Lunch
2:00-2:50 Aaron Lauda
The odd nilHecke algebra and categorified quantum sl(2)
2:50-3:20 Coffee Break
3:20-4:10 Scott Morrison
Invariants of 4-manifolds from Khovanov homology
4:10-4:40 Coffee Break
4:40-5:30 Raphaël Rouquier
Adjoint braid group actions
7:00 Dinner (details to be announced)
Sunday, October 16
9:00 -9:30 Coffee
9:30 - 10:20 James Dolan
Projective geometry = dimensional analysis
10:20- 10:35 Coffee Break
10:35 - 11:25 Volodymyr Mazorchuk
2-representations of finitary 2-categories
11:25 - 11:40 Coffee Break
11:40- 12:30 Joel Kamnitzer
Buildings and Spiders

 

REGISTERED ATTENDEES as of October 24, 2011

Full Name University/Affiliation
Arkhipov, Sergey University of Toronto
Biland, Erwin Université Laval
Bischof, Bryan Kansas State University
Calmès, Baptiste Université d'Artois
Cautis, Sabin Columbia University
Chen, Hongjia Wilfrid Laurier University
Chen, Xueqing University of Wisconsin-Whitewater
Dancso, Zsuzsanna Institute for Advanced Study
Dimitrov, Ivan Queen's University
Dolan, James  
Dlab, Vlasta Carleton University
Egger, Jeff  
Elias, Benjamin Massachusetts Institute of Technology
Fischer, Aron CUNY Graduate Centre
Fontaine, Bruce University of Toronto
Halacheva, Iva University of Toronto
Hannigan-Daley, Brad University of Toronto
Hoffnung, Alexander University of Ottawa
Huard, Francois Bishop's University
Kamnitzer, Joel University of Toronto
Klein, Florian University of Oxford
Lauda, Aaron University of Southern California
Lemay, Joel University of Ottawa
Li, Travis Songhao University of Toronto
Licata, Anthony Institute for Advanced Study
Mackaay, Marco Universidade do Algarve
Majard, Dany Kansas State University
Malagón-López, José University of Ottawa
Mazorchuk, Volodymyr University of Uppsala
McCurdy, Micah Saint Mary's University
McGerty, Kevin Imperial College London
Mirmohades, Djalal Uppsala University
Morgan, Stephen University of Toronto
Morrison, Scott University of California, Berkeley
Morton, Jeffrey Instituto Superior Tecnico
Nilsson, Jonathan Uppsala University
Pospichal, Tomas Carleton University
Putyra, Krzysztof Columbia University
Rouquier, Raphaël University of Oxford
Rowe, Daniel University of Toronto
Salmasian, Hadi University of Ottawa
Savage, Alistair University of Ottawa
Thind, Jaimal University of Toronto
Treumann, David Northwestern University
Vaz, Pedro University of Zurich and IST Lisbon
Wagner, Emmanuel Université de Bourgogne
Webster, Ben Northeastern University
Williamson, Geordie University of Oxford
Wu, Enxin University of Western Ontario
Yacobi, Oded University of Toronto
Zainoulline, Kirill University of Ottawa
Zhang, Lucy Liuxuan University of Toronto
Zhong, Changlong University of Ottawa

 


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