Video Lectures

Dimers and 3-Webs

Richard Kenyon

This is joint work with Haolin Shi (Yale). 3-webs are bipartite, trivalent, planar graphs. They were defined and studied by Kuperberg who showed that they correspond to invariant functions in tensor products of SL_3-representations. Webs and...

Ellenberg and Gijswijt drastically improved the best known upper asymptotic bound for the cardinality of a cap set in 2016. Tao introduced the notion of slice rank for tensors and showed that the Ellenberg-Gijswijt proof can be nicely formulated...

Let V be a complex vector space and consider symmetric d-linear forms on V, i.e., linear maps Symd(V)→>C. When V is finite dimensional and d>2, the structure of such forms is very complicated. Somewhat surprisingly, when V has countably infinite...

Several equivalent definitions of rank for matrices yield non-equivalent definitions of rank when generalized to higher order tensors. Understanding the interplay between these different definitions is related to important questions in additive...