Speaker:  Alexander Postnikov (MIT)

Title:  Polytopes, tilings, total positivity, clusters, and amplitudes. 

Abstract: This talk is complementary to Lauren Williams' recent talk.  We'll
discuss several motivating examples from algebra/geometry/physics and
related combinatorial objects (plabic graphs, tilings, and
positroids).   We'll emphasize the connections between these objects
and polyhedral geometry.

This combinatorial structure can be described in elementary terms
accessible to high school students as a game on a certain class of
tilings of polygons by triangles.

This game on tilings is related to Lusztig's theory of total
positivity (in type A) and to works by Arkani-Hamed et al on
scattering amplitudes. It helps to construct the geometric RSK
correspondence, to prove the Littlewood-Richardson rule, to describe
Berenstein-Zelevinsky polytopes and string cones of Kashiwara's
parametrizations of gl_n-crystals, to generalize the octahedron
recurrence, etc.

We'll mention different directions to extend these combinatorial
structures to other Cartan-Killing types and beyond the planar limit.