Conference: Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification

University Of Southern California, Los Angeles CA

Investigators

Abstract

The award will provide funding for the sixth and seventh meetings of the Canada-Mexico-USA Conference Series in Representation Theory, Noncommutative Algebra, and Categorification. These meetings will take place at the Universidad Nacional Autónoma de México in Mexico City in June 2024 and at the University of Southern California in Los Angeles in August 2025. Representation theory is a branch of mathematics that studies symmetries of physical theories and mathematical objects. Often, the main objects in representation theory are only the shadows of richer structures that are recovered through deeper study. Noncommutative algebra is a related branch of mathematics 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, categorification, and noncommutative algebra; on fostering an environment for the establishment of international collaborations between Canada, Mexico, and the USA in these research areas; and on exposing graduate students, post-docs, and early-career faculty in the three countries to current developments in the field. A poster session will run through the full meeting where early-career attendees will present their research. The main scientific topics for the sixth meeting in Mexico City will be geometric, algebraic, and homological methods in representation theory, representation theoretic and homological properties of noncommutative algebras, and the investigation of those problems using categorical methods. The talks will cover some of the most recent trends, including the following: cluster algebras, monoidal and additive categorifications, quantum symmetries, finite tensor categories, representations of quantized affine Kac-Moody algebras, Calabi-Yau algebras and triangulated categories, Hopfological algebra, web approaches to modular representation theory, and representation theoretic aspects of Heegaard-Floer homology. The website for the 2024 conference is https://sites.google.com/im.unam.mx/canadausmexico-2024/. 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.