When posed with studying problems in pure mathematics, and especially problems that involve knowing spatial information, having knowledge of the symmetries that these problems possess is fundamental in understanding the nature of the problems. These symmetries can be either the direct object of study (as in representation theory), give new constructions to study (as group actions and quotients have given rise to orbifolds and stacks), contribute towards knowing the “correct” information on which to focus (as in equivariant descent, equivariant algebraic geometry, and equivariant algebraic topology), and generally give richer insight into the underlying structure of the problems we study. What is interesting about these different incarnations of symmetry and structure is that for each different mathematical discipline we have a different way with which to view and work with symmetries and equivariance. In this session, we seek to bring together researchers in all areas of mathematics to share our relative perspectives on equivariance and symmetry to learn from each other and help further our own works by using these new insights. In particular, we would like to bring together researchers in algebraic geometry, algebraic topology, arithmetic geometry, category theory, differential and symplectic geometry, (equivariant) homotopy theory, Hopf algebras, (p-adic) representation theory, sheaf theory, stack theory, topological data analysis, topological complexity theory, and other related areas.

A Hopf algebra is an algebra for which it is possible to define the tensor product of two modules. Hopf algebras are currently an area of very intense research, mainly motivated by its many connections to other fields and its many applications, ranging from conformal field theory to quantum computing. Conformal field theory and quantum computing are therefore also two of the related topics that are mentioned in the title; others include tensor categories, quantum groups, algebraic groups, and Hopf orders.