# Seminar, Pavel Etingof (MIT), New symmetric tensor categories in positive characteristic

## Date:

Tuesday, September 25, 2018, 4:00pm to 5:00pm

## Location:

Jefferson 356

Title. New symmetric tensor categories in positive characteristic

Abstract. We construct and study a nested sequence of finite symmetric tensor
categories $${\rm Vec}=\mathcal C_0\subset \mathcal C_1\subset\cdots\subset \mathcal C_n\subset\cdots$$
over a field of characteristic 2 such that $$\mathcal C_{2n}$$ are
incompressible, i.e., do not admit tensor functors into
tensor categories of smaller Frobenius--Perron dimension.
This generalizes the category $$\mathcal C_1$$ described by S. Venkatesh and the category $$\mathcal C_2$$ defined by V. Ostrik.
The Grothendieck rings of the categories $$\mathcal C_{2n}$$ and $$\mathcal C_{2n+1}$$ are both isomorphic to the ring of real cyclotomic integers defined by a primitive $$2^{n+2}$$-th root of unity, $${\mathcal O}_n=\Bbb Z[2\cos(\pi/2^{n+1})]$$. We expect that the category $$\mathcal C_{2n}$$ is a reduction to characteristic 2 of the Verlinde category at the $$2^n$$-th root of unity, and that there exists similar non-semisimple reduction of the Verlinde category at the $$p^n$$-th root of unity to characteristic p when . This is joint work with Dave Benson.