SCIENTIFIC PROGRAMS AND ACTIVITIES

October 20, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th ANNIVERSARY YEAR
July 3-6, 2012
WORKSHOP ON ALGEBRAIC MONOIDS, GROUP EMBEDDINGS
AND ALGEBRAIC COMBINATORICS

Hosted by the Fields Institute

Organizers: Mahir Can (Tulane), Zhenheng Li (University Of South Carolina),
Benjamin Steinberg (Carleton), Qiang Wang (Carleton)

Registration on site July 3
Fees: $50, $25 for students and PDF, waived for invited speakers
Registration fees cover meeting materials and coffee breaks
Speakers Abstracts Reimbursement information for funded participants Registered Participants Toronto
Accommodation in Toronto

Overview

The Workshop will consist of 3 minicourses on introductory topics aimed at graduate students staggered throughout the four days. These tutorials will introduce the necessary background for the remaining research talks, which form the second component of the workshop. We anticipate that these research talks will outline future directions of research and lead to active collaborations between the participants. It is anticipated that the nature of this event will attract interaction between researchers of different countries and enable graduate students from various universities to communicate directly with each other. This workshop, which is funded by both Fields Institute and NSF, is in honour of the 60th birthdays of Mohan Putcha and Lex Renner, and will be taking place at the Fields Institute.

The main goal of the proposed workshop is to stimulate research on the interplay between algebraic monoids, group embeddings and algebraic combinatorics. By fostering contact between people with different backgrounds and strengths, we hope to gain a better understanding of algebraic monoids, including both their structure and their representation theory. Another central goal of the workshop is to seek a better understanding of the connections between algebraic monoids and the geometry of embeddings. Reductive monoids are group embeddings of a particular kind. They can be understood as reductive monoids, and also as spherical varieties. Their structure is sufficiently rich to provide hints and examples for more general problems about spherical varieties. Another aim of this workshop is to catalyze the interactions between combinatorics and algebraic monoids to further the understanding of the representation theory of an arbitrary (reductive) monoid and to further enrich the theory of combinatorics. Finally, it is an important goal of this workshop to prepare graduate students for research in this area and in particular to suggest thesis projects.

Tuesday July 3, 2012
8:45-9:00 Onsite registration and coffee
9:00 – 9:45 Stephen Doty
Representation Theory of Reductive Normal Algebraic Monoids
9:45 – 10:15 Coffee break
10:15 – 11:00 Georgia Benkart
A Talk (Walk) on the McKay Correspondence
11:10 – 12:00 Anne Schilling*
Monoids in Algebraic Combinatorics
12:00-13:30 Lunch
13:30 – 14:20 Eric Jespers*
Groups, Semigroups, Semigroup Rings and Set-Theoretic Solutions of the Yang-Baxter Equation
14:25 – 15:10 Lex E. Renner
The Betti Numbers of Rationally Smooth Simple Embeddings
15:10 – 15:30 Coffee break
15:30 – 16:15 Yuval Roichman
A 0-Hecke Monoid Action on Reduced Words
16:20 – 17:05 Nantel Bergeron
Generalization of nil-Coxeter Monoids
Wednesday, July 4, 2012
8:45-9:00 Morning Coffee
9:00 – 9:45 Mohan Putcha
Regular Linear Algebraic Semigroups

9:45 – 10:15 Coffee break
10:15 – 11:05 Michel Brion*
Algebraic Monoids and Equivariant Embeddings of Algebraic Groups (continued)
11:10 – 12:00 Anne Schilling*
Monoids in Algebraic Combinatorics (continued)
12:00-1:30 Lunch
13:30 – 14:20 Eric Jespers*
Groups, Semigroups, Semigroup Rings and Set-Theoretic Solutions of the Yang-Baxter Equation (continued)
14:25 – 15:10 Jan Okninski
Conjugacy Classes of Left Ideals of Finite Dimensional Algebras
15:10 – 15:30 Coffee break
15:30 – 16:15 Nicolas Thiéry
Algorithmic Representation Theory of Finite Monoids
16:20 – 17:05 Alvaro Rittatore
The Endomorphisms Monoid of a Homogeneous Vector Bundle
17:05 – 17:20 Taking Pictures
Thursday, July 5, 2012
8:45-9:00 Morning Coffee
9:00 – 9:45 Sandeep Varma
On Linear Hodge-Newton Decomposition for Reductive Monoids
9:45 – 10:15 Coffee break
10:15 – 11:05 Michel Brion*
Algebraic Monoids and Equivariant Embeddings of Algebraic Groups (continued)
11:10 – 12:00 Anne Schilling*
Monoids in Algebraic Combinatorics (continued)
12:00- 1:30 Lunch
13:30 – 14:20 Eric Jespers*
Groups, Semigroups, Semigroup Rings and Set-Theoretic Solutions of the Yang-Baxter Equation (continued)
14:25 – 15:10 Stuart Margolis
On the Global Dimension of Left Regular Band Algebras and Leray Numbers
15:10 – 15:30 Coffee break
15:30 – 16:15 Wenxue Huang
The Kernel and Unipotent Radicals in Linear Algebraic Monoids
16:20 – 17:05 Dewey Taylor
Direct product Factorization of Bipartite Graphs With Partition-Reversing Involutions
Friday, July 6, 2012
8:15-8:30 Morning Coffee
8:30-9:15 Ryan Therkelsen
Conjugacy Order in Canonical and Dual Canonical Monoids
9:20-10:10 Michel Brion*
Algebraic Monoids and Equivariant Embeddings of Algebraic Groups (continued)

10:10-10:30 Coffee break
10:30--11:15 Monica Vazirani
Categorifying Quantum Groups
11:20--12:05 Kiumars Kaveh
TBD
12:00-1:30 Lunch
13:30-14:15 Tom Denton
Affine Permutations and an Affine Coxeter Monoid

 

List of Participants as of June 28, 2012

Full Name University/Affiliation
Aker, Kürsat Istanbul Bilgi Üniversitesi
Benkart, Georgia University of Wisconsin at Madison
Berg, Chris Université du Québec à Montréal
Bergeron, Nantel York University
Brion, Michel Universit de Grenoble I
Can, Mahir Bilen Tulane University
Chen, Hongjia Wilfrid Laurier University
De Concini, Corrado Università di Roma "La Sapienza"
Denton, Tom York University/ Fields Institute
Doty, Stephen Loyola University Chicago
Gorzny, Jan University of Toronto
Huang, Wenxue Shantou University
Jespers, Eric Vrije Universiteit Brussel
Joyce, Michael Tulane University
Kaveh, Kiumars University of Pittsburgh
Li, Zhenheng University of South Carolina Aiken
Li, Zhuo Xiangtan University
Liu, Yu Hanshan Normal University
Margolis, Stuart Bar Ilan University
O'Hara, Allen University of Western Ontario
Okninski, Jan Warsaw University
Putcha, Mohan North Carolina State University
Renner, Lex University of Western Ontario
Rittatore, Alvaro Centro de Matemática
Saliola, Franco Université du Québec à Montréal
Sandeep Varma, Vadakkumkoor University of Chicago
Schilling, Anne University of California, Davis
Steinberg, Benjamin The City College of New York
Taylor, Dewey Virginia Commonwealth University
Therkelsen, Ryan Bellarmine University
Thiéry, Nicolas M. Université Paris Sud 11
Tuxanidy Torres, Aleksandr Carleton University
Twelbeck, Tim Tulane University
Vazarani, Monica UC Davis
Vazirani, Monica UC Davis


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