Week of September 24 - September 20
Algebra and Combinatorics
Topic: Group Algebras of Compact Groups and Enveloping Algebras of Profinite-Dimensional Lie Algebras
Karl H. Hofmann | Tulane University
Abstract: 
Join us:
Zoom access:
Time: 3:00
Algebraic Geometry and Geometric Topology Seminar
Topic: Integrals, trees, and spaces of pure braids and string links
Robin M Koytcheff | TBA
Abstract: The based loop space of configurations in a Euclidean space R^n can be viewed as the space of pure braids in R^{n+1}. In joint work with Komendarczyk and Volic, we studied its real cohomology using an integration map from a certain graph complex and recovered a result of Cohen and Gitler. Specifically, the map we studied is a composition of Kontsevich’s formality integrals and Chen’s iterated integrals. We showed that it is compatible with Bott-Taubes integrals for spaces of 1-dimensional string links in R^{n+1}. As a corollary, the inclusion of pure braids into string links in R^{n+1} induces a surjection in cohomology for any n>2. More recently, we showed that the dual to the integration map embeds the homotopy groups of the space of pure braids into a space of trivalent trees. We also showed that a certain subspace of these homotopy groups injects into the homotopy groups of spaces of k-dimensional string links in R^{n+k} for many values of n and k.
Join us:
Zoom access:
Time: 3:00 CT
Week of September 17 - September 13
Applied and Computational Mathematics
Topic: Almost-Periodic Schr\"odinger Operators with Thin Spectra
Jake Fillman | Texas Tech
Abstract: The determination of the spectrum of a Schr\"odinger operator is a fundamental problem in mathematical quantum mechanics. We will discuss a series of results showing that almost-periodic Schr\"odinger operators can exhibit spectra that are remarkably thin in the sense of Lebesgue measure and fractal dimensions: the spectrum can be a Cantor set of zero Lebesgue measure and zero Hausdorff dimension. [joint work with D. Damanik, A. Gorodetski, and M. Lukic]
Join us:
Zoom access:
Time: 2:00
Colloquium
Topic: Our Place Among the Infinities
Bill Taber - JPL (Host: Glatt-Holtz)
Abstract: We can see the planets and smaller bodies of the solar system with earth bound telescopes, but telescopes cannot answer the big questions. How do these bodies “work?” What is their chemistry, their dynamics, their evolution? Where is there water in the solar system? Is there now or has there ever been life anywhere but Earth. To answer the big questions, we cannot do so from the comfort of Earth; we have to go there. To go there requires machines that did not exist 100 years ago: rockets, ultra-stable oscillators, deep space communication antennae, computers, etc. But even more than these machines, it requires mathematics: mathematic to design trajectories from earth to distant bodies; mathematics to navigate the trajectories, mathematics to control the flight of spacecrafts, mathematics to communicate with spacecraft, and mathematics to arrive safely. This talk will sketch out in broad strokes the mathematics of deep space exploration and how it can help us to know our place among the infinities.
Bill Taber is group supervisor of the Mission Design and Navigation Software Group at NASA’s Jet Propulsion Laboratory in Pasadena, California where he has been since 1983. He holds the degrees of Masters in Business Administration from the Peter Drucker School of Management of the Claremont Graduate University at Claremont, California, a Ph. D. in Mathematics M.S. in Mathematic from the University of Illinois at Urbana-Champagne, Illinois, and a B.A. in Mathematics from Eastern Illinois University at Charleston, Illinois.
Join us:
Zoom access: Contact mbrown2@math.tulane.ed
Time: 3:30pm
Graduate Student Colloquium
Topic: Zeros of Orthogonal Polynomials
Victor Bankston | Tulane University
Abstract: We will plot the Krawtchouk polynomials to illustrate the interleaving of zeros of orthogonal polynomials.
Join us:
Zoom access:
Time: 5:00
Week of September 3 - August 30
Applied and Computational Mathematics
Topic: TBA
Beskos ? | TBA
Abstract: TBA
Join us:
Zoom access:
Time: 3:30
Colloquium
Topic: Random matrix theory for high-dimensional time series
Alexander Aue - UC Davis (Host: Didier, Gustavo)
Abstract: This talk is concerned with extensions of the classical Marcenko–Pastur law to time series. Specifically, p-dimensional linear processes are considered which are built from innovation vectors with independent, identically distributed entries possessing zero mean, unit variance and finite fourth moments. Under suitable assumptions on the coefficient matrices of the linear process, the limiting behavior of the empirical spectral distribution of both sample covariance and symmetrized sample autocovariance matrices is determined in the high-dimensional setting for which dimension p and sample size n diverge to infinity at the same rate, enabling the use of results from random matrix theory. The presented theory extends existing contributions available in the literature for the covariance case and is one of the first of its kind for the autocovariance case. Several applications are discussed to highlight the potential usefulness of the results. The talk is based on joint work with Haoyang Liu (New York Fed) and Debashis Paul (UC Davis).
Join us:
Zoom access: Contact mbrown2@math.tulane.edu
Time: 3:30pm
