Events
Department of Mathematics and Statistics
Texas Tech University
Weyl law describes the asymptotic behavior of eigenvalues. I will introduce the eigenvalue problem of the Schrodinger operators with singular potentials on compact manifolds. In recent works with Xiaoqi Huang (U. of Maryland), we proved the pointwise Weyl laws for the Schrodinger operators with singular potentials, and showed that they are sharp by constructing examples. This work extends the 3d results of Frank-Sabin (2020) to any dimensions.
This Job Candidate Colloquium is held in conjunction with the Analysis seminar group. Please virtually attend Monday the 13th at 4 PM CDT via this Zoom link.
Time series often experience structural changes due to external events or internal systematic changes. Over the last two decades changepoint analysis has received considerable attention. Most changepoint methods assume IID model errors; however, time series data are typically autocorrelated. As a known difficult problem in changepoint analysis, the challenge comes from the fact that changepoints can mask as natural fluctuations in a serially dependent process and vice versa. My research aims to develop a gradient descent based PELT approach to detect the mean shifts in an AR(p) series. The proposed algorithm is supported by both proofs and simulations.
Dr. Shi's Job Colloquium talk is sponsored by the Statistics seminar group. Please virtually attend via this Zoom link. Passcode: b0UPyX
In this talk, we present two different approaches on overcoming the curse of dimensionality for the model reduction and the numerical schemes for high dimensional PDEs. For the first part, we introduce the framework on constructing structure-preserving machine learning (ML) moment closure models for kinetic. Most of the existing ML closure models are not able to guarantee the stability, which directly causes blow up in the long-time simulations. In our work, with carefully designed neural network architectures, the ML closure model can guarantee stability (or hyperbolicity). Moreover, other mathematical properties, such as entropy stability, Galilean invariance, and physical characteristic speeds, are also discussed. Extensive benchmark tests show the good accuracy, long-time stability, and good generalizability of our ML closure model.
For the second part, we introduce our work on adaptive sparse grid discontinuous Galerkin (DG) schemes for nonlinear PDEs in multidimensions. Due to the difficulty in efficiently projecting a nonlinear function onto sparse grid DG space, previous work mainly focuses on linear problems. To generalize the sparse grid DG schemes from linear problems to nonlinear cases, we first apply a class of interpolatory multiwavelets to treat nonlinear terms, then use fast wavelet transform to convert point values to the coefficients of the hierarchical wavelets, and lastly perform fast matrix-vector multiplication compute integrals over elements and edges in DG schemes. The resulting algorithm achieves similar computational complexity as linear equations and is successfully applied to several important classes of nonlinear PDEs.
This Job Colloquium is held in tandom with the Applied Math seminar group. Please virtually attend Wednesday the 15th at 4 PM CDT via this Zoom link.
Dynamical systems are present latently or explicitly in most phenomena around us, such as in physical systems, signal processing, control, or even in the mechanisms of numerical methods. Some classical questions in this field are forecasting, reconstruction, and the identification of various forms of coherence or patterns. However, there are no methods that execute these tasks equally effectively across all systems, due to the varied nature and complexity of the dynamics. In this talk, we take a closer look at these tasks and show how they are related to core concepts of the underlying dynamics, such as the spectral measure, geometry and fractal dimensions of its attractor, as well as global properties such as (nonuniform) hyperbolicity. Furthermore, several fundamental questions or tasks in the disparate fields of Harmonic Analysis, Statistics, and Geometry can be formulated in terms of a latent dynamical process. For example, the outcome of Fourier averaging or spectral tapering of signals is determined by the spectral measure; the limiting behavior of the graph Laplacian on data is determined by the geometry of the underlying fractal attractor; and the distribution of windowed statistics from data can be stated in terms of a skew-product dynamical system. These connections reveal a rich intersection of dynamics, signal processing and geometry. I explore various aspects of such connections, introduce some recent results in these directions, and present some intriguing open questions.
Dr. Das' Job Colloquium talk is sponsored by the PDGMP seminar group. Please virtually attend via this Zoom link. Passcode: Das
Abstract: We propose and implement tests for the existence of a common stochastic discount factor (SDF). Our tests are agnostic because they do not require macroeconomic data or preference assumptions; they depend only on observed asset returns. After examining test features and power with simulations, we apply the tests empirically to data on U.S. equities, bonds, currencies, commodities and real estate. The empirical evidence is consistent with a unique positive SDF that prices all assets and satisfies the Hansen/Jagannathan bounds.
Brief Bio: Prof. Roll is known in particular for his work on portfolio theory and asset pricing. He has extensive business experience, having been a consultant for a range of corporations, law firms, and government agencies in addition to serving on boards and founding several businesses himself. At Boeing the early 1960s, he worked on the Minuteman missile and the Saturn moon rocket. He was a vice president at Goldman, Sachs & Co. in the 1980s, where he founded and directed the mortgage securities group.
Previously, Richard has been on the faculty at UCLA, where he held the Joel Fried Chair in Applied Finance in the Anderson School of Management and is now a professor emeritus; at Carnegie Mellon University; the European Institute for Advanced Study of Management in Brussels; and the French business school Hautes Etudes Commerciales (HEC) near Paris. Roll holds a Ph.D. in economics, finance, and statistics from the University of Chicago, as well as an M.B.A. from the University of Washington and a B.A.E. from Auburn University. He has received honorary doctorates from universities in both France and Germany.
In addition to his published books and journal articles, he is or has been an associate editor of 11 different journals in finance and economics. Among his honors, he has won the Graham and Dodd Award for financial writing four times and the Leo Melamed Prize for financial research. In 2009, he was named Financial Engineer of the Year by the International Association of Financial Engineers and in 2015 was one of two recipients of the Onassis Prize in Finance. He is a past president of the American Finance Association and a fellow of the Econometric Society. See the colloquium at this link.  | Tuesday
Sep. 14
3:30 PM
MATH 016
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| Real-Algebraic Geometry
Tangent Space
David Weinberg
Department of Mathematics and Statistics, Texas Tech University
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N/A
Bacterial swimming mediated by flagellar rotation is one of the most ubiquitous forms of cellular locomotion that plays a major role in many biological processes. Here, a typical swimming path of flagellated bacteria looks like a random walk with no purpose, but the random movement becomes modified as environmental conditions change. Modified random movement is particularly characterized by their motility pattern or a combination of their swimming modes. We present several distinct motility patterns exhibited by bacterial species and discuss a recently reported swimming mode – some bacterial species can swim backward by wrapping their flagella around the cell body. By introducing a mathematical model of a polarly flagellated bacterium through the fluid, we investigate what mechanism differentiates swimming modes and how a combination of the swimming modes affects their swimming pattern. Furthermore, we suggest benefits of their swimming pattern in complex native habitats. This is a joint work with S. Lim (Univ. of Cincinnati), Y. Kim (Chung-Ang Univ.), and W. Lee (National Institute for Mathematical Sciences, South Korea).
Please virtually attend this week's Biomath seminar via this Zoom link. Passcode: BfriM6
In this talk, I will begin by introducing geometric structures on bordisms. I will then motivate and introduce the fully extended bordism category. Finally, I will end with the statement of the geometric cobordism hypothesis.
Please virtually attend Dr. Shi's Departmental Colloquium talk.
See the colloquium at this link.