Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, November 12, 2020.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, November 12, 2020

7:00 pm in Zoom,Thursday, November 12, 2020

#### Vertices and lattice points of Schubitopes

###### Neil Fan (Sichuan University)

Abstract: The Newton polytope of a multivariate polynomial f is the convex hull of the exponent vectors of f. In this talk, we will discuss the Newton polytopes of several important families of polynomials in algebraic combinatorics, such as Schubert polynomials, Grothendieck polynomials, key polynomials and Demazure atoms. We establish a combinatorial algorithm to generate the vertices of a more general family of polytopes, called Schubitopes, which include the Newton polytopes of Schubert and key polynomials as special cases. As an application, we confirm a conjecture of Monical, Tokcan and Yong, which asserts that the vertices of the Newton polytope of a key polynomial can be generated by permutations in a Bruhat interval. Moreover, we will give a characterisation of the lattice points in the Newton polytopes of key polynomials, which was also originally conjectured by Monical, Tokcan and Yong. This talk is based on joint work with Peter L. Guo, Simon Peng and Sophie Sun. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.