SCIENTIFIC PROGRAMS AND ACTIVITIES

October 18, 2017
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
May 4-5, 2015
Workshop From Lie Algebras To Group Schemes
at the University of Ottawa and Carleton University


Organizers
:
• Yuly Billig, Carleton • Erhard Neher, uOttawa
• Alistair Savage, uOttawa • Kirill Zaynullin, uOttawa

Overview

Emerging from foundational work by Borel, Chevalley, Demazure, Grothendieck, Serre and Tits, the theory of group schemes has become an important part of the modern mathematical culture. Inspired by the theory of Lie algebras and groups on the one hand and classical algebraic geometry on the other, group schemes have developed into an important tool for understanding representation theory, linear algebraic groups, homogeneous spaces and torsors. Several deep open conjectures in modern algebraic geometry, number theory and representation theory (e.g., Serre's conjectures and the Langland's program) are formulated using the language of group schemes.

One example of important work in the theory of group schemes is the celebrated Grothendieck--Serre conjecture of the 1960's, which stated that any rationally trivial G-torsor, where G is a reductive group scheme over a regular local ring, is locally trivial in the Zariski topology. The study of this problem has a long history, with contributions made by many famous mathematicians (beginning with Serre himself). The problem has only recently been solved by Fedorov and Panin in 2012-2014. Another striking example is the theory of motives and the proof of the Milnor conjecture by Voevodsky, which was essentially based on the computations of the motives of certain homogeneous varieties under the action of the orthogonal group scheme.

This workshop will bring together leading experts and junior mathematicians working in this exciting field. It will include expository lectures aimed at graduate students and postdoctoral fellows, as well as research talks. There is financial support available for junior participants. Those interested should submit their request online.

 

Workshop

The workshop activities will take place at 585 King Edward Avenue, Room B005 (on the University of Ottawa campus).

Schedule

Day 1 - Monday May 4, 2015.
Time Speaker Title
9:00-9:30am
Coffee & Registration (Room KED 104)
9:30-10:30am Mikhail Kochetov (Memorial University) Affine group schemes and duality between gradings and actions Part 1
10:30-11:00am
Coffee Break
11:00-12:00pm Nikita Karpenko (University of Alberta) Incompressibility of products
12:00-2:00pm
Lunch Break
2:00-2:30pm Jie Sun (Michigan Tech) Universal central extensions of twisted current algebras
2:45-3:15pm John Binder (Massachusetts Institute of Technology) Cusp Forms, Fields of Rationality, and Plancherel Equidistribution
3:15-3:45pm
Coffee Break
3:45-4:45pm Philippe Gille (IMAR, Bucharest and CNRS, Lyon) Parabolic subgroups of reductive group schemes
Day 2 - Tuesday May 5, 2015.
Time Speaker Title
9:00-9:30am
Coffee
9:30-10:30am Mikhail Kochetov (Memorial University) Affine group schemes and duality between gradings and actions Part 2
10:30-11:00am
Coffee Break
11:00-12:00pm Yuri Bahturin (Memorial University of Newfoundland) Group gradings on infinite-dimensional algebras
12:00-2:00pm
Lunch Break
2:00-2:30pm Qiao Zhou (UC Berkeley) Affine Grassmannian, Affine Flag Variety, and Their Global Counterparts
2:45-3:15PM Mohammad Bardestani (University of Ottawa) Howe-Kirillov's orbit method and faithful representation of finite p-groups
3:15-3:45pm
Coffee Break
3:45-4:45pm Stefan Gille (University of Alberta) Milnor-Witt K-Theory of local rings

 

Confirmed Speakers:

  Full Name University/Affiliation
1. Bahturin, Yuri Memorial University of Newfoundland
2. Bardestani, Mohammad University of Ottawa
3. Binder, John Massachusetts Institute of Technology
4. Gille, Philippe IMAR (Bucharest) and CNRS (Lyon)

5. Gille, Stefan University of Alberta
6. Karpenko, Nikita University of Alberta
7. Kotchetov, Mikhail Memorial University
8. Sun, Jie Michigan Tech
9. Zhou, Qiao UC Berkeley

Participants:

Full Name University/Affiliation
Bahturin, Yuri Memorial University of Newfoundland
Behboodi, Gholamreza University of Ottawa
Bernstein, Tobias Trent University
Billig, Yuly Carleton University
Binder, John Massachusetts Institute of Technology
Dlab, Vlasta Carleton University
Dykes, John Carleton University
Dykes, Kathlyn Carleton University
Fintzen, Jessica Harvard University
Gille, Philippe IMAR (Bucharest) & CNRS (Lyon)
Gille, Stefan University of Alberta
Islam, Rabib University of Ottawa
Junkins, Caroline University of Western Ontario
Karimicupour, Camelia University of Ottawa
Karpenko, Nikita University of Alberta
Kotchetov, Mikhail Memorial University
Molladavoudi, Saeid University of Ottawa
Nevins, Monica University of Ottawa
Neher, Erhard University of Ottawa
Pike, Jeffrey University of Ottawa
Racine, Michel University of Ottawa
Savage, Alistair University of Ottawa
Senesi, Prasad Catholic University of America
Sun, Jie Michigan Technological University
Talboom, John Carleton University
Wu, Gang University of Ottawa
Zaynullin, Kirill University of Ottawa
Zhou, Qiao University of California, Berkeley
Zurstraßen, Janina Johannes Gutenberg-Universität

 


 

 

 

 

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