Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, May 3, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      April 2018              May 2018              June 2018
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1  2  3  4  5  6  7          1  2  3  4  5                   1  2
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Thursday, May 3, 2018

1:00 pm in Illini Union Room A ,Thursday, May 3, 2018

#### Spring 2018 Open House

Abstract: The IGL end-of-semester Open House will take place from 1:00 pm to 4:00 pm in Room A at the Illini Union. Come see what the IGL teams have produced this semester!

3:00 pm in 345 Altgeld Hall,Thursday, May 3, 2018

#### A closed non-iterative formula for straightening fillings of Young diagrams

###### Reuven Hodges (Northeastern University )

Abstract: Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straightening process, due to Alfred Young, that expresses a filling of a Young diagram as a sum of semistandard tableaux subject to certain relations. It has been a long-standing open problem to give a non-iterative, closed formula for this straightening process. In this talk I will give such a formula, as well as a simple combinatorial description of the coefficients that arise. Moreover, an interpretation of these coefficients in terms of paths in a directed graph will be explored. I will end by discussing a surprising application of this formula towards finding multiplicities of irreducible representations in certain plethysms and how this relates to Foulkes' conjecture.