##### Department of Mathematics,

University of California San Diego

****************************

### Combinatorics Seminar

## Karola Meszaros

#### Cornell University

## Realizing subword complexes via triangulations of root polytopes

##### Abstract:

Subword complexes are simplicial complexes introduced by Knutson and Miller to illustrate the combinatorics of Schubert polynomials and determinantal ideals. They proved that any subword complex is homeomorphic to a ball or a sphere and asked about their geometric realizations. We show that a family of subword complexes can be realized geometrically via triangulations of root polytopes. This implies that a family of $beta$-Grothendieck polynomials are special cases of reduced forms in the subdivision algebra of root polytopes. Based on joint work with Laura Escobar.

Host: Brendon Rhoades

### November 12, 2015

### 1:00 PM

### AP&M 6402

****************************