SCIENTIFIC PROGRAMS AND ACTIVITIES

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)

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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