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.