Events
Department of Mathematics and Statistics
Texas Tech University
 | Monday
Mar. 20
4 PM
MA 111
|
| Biomathematics
TBA
Rebecca Everett
Mathematics and Statistics, Haverford College
|
No abstract.
Join Zoom Meeting
We discuss several extremal problems in Complex Analysis and Potential Theory. Solutions to some of these problems were found by this speaker and his collaborators. But several other problems remain open. The main focus will be on open problems where it is reasonable to believe that the symmetrization methods and/or the theory of quadratic differentials can be applied.
This paper considers unified estimation and inference in panel autoregressive (AR) models. The AR coefficients are assumed to contain a latent group structure that allows the degree of persistence for each time series to be heterogeneous and unknown. We propose a novel penalized weighted least squares approach to simultaneously identifying the unknown group membership and consistently estimating the AR coefficients, regardless of whether the underlying AR process is stationary, unit-root, near-integrated, or even explosive. Theoretically, we establish the classification consistency, oracle properties, and unified asymptotic normal distributions for the proposed Lasso-type estimators. Empirically, we apply our data-driven method to uncover the existence of firm-level hidden bubbles in the U.S. stock market that have been unaccounted for in previous studies.
Please virtually attend this week's Statistics seminar at 4:00 PM (CDT, UT-5) Monday the 20th via this zoom link
Meeting ID: 976 2118 4707
Passcode: 617889
 | Wednesday
Mar. 22
|
| Algebra and Number Theory
No Seminar
|
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
In this talk, we will recall rigidity properties of (regular) hypersurfaces immersed in space forms of non-negative curvature by using the Simon inequality. Then we study the first eigenvalue of the Jacobi operator on an integral n-varifold with constant mean curvature in space forms. We derive an optimal upper bound and use it to give a new characterization for certain singular Clifford tori and catenoids.
The numerical solution of the radiation transport equation (RTE) is challenging due to the high computational costs and the large memory requirements caused by the high-dimensional phase space. Here we detail an attempt to reduce the memory required, and computational cost of solving RTE by applying the dynamical low-rank (DLR) method, where a memory savings of about an order of magnitude without sacrificing accuracy is observed. The DLR approximation is an efficient technique to approximate the solution to time-dependent matrix differential equations. The desired approximation has three components similar to factors in singular value decomposition (SVD), and each of them is solved by integrating the matrix differential equation projected onto the tangent space of the low-rank manifold. This talk presents our recent work that builds on the established DLR method and aims to enable low-rank schemes for practical radiation transport applications. We propose a high-order/low-order (HOLO) algorithm to overcome the conservation issues in the low-rank scheme by solving a low-order equation with closure terms computed via a high-order solution calculated using DLR. With the properly chosen rank, the high-order solution well approximates the closure term, and the low-order solution can be used to correct the conservation bias in the DLR evolution. This improvement goes a long way to making the method robust enough for a variety of physics applications. We also introduce a low-rank scheme with discrete ordinates discretization in angle (SN method). This low-rank-SN system allows for an efficient algorithm called ``transport sweep," which is highly desirable in computation. The derived low-rank SN equations can be cast into a triangular form in the same way as standard iteration techniques.
When: 4:00 pm (Lubbock's local time is GMT -5)
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: 940 7062 3025
* Passcode: applied
About the speaker. Dr. Ryan McClarren, Associate Professor of Aerospace and Mechanical Engineering at the University of Notre Dame, has applied simulation to understand, analyze, and optimize engineering systems throughout his academic career. He has authored numerous publications in refereed journals on machine learning, uncertainty quantification, and numerical methods, as well as three scientific texts: Machine Learning for Engineers, Uncertainty Quantification and Predictive Computational Science: A Foundation for Physical Scientists, and Engineers and Computational Nuclear Engineering and Radiological Science Using Python. He was recently named Editor-in-Chief of the Journal of Computational & Theoretical Transport. A well-known member of the computational nuclear engineering community, Dr. McClarren has won research awards from NSF, DOE, and three national labs. Prior to joining Notre Dame in 2017, he was Assistant Professor of Nuclear Engineering at Texas A&M University, and previously a research scientist at Los Alamos National Laboratory in the Computational Physics and Methods group.