2026-2027 Mathematics Colloquium
Upcoming Talks:
September 17 - 12:30pm - Zoom
Uzi Smilansky (Weizmann Institute)
- Title: Characterization of Chaotic Evolution in Quantum Systems
- Abstract: In classical mechanics, chaotic behavior is characterized by the exponential growth of the distance between classical orbits which are initially close together -the “butterfly effect”. The Lyapunov exponent provides a measure of this separation process. This concept cannot be directly adapted to quantum mechanical systems, in particular for systems which do not have a classical counterpart. I shall present a new method to define the quantum version of the Lyapunov exponent for arbitrary quantum systems, presented by Hermitian matrices of (arbitrarily large) but of finite dimension. I shall also describe the quantum analogue of a few other measures of classical chaotic dynamics, such as e.g., the growth rate of the entropy during evolution. After explaining the concepts and the method, I shall show a few applications to matrix ensembles of various types, and close with a summary of open problems.
September 24 - 3:30pm - SDRICH 207
Hiroyoshi Mitake (Waseda University)
- Title: TBA
- Abstract: TBA
October 1 - 3:30pm - SDRICH 207
Hung Tran (University of Wisconsin-Madison)
- Title: TBA
- Abstract: TBA
October 12 - 3:30pm - SDRICH 324
Christopher Seaton (Skidmore College)
- Title: TBA
- Abstract: TBA
October 22 - 3:30pm - SDRICH 207
Nicholas Mayers (Kennesaw State University)
- Title: Well-behaved Kohnert posets
- Abstract: Kohnert polynomials form a family of polynomials indexed by diagrams that consist of unit cells arranged in the first quadrant. Many families of well-known polynomials have been shown to be examples of Kohnert polynomials, including key, Schur, and Schubert polynomials. Given a diagram D, the monomials occurring in the corresponding Kohnert polynomial encode diagrams formed from D by applying sequences of certain moves, called "Kohnert moves," each of which alters the position of at most one cell. In this talk, we focus on the underlying sets of diagrams which generate the monomials of Kohnert polynomials. With each such collection of diagrams, one can associate a poset structure which is known to not, in general, be well-behaved. In particular, the corresponding "Kohnert posets" generally do not have a unique minimal element, are not ranked, and are not lattices. Here, we will focus on recent attempts to find conditions under which Kohnert posets are well-behaved in the sense that they have a unique minimal element, are ranked, or are EL-Shellable. No background knowledge concerning posets is assumed.
October 29 - 4:00pm - MMSCI 101
Nick Trefethen (Harvard)
- Title: The AAA Algorithm for Rational Approximation
Abstract: With the introduction of the AAA algorithm in 2018 (Nakatsukasa-Sete-T., SISC), the computation of rational approximations changed from a hard problem to an easy one. We've been exploring the implications of this transformation ever since. This talk will review the algorithm and then present demonstrations of applications in areas including interpolation of missing data, analytic continuation, analysis of solutions of dynamical systems, model order reduction, computation of complex resonances, numerical computation of the Schwarz function, and solution of planar Laplace, Stokes, and Helmholtz problems.
October 30 - 3:30pm - MMSCI 301
Nick Trefethen (Harvard)
- Title: Quadrature = Rational Approximation
Abstract: Whenever you see a string of quadrature nodes, you can consider it as a branch cut defined by the poles of a rational approximation to the Cauchy transform of a weight function. The aim of this talk is to explain this statement and show how it opens the way to calculation of targeted quadrature formulas for all kinds of applications. Gauss quadrature is an example, but it is just the starting point, and many more examples will be shown. I hope this talk will change your understanding of quadrature formulas. This is joint work with Andrew Horning.
November 12 - 3:30pm - SDRICH 207
Yifeng Yu (UC Irvine)
- Title: TBA
- Abstract: TBA
Recent Talks:
Click here to see a list of past colloquium talks.