Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification

Catholic University Of America, Washington DC

Investigators

Abstract

The conference "Interactions of quantum affine algebras with cluster algebras, current algebras and categorification" will take place at the Catholic University of America in Washington, DC on June 2-8, 2018. The conference will focus on problems related to, or motivated by, representations of infinite dimensional Lie algebras and their quantum analogues. The recent rapid growth, rising prominence, and emerging connections between these topics underscores the timely need for a conference that focuses on new connections by bringing together leading researchers who work on different aspects of these subjects. A main goal of the conference is to expose graduate students and early-career researchers to recent developments in representation theory. In an effort to foster their interest and engagement, the four day conference will be preceded by a three day summer school/workshop for junior researchers. Infinite-dimensional Lie algebras and their quantum analogues play a prominent role in mathematics and mathematical physics. In recent decades their representation theory has been connected with a number of different subjects, such as algebraic geometry, algebraic topology, combinatorics and cluster algebras, to name but a few. The talks will focus on topics such as crystal and canonical bases, Weyl, Demazure and Kirillov-Reshetikhin modules and interaction between them, highest weight categories, Khovanov-Lauda-Rouquier algebras and their applications to categorification, cluster algebras and related structures, geometric methods in infinite dimensional representation theory (in particular, the role of quiver varieties), and map algebras. A special emphasis will be placed on interactions between various structures. Further details can be found at the conference website: http://www.mi.uni-koeln.de/~dkus/. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.