Events for 04/04/2024 from all calendars

Seminar on Banach and Metric Space Geometry

Time: 10:00AM - 11:00AM

Location: BLOC 302

Speaker: Rubén Medina, Universidad de Granada

Title: On nonlinear approximation properties and a problem of Godefroy and Ozawa

Abstract: In this talk we will focus on nonlinear analogues of classical approximation properties in separable Banach spaces. More specifically, we will present different properties that have been conjectured to hold in every separable Banach space by N. Kalton (2012) as well as by G. Godefroy and N. Ozawa (2014). Regarding the problem raised by Godefroy and Ozawa, we will present certain advances produced in the last three years in collaboration with Petr Hájek, some of which hint towards a negative solution. We will also comment some positive results for 'large' families of spaces and connections with linear approximation properties.

Stochastic Processes Seminar

Time: 10:00AM - 11:00AM

Location: ZOOM

Speaker: Tianxu Wang, University of Alberta

Title: Stochastic generalized Kolmogorov systems with small diffusion: I. Explicit approximations for invariant probability density function

Abstract: This paper focuses on studying the long-term coexistence states of stochastic generalized Kolmogorov systems with small diffusion. We establish a mathematical framework for approximating the invariant probability measures (IPMs) and density functions (IPDFs) of these systems. Compared with the existing approximation methods available only for systems with non-degenerate linear diffusion, this paper introduces two new and easily implementable approximation methods, the log-normal approximation (LNA) and updated normal approximation (uNA), which can be used for systems with not only non-degenerate but also degenerate diffusion. Moreover, we utilize the Kolmogorov-Fokker-Planck (KFP) operator and matrix algebra to develop algorithms for calculating the associated covariance matrix and verifying its positive definiteness. Our new approximation method exhibits good accuracy in approximating the IPM and IPDF at both local and global levels, and significantly relaxes the minimal criteria for positive definiteness of the solution of the continuous-type Lyapunov equation. We demonstrate the utility of our method in several application examples from biology and ecology.

Noncommutative Geometry Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Zhengwei Liu , Tsinghua University

Title: Quantum Fourier Analysis and Categorification Criteria

Abstract: We give a quick review of recent developments in quantum Fourier analysis. We derive the primary categorification criteria from complete positivity and apply it to answer three questions proposed by Jones, Wang and Etingof in 2015, 2017 and 2019 respectively.

Maxson Lecture Series

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: David Eisenbud, University of California, Berkeley

Title: Infinite Resolutions I: Some history, and the smallest resolutions.

AMUSE

Time: 6:00PM - 7:00PM

Location: BLOC 306

Speaker: Dr. Guy Battle, Texas A&M University, Mathematics

Title: Nano-Electric Crystal Ball Calculation as a Problem in Number Theory

Abstract: Consider nano-crystals based on an arbitrary salt compound (with no regard for whether the technology for creating a chosen shape even exists). We pursue the problem of calculating the net electric charge due to a difference between the number of alkali ions and the number of halogen ions. If the crystal has an I^infinity shape of arbitrary size, then the net charge is essentially zero - i.e., zero plus or minus the fundamental unit of charge. In the case where the crystal has an I^1 shape, we derive an expression for the net charge that has the same order of magnitude as the area of the surface for an arbitrarily large size. In the case where the crystal has an I^2 shape, the problem of calculating the net charge for an arbitrary radius seems to be open. We discuss a couple of partial results.