Total Positivity, graphs, tilings and Weakly separated sets

Combinatorics Seminar
Friday, December 9, 2011 - 15:05
1 hour (actually 50 minutes)
Skiles 005
University of Michigan, Ann Arbor
Wiring diagrams are classical objects of combinatorics. Plabic graphs were defined by Postnikov, to study the total positivity of the Grassmannian. We will show how to generalize several definitions and properties of wiring diagrams to Plabic graphs, proving a conjecture by Leclerc-Zelevinsky and Scott on the way. We will begin with a brief introduction to total positivity and end with connection to cluster algebras. Major part of the talk comes from a joint work with Alexander Postnikov and David Speyer.