Geometry, Combinatorics and Integral Systems Seminar - Chris Fraser

February 6, 2018
Thursday, February 15, 2018 - 3:00pm to 4:00pm
Math Building 317
math_sculpture

Title: Webs, dimers, and total positivity

Speaker: Chris Fraser (IUPUI)

Abstract: I will formulate a higher-rank version of the boundary measurement map for weighted planar bipartite networks in the disk. This map sends a network to a linear combination of SLr tensor invariants known as webs, and is defined using the r-fold dimer model on the network. When r equals 1, our map is Postnikov's boundary measurement used to coordinatize positroid strata. The main result is that the higher rank map factors through Postnikov's map. As a corollary, we deduce a complete set of diagrammatic relations between SLr webs, reproving a result of Cautis-Kamnitzer-Morrison in the classical (q=1) setting. We establish compatibility between our map and restriction to positroid strata. This is joint with Thomas Lam and Ian Le.

Seminar URLhttps://people.math.osu.edu/anderson.2804/gcis/

 

S M T W T F S
 
 
 
1
 
2
 
3
 
4
 
5
 
6
 
7
 
8
 
9
 
10
 
11
 
12
 
13
 
14
 
15
 
16
 
17
 
18
 
19
 
20
 
21
 
22
 
23
 
24
 
25
 
26
 
27
 
28
 
29
 
30
 
31