Tensor Categories and their Modules (course) -- Tensor Categories and their Modules

In the first half of 2024, there will be a learning seminar on tensor categories and
their modules at the University of Sydney.  We welcome you to join us if you are
interested, or to forward this email to other interested parties.  

Seminar details: Website: https://sites.google.com/view/tensorcategories/home 

Meeting time: Wednesdays from 10am-12pm, starting on 21 Feb.  (Talks will take place
during USyd’s semester 1.)  

Location: University of Sydney, Carslaw Building, Room 830

Seminar description: Tensor categories are the categorical analogue of rings.  They
naturally arise when considering categories of objects which can be multiplied; e.g.
representations of groups.  They are ubiquitous in representation theory, and also play
an important role in algebraic geometry, infinite dimensional Lie algebras, conformal
field theory, operator algebras, invariants of knots and 3-manifolds, and number
theory.  

The philosophy of representation theory tells us that to understand rings, we should
study their modules.  Lifting this to the level of categories motivates the study of
2-representations, or modules over tensor categories.  In this learning seminar, we will
study some classical and beautiful examples of such module categories.  We will start
with the basics of tensor categories, following [EGNO15].  We will try to make this
brief.  Then we will proceed with a tour of examples, with a particular focus on
Verlinde categories and Soergel bimodules.  In the second half of the course, we will
discuss the basics of module categories, then examine the module categories for our
running examples.  Additional topics will be driven by participant interest/willingness
to give talks.  

If you have questions or suggestions, please email the organizers
alexander.sherman@sydney.edu.au and a.romanov@unsw.edu.au.