Modular Categories--Their Representations, Classification, and Applications (16w5049)


(Microsoft Research)

(Louisiana State University)

Dmitri Nikshych (University of New Hampshire)

(Texas A&M University)


The Casa Matemática Oaxaca (CMO) will host the "Modular Categories--Their Representations, Classification, and Applications" workshop from August 14th to August 19th, 2016.

Modular categories are intricate organizing algebraic structures appearing in a variety of mathematical subjects including topological quantum field theory, conformal field theory, and representation theories of quantum groups, von Neumann algebras, and vertex operator algebras. Just as group theory is used to describe classical symmetry and classical crystals of matter, the theory of modular categories is used to study quantum symmetry and topological phases of matter such as the fractional quantum Hall liquids and topological insulators. Modular categories also underpin the foundations of topological quantum computation.

In this workshop, we will study the mathematical structures of modular categories---their classification and representations, and explore their applications to gapped states of quantum matter and quantum computing. The workshop will bring applied and theoretical researchers in close contact to establish a cohesive community of researchers working in modular categories and their applications. We expect to find new approaches to old problems and open new directions on a mathematical structure that sits in the triple juncture of mathematics, physics, and computer science. Exploration of this area can push the boundaries of our understanding of quantum mathematics, new quantum states of matter, and simultaneously generate quantum information technologies with potentially great societal impact.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry.

The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.