Events
Department of Mathematics and Statistics
Texas Tech University
Tools for quantifying the discrepancy between probability distributions, such as relative entropy and optimal transport metrics, are important in many areas of probability, statistics, and machine learning. Generically called divergences, such objects are especially useful in data-driven contexts when they have a variational representation. In this talk I will present the extension of the classical Donsker-Varadhan variational formula to the family of Rényi divergences and discuss its application to differential privacy. I will also present a second variational representation of Rényi divergences that exhibits significantly reduced variance for large values of the Rényi parameter, including for worst-case regret. Finally, I will discuss a technique for constructing regularized Rényi divergences by combining them with integral probability metrics, such as 1-Wasserstein, and will demonstrate their use in generative adversarial networks.
Please attend this week's Statistics seminar at 4 PM (UT-6) Monday via this Zoom link.
Meeting ID: 995 5081 3789
Passcode: 806409
Abstract pdf
There are several mathematical models for field theories, including the functorial approach of Atiyah–Segal and the factorization algebra approach of Costello–Gwilliam. I'll discuss how to think about line operators in these contexts, and the different strengths of each method. Motivated by work of Freed–Moore–Teleman, I'll explain how to exploit both models to say something about certain gauge theories. This is based on joint work with Owen Gwilliam.Over the past 30 years, magnetic resonance imaging (MRI) has become a ubiquitous tool for accurately visualizing brain structures. Understanding the structural characteristics of the brain is essential for disease diagnosis and treatment. However, the quantification of complex brain structures remains challenging due to issues with shape extraction, representation, and modeling. This talk will introduce efficient frameworks of elastic shape analysis to model cross-sectional and longitudinal shape changes in 3D brain subcortical structure surfaces. We develop a set of tools to systematically quantify differences in surface shapes from raw structural MRI data. We apply the developed approaches to the Grady Trauma Project (GTP) and three longitudinal neuroimaging data sets (ADNI, HCP, and OpenPain). In the GTP data set, we integrate accurate morphological features and other clinical covariates to model post-traumatic stress disorder (PTSD) outcomes, which provides a vital tool to visualize localized deformations in brain anatomy and predict PTSD severity. With the longitudinal neuroimaging data sets, we showcase the wide applications of our framework in estimating continuous spatiotemporal shape changes from sparse longitudinal data, building life-span growth patterns, and comparing shape development differences among different groups for Alzheimer's disease and aging.
Please attend this week's Statistics seminar at 4 PM (UT-6) Monday via this Zoom link.
Meeting ID: 964 5703 4196
Passcode: 442950
The theory of p-elastic curves is a classical topic that dates back to the beginnings of the Calculus of Variations. Since then, these variational problems have been ubiquitous in Differential Geometry, Geometric Analysis and Mathematical Physics. In this talk, after reviewing the latest results on the theory, we will suggest open problems and discuss potential approaches to solve them.
Abstract. The time-independent Boltzmann neutron transport equation is an integro-differential equation for the neutron angular flux describing the location in space, energy, and direction of neutrons in a physical system of interest such as a nuclear reactor. Discretization of the neutron transport equation is driven by the physics of neutron interactions in matter, and in most cases of interest to nuclear engineers, generates large linear systems of equations. Recently, the tensor train (TT) technique has been shown to provide a useful low-rank approximation framework for high dimensional problems. Here we present a new approach to solve the neutron transport equation in Cartesian geometry using the TT representation of
the governing equations. The TT representation is explicitly constructed from the discretization of the governing equations using diamond differencing in space, multigroup-in-energy, and discrete ordinate collocation in angle. The proposed methodology is verified/validated by solving the canonical example of the k-effective eigenvalue neutron transport problem, which describes the criticality of a nuclear system such as a reactor. We compare and contrast accuracy and time complexity of the proposed TT approach to results obtained from PARTISN, the Los Alamos National Laboratory neutral particle transport code.
When: 4:00 pm (Lubbock's local time is CST)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 968 6501 7586
* Passcode: Applied
 | Wednesday
Nov. 15
7 PM
MA 108
|
| Mathematics Education
Math Circle
Jeff Lee
Department of Mathematics and Statistics, Texas Tech University
|
Math Circle Fall Poster
Abstract pdf
The AWM Raiders is hosting a series of "Meet the Professors" meetings throughout November, 2023. The professors from our department share their specialized knowledge of their research for a maximum of 7-10 minutes. The discussions range from Mathematical Physics to Biomath. This virtual event provides an opportunity for current and prospective students to know more about the ongoing research in the department from the professors themselves. Additionally, these events may foster collaboration between professors and graduate students.
Today's schedule pdf
The Meet the Professors meeting series is sponsored by the Raiders Chapter of AWM graduate student group and may be attended virtually at
3 PM (UT-6) via this Zoom link.
Meeting ID: 953 5112 5986
Passcode: AWM
