Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 1, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery. 
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Thursday, February 1, 2018

2:10 pm in 241 Altgeld Hall,Thursday, February 1, 2018
Graduate Student Number Theory Seminar

Modular Forms and Moduli of Elliptic Curves

Ningchuan Zhang (UIUC)

Abstract: In this talk, I’ll explain why modular forms are global sections of the sheaf of invariant differentials over the moduli stack of elliptic curves. In the end, I’ll mention the $q$-expansion principle and integral modular forms. No knowledge of stack is assumed for this talk. Please note this talk will start 10 minutes later than the regular time.

Submitted by jli135
3:00 pm in 345 Altgeld Hall,Thursday, February 1, 2018
Algebra, Geometry and Combinatorics

Standard Rothe Tableaux

Neil J. Y. Fan (Sichuan University and UIUC)

Abstract: Edelman and Greene constructed a bijection between the set of standard Young tableaux and the set of balanced Young tableaux of the same shape. Fomin, Greene, Reiner and Shimozono introduced the notion of balanced Rothe tableaux of a permutation w, and established a bijection between the set of balanced Rothe tableaux of w and the set of reduced words of w. In this talk, we introduce the notion of standard Rothe tableaux of w, which are tableaux obtained by labelling the cells of the Rothe diagram of w such that each row and each column is increasing. We show that the number of standard Rothe tableaux of w is smaller than or equal to the number of balanced Rothe tableaux of w, with equality if and only if w avoids the four patterns 2413, 2431, 3142 and 4132. When w is a dominant permutation, i.e., 132-avoiding, the Rothe diagram of w is a Young diagram, so our result generalizes the result of Edelman and Greene.

Submitted by lescobar