- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 21, 2024 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Evgeny Mukhin – Indiana University Indianapolis – https://science.indianapolis.iu.edu/people-directory/people/mukhin-evgeny.html
- Organizer
- Alex Dunn, Xiaoyu He, Rose McCarty, Dmitrii Ostrovskii, and Wei Zhu
The totally non-negative Grassmannian is the set of points in a real Grassmannian such that all Plucker coordinates have the same sign (some can be zero). I will show how points in totally non-negative Grassmannians arise from the spaces of polynomials in one variable whose Wronskian has only real roots. Then I will discuss a similar result for the spaces of quasi-exponentials.
The main statements of this talk should be understandable to an undergraduate student. Somewhat surprisingly, the proofs use the theory of quantum integrable systems related to $GL(n)$. I will try to explain the logic of such proofs in a gentle way.
This talk is based on a joint work with S. Karp and V. Tarasov.