Seminar Event Detail


Combinatorics

Date:  Friday, November 07, 2014
Location:  3866 East Hall (4:10 PM to 5:00 PM)

Title:  Cohomology classes of rank varieties and a counterexample to a conjecture of Liu

Abstract:   Given any diagram (a finite collection of boxes on a grid), one can define an associated symmetric function. In many cases, these symmetric functions contain interesting and nontrivial information related to the diagram: for Young diagrams one obtains Schur functions; for skew diagrams, skew Schur functions; for permutation diagrams, Stanley symmetric functions, which describe reduced words. Liu defined a collection of subvarieties of the Grassmannian indexed by diagrams, and conjectured that their cohomology classes are represented by the corresponding diagram symmetric functions. I will give a counterexample to Liu's conjecture. I will also discuss a connection to rank varieties (a special case of Knutson-Lam-Speyer's positroid varieties), and some new results on their cohomology classes.

Files:


Speaker:  Brendan Pawlowski
Institution:  U. Minnesota

Event Organizer:     

 

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