Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

To have your events added or removed from this calendar, please contact OUR at ugresearch@illinois.edu

Department Colloquium: Grothendieck Shenanigans

Event Type: Seminar/Symposium
Sponsor: Department of Mathematics
Location: Altgeld 245
Date: Feb 20, 2025 4:00 pm
Speaker: Leonid Petrov (Virginia)
Views: 8
Originating Calendar: Mathematics Colloquium & Named Lectures; Abstract: In 2017, Richard Stanley posed a fascinating question:

What is the asymptotically largest value of a principal specialization of a Schubert polynomial, and which permutation achieves it?

Although this problem remains out of reach in its full generality, we explore a related scenario by replacing Schubert polynomials with nonsymmetric Grothendieck polynomials. We define an ensemble of random permutations, where each permutation w\in S_n is assigned a probability proportional to the value of the corresponding Grothendieck polynomial. We then ask:

What do these "Grothendieck random permutations" typically look like for large n?

We show that these permutations have a limit shape (in the sense of permutons), and their fluctuations are governed by distributions from the Kardar-Parisi-Zhang universality class. Based on joint work with Alejandro Morales, Greta Panova, and Dmitriy Yeliussizov ([arXiv:2407.21653](https://arxiv.org/abs/2407.21653)).

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