Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, March 5, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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1    1  2  3  4  5  6  7             1  2  3  4
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Thursday, March 5, 2020

11:00 am in 241 Altgeld Hall,Thursday, March 5, 2020

#### To Be Announced

###### Shiang Tang (Illinois Math)

3:00 pm in 347 Altgeld Hall,Thursday, March 5, 2020

#### Fulton's Conjecture, Extremal Rays, and Applications to Saturation

###### Joshua Kiers   [email] (University of North Carolina, Chapel Hill)

Abstract: We begin by recalling a conjecture of Fulton on Littlewood-Richardson coefficients and discussing two generalizations. With a little lemma from algebraic geometry, we find ourselves on the way to naming the extremal rays of the "eigencone'' of asymptotic solutions to the branching question in representation theory of semisimple Lie groups. After giving an algorithm for finding all such extremal rays, generalizing some prior work joint with P. Belkale, we report on progress on the saturation conjecture for types $D_5$, $D_6$, and $E_6$.

4:00 pm in 245 Altgeld Hall,Thursday, March 5, 2020

#### Plane Trees and Algebraic Numbers

###### George Shabat (Russian State University for the Humanities and Independent University of Moscow)

Abstract: The main part of the talk will be devoted to an elementary version of the deep relations between the combinatorial topology and the arithmetic geometry. Namely, an object defined over the field of algebraic numbers, a polynomial with algebraic coefficients and only two finite critical values, will be associated to an arbitrary plane tree. Some applications of this construction will be presented, including polynomial Pell equations and quasi-elliptic integrals (going back to N.-H. Abel). The relations with finite groups and Galois theory will be outlined. At the end of the talk the possible generalizations will be discussed, including the dessins d'enfants theory initiated by Grothendieck.