Department of

# Mathematics

Seminar Calendar
for Algebra, Geometry and Combinatorics events the year of Tuesday, March 26, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2019            March 2019             April 2019
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2                   1  2       1  2  3  4  5  6
3  4  5  6  7  8  9    3  4  5  6  7  8  9    7  8  9 10 11 12 13
10 11 12 13 14 15 16   10 11 12 13 14 15 16   14 15 16 17 18 19 20
17 18 19 20 21 22 23   17 18 19 20 21 22 23   21 22 23 24 25 26 27
24 25 26 27 28         24 25 26 27 28 29 30   28 29 30
31


Thursday, February 14, 2019

3:00 pm in 347 Altgeld Hall,Thursday, February 14, 2019

#### Quiver varieties and root multiplicities for symmetric Kac-Moody algebras

###### Peter Tingley   [email] (Loyola University, Chicago)

Abstract: We discuss combinatorial upper bounds on dimensions of certain imaginary root spaces for symmetric Kac-Moody algebras. These come from a realization of the infinity crystal using quiver varieties. The framework is quite general, but we only work out specifics for one special case. We conjecture that our bound is quite tight, and give both computational evidence and heuristic justification for this conjecture, but unfortunately not a proof.

Thursday, March 28, 2019

3:00 pm in 347 Altgeld Hall,Thursday, March 28, 2019

#### Complexity, Combinatorial Positivity, and Newton Polytopes

###### Colleen Robichaux   [email] (UIUC)

Abstract: The nonvanishing problem asks if a coefficient of a polynomial is nonzero. Many families of polynomials in algebraic combinatorics admit combinatorial counting rules and simultaneously enjoy having saturated Newton polytopes (SNP). Thereby, in amenable cases, nonvanishing is in the complexity class ${\sf NP}\cap {\sf coNP}$ of problems with "good characterizations''. This suggests a new algebraic combinatorics viewpoint on complexity theory. This paper focuses on the case of Schubert polynomials. These form a basis of all polynomials and appear in the study of cohomology rings of flag manifolds. We give a tableau criterion for nonvanishing, from which we deduce the first polynomial time algorithm. These results are obtained from new characterizations of the Schubitope, a generalization of the permutahedron defined for any subset of the $n\times n$ grid, together with a theorem of A. Fink, K. Meszaros, and A. St. Dizier (2018), which proved a conjecture of C. Monical, N. Tokcan, and A. Yong (2017). This is joint work with Anshul Adve and Alexander Yong.

Thursday, May 2, 2019

3:00 pm in 347 Altgeld Hall,Thursday, May 2, 2019

#### Cell Decompositions for Rank Two Quiver Grassmannians

###### Dylan Rupel (Michigan State University)

Abstract: TBA

Tuesday, May 21, 2019

11:00 am in 347 Altgeld Hall,Tuesday, May 21, 2019

Abstract: TBA