This grant will fund participation of U.S.-based researchers in the US-Mexico Conferences on Representation Theory, Categorification, and Non-Commutative Algebra that will take place at Universidad Nacional Autonoma de Mexico in Mexico City, January 15-18, 2015 and the University of Southern California, Los Angeles, January 14-17, 2016. Representation theory is a major branch of mathematics that studies symmetries of of physical theories and of mathematical objects. Often the main objects in representation theory are only the shadow of richer structures that are recovered through deeper study. Non-commutative algebra is another major, related branch of algebra that studies deformations of commutative objects found in quantum theories, representation theory, and geometry. The foci of the conferences will be on recent advances at the interface of representation theory and non-commutative algebra; on fostering an environment for the establishment of international collaborations between the US and Mexico in this research areas; and on exposing graduate students, post-docs, and young faculty in both countries to current developments in the field. The conference series has an international component and is co-funded by the International Science and Engineering Section.
The PIs will organize one four-day conference each academic year that will alternate between the US and Mexico. The main scientific topics of the conference series will be algebraic, geometric and homological methods in representation theory, categorification, and non-commutative algebra. The talks will cover some of the most recent trends including: cluster algebras, quantum groups, monoidal and additive categorifications, Calabi-Yau algebras and categories, and non-commutative projective algebraic geometry.
