Events
Department of Mathematics and Statistics
Texas Tech University
We'll discuss a construction that produces non-unique entropy solutions of the isentropic compressible euler equations. The construction will be a Nash iterative convex integration scheme and will produce continuous velocity fields with smooth density. As a consequence, we'll demonstrate solutions that produce entropy without the formation of a shock. This is joint work with Hyunju Kwon.
No abstract.
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In this talk, I will first talk about the filtering algorithm for the case of degenerate observation noise using stochastic approximation approach. And an example will be presented to demonstrate the algorithm. Then I will mainly introduce a new class of deep neural network-based numerical algorithms for nonlinear filtering named deep filter. It presents a computationally feasible procedure for regime-switching diffusions. In lieu of the traditional conditional-distribution-based filtering that suffers from curse of dimensionality, we convert it to a problem in a finite-dimensional setting to approximate the optimal weights of a neural network. Then we construct a stochastic gradient-type procedure to approximate these weight parameters, and develop another recursion for adaptively approximating the optimal learning rate. We show the convergence of the continuous time interpolated learning rate process using stochastic averaging and martingale methods. An error bound will be obtained for parameters of the neural network. Several examples will be presented to show the robustness of the algorithm. This is based on joint work with Prof. George Yin and Prof. Qing Zhang.
Please virtually attend this week's Statistics seminar at 4:00 PM (CST, UT-6) Monday the 6th via this zoom link
Meeting ID: 930 6316 7145
Passcode: 432384
The third string bordism group is known to be $\mathbb{Z}/24\mathbb{Z}$. Using Waldorf's notion of a geometric string structure on a manifold, Bunke--Naumann and Redden have exhibited integral formulas involving the Chern-Weil form representative of the first Pontryagin class and the canonical 3-form of a geometric string structure that realize the isomorphism $Bord_3^{String} \to \mathbb{Z}/24\mathbb{Z}$ (these formulas have been recently rediscovered by Gaiotto--Johnson-Freyd--Witten). In the talk I will show how these formulas naturally emerge when one considers the U(1)-valued 3d TQFTs associated with the classifying stacks of Spin bundles with connection and of String bundles with geometric structure. Joint work with Eugenio Landi (arXiv:2209.12933).
 | Wednesday
Mar. 8
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| Algebra and Number Theory
No Seminar
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Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
This week's PDGMP seminar may be attended at 3:00 PM CDT (UT-5) via this Zoom link.
Meeting ID: 933 4646 9342
Abstract. In this talk, I shall first discuss a newly developed theory of weak fractional (differential) calculus and fractional Sobolev spaces. The focus is the introduction of a weak fractional derivative concept which is a natural generalization of integer order weak derivatives and helps to unify multiple existing fractional derivative concepts. Based on the weak fractional derivative concept, new fractional-order Sobolev spaces can be naturally defined and many essential properties of those Sobolev spaces can also be established. I shall then introduce a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations, the new framework and theory are based on the aforementioned theory of weak fractional derivatives and their associated fractional order Sobolev spaces. It leads to new fractional differential equations, including one-side fractional Laplace operators and future value problems. Finally, if time permits, I shall also briefly introduce some new finite element (and DG) methods for approximating the weak fractional derivatives and the solutions of fractional calculus of variations problems and their associated fractional differential equations.
About the speaker. Dr. Xiaobing Feng is a professor and the department head of the Department of Mathematics at the University of Tennessee. He obtained his Ph.D. degree from Purdue University in Computational and Applied Mathematics in 1992 under the direction of the late Professor Jim Douglas, Jr. His primary research interest is numerical solutions of deterministic and stochastic nonlinear PDEs which arise from various applications including fluid and solid mechanics, subsurface flow and poroelasticity, phase transition, forward and inverse scattering, image processing, optimal control, systems biology, and data assimilation.
When: 4:00 pm (Lubbock's local time is GMT -6)
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 Applied Mathematics Seminar:
- To be notified about TTU's Applied Mathematics Seminar on a weekly basis please send e-mail to igtomas@ttu.edu
- To check some our past and future speakers check this link
 | Wednesday
Mar. 8
7 PM
MA 108
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| Mathematics Education
Math Circle
Alvaro Pampano
Department of Mathematics and Statistics, Texas Tech University
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Math Circle Fall Poster