| Talk_id | Date | Speaker | Title |
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23769
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Wednesday 2/5
3:00 PM
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Aklilu Zeleke, MSU
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New and Old Combinatorial Identities Part II
- Aklilu Zeleke, MSU
- New and Old Combinatorial Identities Part II
- 02/05/2020
- 3:00 PM - 3:50 PM
- C517 Wells Hall
Using a probabilistic approach, we derive some interesting identities involving beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.
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24774
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Wednesday 2/19
3:00 PM
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Anna Weigandt, University of Michigan
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Derivatives of Schubert polynomials
- Anna Weigandt, University of Michigan
- Derivatives of Schubert polynomials
- 02/19/2020
- 3:00 PM - 3:50 PM
- C517 Wells Hall
We describe the action of a differential operator when applied to the Schubert basis. We use this to give a short proof of the Macdonald identity. We also discuss an application to the study of the (strong) Sperner property of the weak order on the symmetric group. This property was proven by Gaetz and Gao (2018). Our description of the differential operator leads to a proof of a determinant conjecture of Stanley (2017), which also implies the Sperner property. This is joint work with Zachary Hamaker, Oliver Pechenik and David E Speyer.
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24780
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Thursday 2/27
3:00 PM
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Zachary Hamaker, University of Florida
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Schubert calculus, involutions and symmetric matrices
- Zachary Hamaker, University of Florida
- Schubert calculus, involutions and symmetric matrices
- 02/27/2020
- 3:00 PM - 3:50 PM
- D227A Wells Hall
In his "Kalkul der abzahlende Geometrie”, Schubert introduced a powerful non-rigorous method for solving enumerative geometry problems known as Schubert calculus. Making this method rigorous motivated a great deal of 20th century algebraic geometry. Since the combinatorics of permutations is central to this theory, combinatorialists have made major contributions to Schubert calculus broadly construed. We will overview some highlights from this field, develop a parallel theory based on the combinatorics of involutions in the symmetric group and conclude by using this work to describe fundamental properties of the geometry of symmetric matrices. This work is joint with Eric Marberg and Brendan Pawlowski.
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