Summer Graduate School
| Parent Program: | -- |
|---|---|
| Location: | SLMath: Eisenbud Auditorium, Atrium |
Show List of Lecturers
- Cain Edie-Michell (University of New Hampshire)
- Julia Plavnik (Indiana University)
Show List of Teaching Assistants
- Agustina Czenky (University of Southern California)
- Sean Sanford (University of Edinburgh; Indiana University)
Tensor categories have proven to be an indispensable tool in modern mathematics. Several such occurrences include; the representation theory of a Hopf algebra, the standard invariant of a finite depth subfactor, and as the value of a point in a fully extended topological quantum field theory. Intuitively, tensor categories can be thought of as a generalization of a group which now encodes a much larger class of “quantum” symmetries.
The purpose of this summer school will be to introduce students to the world of tensor categories. We will approach this topic in a variety of ways. Beyond simply exploring the formal definitions, many examples will be introduced and studied, and the natural occurrences of tensor categories “in the wild” will be explored. One such example will be the Temperley-Lieb-Jones category, and the corresponding “quantum” knot invariants.
This school will consist of two related lecture courses. The first will focus on the basic concepts and general structure of tensor categories. The second will focus on key examples of tensor categories, as well as the modern construction techniques for building these examples. Students will come away from these lecture series with the prerequisites required to begin a research-level project on tensor categories.
School Structure
There will be 2 lectures per day. Each lecture will be followed by a collaborative session. These sessions will be led by the teaching assistants in coordination with the relevant lecturer for that day.
Prerequisites
It is recommended that the student study either chapters 1-4 of Representation Theory by Fulton and Harris, or chapters 1-4 of Representation Theory of Finite Groups by Steinberg to gain the required knowledge in group representation theory. Also recommended to read chapters 1 and 2 of Basic Category Theory by Leinster to gain a working knowledge of the basic category theory required for the lecture topics.
Application Procedure
For eligibility and how to apply, see the Summer Graduate Schools homepage.
fusion categories
modular tensor categories
modular functors
String diagrams
graphical calculi
Braided monoidal categories
ribbon categories
Subfactors and their classification
Group rings of finite groups and their modules
Anyons