Workshop on Algebraic Monoids, Group Embeddings and Algebraic Combinatorics

Tulane University, New Orleans LA

Investigators

Abstract

The workshop ``Algebraic Monoids, Group Embeddings and Algebraic Combinatorics" will take place at the Fields Institute, Toronto, Ontario on July 3--6, 2012. It consists of two major components. First of all, there will be 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. The organizers of the workshop are Mahir Can (Tulane University), Zhenheng Li (University of South Carolina), Benjamin Steinberg (City College of New York) and Qiang Wang (Carleton University, Canada). The theory of algebraic monoids, originated independently by M. Putcha and L. Renner in 1980, is a natural synthesis of algebraic group theory (Chevalley, Borel, Tits) and torus embeddings (Mumford, Kempf, et al). It is a significant part of the theory of spherical embeddings (Brion, Luna, Vust) and horospherical varieties (Popov, Vinberg). Symmetric varieties (De Concini, Procesi) are closely related to algebraic monoids. Algebraic combinatorics studies discrete structures arising from an algebraic context. It is a broad and important discipline of mathematics with applications in quantum chemistry, statistical biology, statistical physics, theoretical computer science and so forth. In recent years there has been a tremendous progress on the combinatorial aspects of the above mentioned embedding theories, relating their underlying algebraic structures to the classical notions in algebraic combinatorics. The workshop will provide a unique opportunity to bring together some of the principal investigators from different countries, junior researchers, and graduate students. It will outline future directions of research on algebraic monoids, group embeddings, and algebraic combinatorics. This workshop will prepare graduate students for research in related areas and suggest thesis projects. More information about the workshop can be found at: http://www.fields.utoronto.ca/programs/scientific/12-13/monoids/index.html This grant will provide funding for U.S. researchers to participate and benefit from this timely international workshop, which will stimulate research on the interplay between algebraic monoids, group embeddings, and algebraic combinatorics. It will help establish collaborations among the participants, including students and faculty from non-Ph.D.-granting institutions, as well as female students and professors. It will potentially help establish connections between U.S. and international academic institutions.