The grant will support US based mathematicians to participate in the semester "New Directions in Lie theory" (www.crm.math.ca/LieTheory2014/) to be held at the Centre de Recherches Mathematiques at the University of Montreal from January 1 to June 30, 2014; the first activity supported by this award will take place January 6--17, 2014. The overall goals of the thematic semester is to highlight the current research in Lie theory and its applications to other fields. This will be achieved by having four workshops and four mini-courses. The mini-courses are split into two winter schools and are designed to prepare students and postdoctoral fellows to take advantage of the workshops. The workshops will focus on recent developments in combinatorial representation theory, Hall and cluster algebras, mathematical physics and categorification. One of the aims is to highlight the connections between these four avenues of research. For instance, the combinatorics of q-characters has been important in both Hall and cluster algebras and categorification. The ideas coming from integrable systems, such as the Q-systems, has had a major impact on combinatorial representation theory and cluster algebras. The speakers of each workshop have been chosen to reflect the synergy between these different directions in Lie theory.
Lie theory is a central area of contemporary mathematics. The structure and representation theory of Lie groups and Lie algebras have resulted in important applications in physics and other branches of mathematics and, in turn, Lie theory has benefited from these connections. The Centre de Recherches Mathematiques at the University of Montreal is world renowned for its thematic semesters, scientific workshops and outreach activities and is one of Canada's national centers for fundamental research in mathematics and their applications. This grant will foster international collaborations and to increase connections between US and Canadian researchers. The interactions with a diverse community of mathematicians will help young mathematicians to develop a strong research program. They will be able to take advantage of the opportunities for international collaborations. The opportunity to speak at the workshop and/or the thematic seminar will help them to disseminate their work to senior mathematicians. This will also help them to apply for international postdoctoral positions which frequently need a local mentor. The interactions between the senior mathematicians from the US and international graduate students will also help to broaden the pool of applications to US graduate programs.
