Date: | October 23, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Shilin Yu, TAMU |
Title: | Families of representations of Lie groups |
Abstract: | Beilinson and Bernstein generalized the Borel-Weil-Bott theorem and showed that representations of a (noncompact) reductive Lie group G can be realized as D-modules on flag variety. In this talk, I will show that such D-modules live naturally in families, which explains a mysterious analogy between representation theory of the group G and a related semidirect product group due to Mackey, Higson and Afgoustidis. Connection with Kirillov's coadjoint orbit method will be discussed. The talk is based partially on joint projects with Qijun Tan, Yijun Yao and Conan Leung. |
Date: | October 24, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 220 |
Speaker: | Rostyslav Kravchenko, Northwestern University |
Title: | TBA |
Abstract: | TBA |
Date: | October 24, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Siran Li, Rice University |
Title: | Nonlinear PDEs Seminar |
Abstract: | Title: Singular limits of Navier--Stokes and Euler equations with geometric effects. Abstract: The Navier--Stokes and Euler equations are the PDEs describing the conservation of mass and momentum of fluids. One of the important topics of mathematical hydrodynamics is the singular limit problems. In this talk we discuss three studies on singular limits, with linkages to differential geometry. 1. For the incompressible Euler equations on $\mathbb{R}^2$ or $\mathbb{T}^2$, we establish a direct analogue with the Gauss--Codazzi equations in differential geometry. Thus, an inherent direct application of the results on isometric embeddings can lead to the existence of ''wild'' Euler solutions with low regularity, which are continuous in time. This may provide further insight to the works by De Lellis, Szekelyhidi and coauthors. 2. For the incompressible Navier--Stokes equations with Navier boundary conditions on a regular surface embedded in $\mathbb{R}^3$, we prove that the strong solution in $H^{r+1}$ converges in $H^r$ to that of the Euler equations, when $r \geq 5/2$. 3. For a ''nozzle'' with $n$-dimensional base manifold $M$ and $d$-dimensional varying cross-sections $\epsilon F$, we show that, as $\epsilon \rightarrow 0$, the suitable weak solutions to the compressible Navier--Stokes equations on the nozzle converge to weak solutions of some limiting equations on $M$, which contain the $d$-dimensional measure of the cross-sections as a variable. This extends the work by Bella--Feireisl--Lewicka--Notovny. (Joint with Profs. Amit Acharya, Gui-Qiang Chen, Zhongmin Qian, Marshall Slemrod and Dehua Wang) |
Date: | October 24, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 628 |
Speaker: | Y. Wang |
Title: | Strassen's asymptotic rank |
Date: | October 25, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Giorgio Bornia, Texas Tech |
Title: | Some questions arising in PDE-constrained optimal control and numerical linear algebra |
Abstract: | The talk will be divided in two parts. In the first one, we address some issues arising in a certain class of boundary optimization problems. Common boundary optimal control problems yield a mismatch between the regularity of solutions on the domain and their boundary data. We discuss a reformulation of these problems with a lifting approach whose goal is to fix this regularity mismatch. Moreover, this approach provides additional benefits when applied to constraints characterized by compatibility conditions on the boundary data, such as those arising for the incompressible Navier-Stokes equations. In the second part of the talk, we discuss an analysis of preconditioning schemes for the numerical solution of Rayleigh-Bénard convection problems discretized with inf-sup stable finite element spaces. The analysis is carried out using a notion of field-of-values (FOV) equivalence between the preconditioner and the system matrix. Numerical results are discussed for both topics. |
Date: | October 25, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 220 |
Speaker: | Guoliang Yu, Texas A&M |
Title: | TBA |
Abstract: | TBA |
Date: | October 25, 2017 |
Time: | 5:30PM - 6:30PM |
Location: | BLOC 628 |
Speaker: | Student Panel |
Title: | Panel discussion: preparing for qualifying exams |
Date: | October 25, 2017 |
Time: | 6:00PM - 00:00AM |
Location: | BLOC 220 |
Speaker: | Dr. Darren Hartl, Texas A&M University, Department of Aerospace Engineering |
Title: | Advantageous couplings: the science and math behind multifunctional materials and structures |
Abstract: | The development of active and adaptive aerospace structures based on the behavior of unique materials has been considered with great fervor especially since the various federally funded efforts of the 1990's. What is new and highly enabling is the increased fidelity of three-dimensional mathematical models and especially the implementation of these models into ever more comprehensive design frameworks. Given the sustained improvement of such design tools, full analysis-driven optimization considering such concepts as coupled fields and uncertainty may soon become common practice in the multifunctional structure design community. This will enable both the increased performance of current concepts and an expansion in creativity regarding the kinds of material and structural configurations considered. This talk will review recent multifunctional material and structures modeling and design efforts with which Dr. Hartl has been involved over the last three years as well as his current research efforts at Texas A&M. Some of the advances in multifunctional aerospace structural modeling and design will be highlighted. Design concepts such as liquid metal-based reconfigurable antennas and morphing components will be described, and design approaches leveraging evolutionary genetic programming will be shared.” |
Date: | October 27, 2017 |
Time: | 10:30AM - 11:30AM |
Location: | BLOC 628 |
Speaker: | Michael Brannan, TAMU |
Title: | Finite input/output games, strategies, correlations, and related operator algebras. (Part 2) |
Abstract: | This is a continuation from the previous lecture: Over the next two lectures, I will present the basic notions around two player finite input/output games, strategies (deterministic, probabilistic, winning etc...), and the various correlation matrices that arise. We will then focus on the class of synchronous games and the relation between perfect strategies and the existence of certain tracial states on a universal associated to the game. We will follow section 9.4 thru Chapter 10 in the following notes: http://www.math.uwaterloo.ca/~vpaulsen/EntanglementAndNonlocality_LectureNotes_7.pdf |
Date: | October 27, 2017 |
Time: | 1:50PM - 2:50PM |
Location: | BLOC 628 |
Speaker: | Yulia Meshkova, Chebyshev Laboratory, St.Petersburg State University |
Title: | Homogenization of periodic hyperbolic systems with the corrector |
Date: | October 27, 2017 |
Time: | 3:00PM - 3:50PM |
Location: | BLOC 117 |
Speaker: | Laura Colmenarejo, York University |
Title: | TBA |
Date: | October 27, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 628 |
Speaker: | Xiaoxian Tang, TAMU |
Title: | TBA |
Date: | October 27, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 220 |
Speaker: | Michael Brannan, TAMU |
Title: | Amenable quantum groups are not always unitarizable |
Abstract: | A well-known theorem of Day and Dixmier from around 1950 states that if G is an amenable locally compact group, then any uniformly bounded representation of G on a Hilbert space is similar to a unitary representation. In short, amenable groups are ``unitarizable''. In this talk, I will focus on the question of whether a version of the Day-Dixmier unitarizability theorem holds in the more general framework of locally compact quantum groups. It turns out that the answer to this question is no: In joint work with Sang-Gyun Youn (Seoul National University), we show that many amenable quantum groups (including all Drinfeld-Jimbo-Woronowicz q-deformations of classical compact groups) admit non-unitarizable uniformly bounded representations. |
Date: | October 31, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Alex Mahalov, Arizona State University |
Title: | Nonlinear PDE's seminar |
Abstract: | Title:Stochastic Three-Dimensional Navier-Stokes Equations + Waves: Averaging, Convergence, Regularity and Nonlinear Dynamics |
Date: | November 1, 2017 |
Time: | 12:00PM - 1:00PM |
Location: | BLOC 628 |
Speaker: | Dr. Vitaly Katsnelson, Rice University, Applied Math DEpartment |
Title: | Reconstruction of a piecewise smooth wave speed from exterior measurements |
Abstract: | We will discuss how to reconstruct a piecewise smooth wave speed inside a domain D with boundary using only measurements taken outside of D; such measurements are akin to having a hyperbolic Neumann-to-Dirichlet map as one's given data. The main obstacle is the internal multiple scattering occurring within D due to the interfaces. We will show how to control and eliminate these internal multiples to eventually reconstruct the location of the interfaces and the wave speed itself. Our methods work for the local inverse problem as well. Numerical simulations will also be presented. |
Date: | November 1, 2017 |
Time: | 1:45PM - 2:45PM |
Location: | BLOC 220 |
Speaker: | John Doyle, Louisiana Tech University |
Title: | Dynamical modular curves and strong uniform boundedness |
Abstract: | In an unpublished 1996 preprint, Nguyen and Saito proved the strong uniform boundedness conjecture for torsion points on elliptic curves over function fields by reducing the problem to that of showing that the gonalities of the modular curves Y_1(n) tend to infinity. By studying the geometry of dynamical modular curves, we have recently proven uniform boundedness of preperiodic points for certain interesting families of polynomial maps over function fields. I will discuss this result as well as a consequence for the dynamical uniform boundedness conjecture over number fields, originally posed by Morton and Silverman. This is joint work with Bjorn Poonen. |
Date: | November 1, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Natalia Kopteva, University of Limerick, Ireland |
Title: | TBA |
Date: | November 1, 2017 |
Time: | 6:00PM - 00:00AM |
Location: | BLOC 220 |
Speaker: | Dr. Maurice Rojas, Department of Mathematics, Texas A&M University |
Title: | TBA |
Date: | November 3, 2017 |
Time: | 10:00AM - 4:00PM |
Location: | BLOC 220 |
Title: | UT Austin - TAMU probability day |
Abstract: | https://sites.google.com/site/austintamuprob/ Please register by October 25th. |
Date: | November 3, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 628 |
Speaker: | John Calabrese, Rice University |
Title: | TBA |
Date: | November 4, 2017 |
Time: | 09:00AM - 6:00PM |
Location: | U. Houston |
Speaker: | Brazos Analysis Seminar |
Title: | Brazos Analysis Seminar |
Abstract: | https://sites.google.com/site/brazosanalysisseminar/ |
Date: | November 5, 2017 |
Time: | 09:00AM - 1:00PM |
Location: | U. Houston |
Speaker: | Brazos Analysis Seminar |
Title: | Brazos Analysis Seminar |
Abstract: | https://sites.google.com/site/brazosanalysisseminar/ |
Date: | November 6, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Bo Lin, UT Austin |
Title: | TBA |
Date: | November 7, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Suncica Canic, University of Houston |
Title: | Nonlinear PDEs Seminar |
Abstract: | Title: A mathematical framework for proving existence of weak solutions to a class of fluid-structure interaction problems |
Date: | November 7, 2017 |
Time: | 5:00PM - 6:00PM |
Location: | BLOC 628 |
Speaker: | E. Ventura, TAMU |
Title: | ... after Christiandl et. al. |
Date: | November 8, 2017 |
Time: | 2:00PM - 3:00PM |
Location: | BLOC 628 |
Speaker: | Rufus Willett, University of Hawai'i |
Title: | TBA |
Date: | November 8, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Diane Guignard, TAMU |
Title: | A posteriori error estimation for PDEs with random input data |
Abstract: | In this talk, we perform a posteriori error analysis for partial differential equations with uncertain input data characterized using random variables. Considering first small uncertainties, we use a perturbation approach expanding the solution of the problem with respect to a parameter ε that controls the amount of uncertainty. We derive residual-based a posteriori error estimates that control the two sources of error: the finite element discretization and the truncation in the expansion. The methodology is presented first on an elliptic equation with random coefficients and then on the steady-state Navier-Stokes equations on random domains. In the case of large uncertainties, we use instead the stochastic collocation method for the random space approximation. We present a residual-based a posteriori error estimate that provides an upper bound for the total error, which is composed of the finite element and the stochastic collocation errors. The stochastic error estimator is then used to drive an adaptive sparse grid algorithm. Several numerical examples are presented to illustrate the theoretical findings. |
Date: | November 8, 2017 |
Time: | 6:00PM - 00:00AM |
Location: | BLOC 220 |
Speaker: | Dr. Kamran Entesari, Texas A&M University, Department of Electrical and Computer |
Title: | TBA |
Date: | November 10, 2017 |
Time: | 1:50PM - 2:50PM |
Location: | BLOC 628 |
Speaker: | Joint with Nonlinear PDE Seminar |
Date: | November 10, 2017 |
Time: | 3:00PM - 3:50PM |
Location: | BLOC 117 |
Speaker: | Henry Tucker, UC San Diego |
Title: | TBA |
Date: | November 10, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 220 |
Speaker: | Florin Boca, University of Illinois at Urbana-Champaign |
Title: | TBA |
Abstract: | TBA |
Date: | November 10, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 628 |
Speaker: | Alicia Harper, Brown University |
Title: | Factorization of maps of Deligne-Mumford stacks |
Date: | November 13, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Abraham Martín del Campo, CIMAT |
Title: | TBA |
Date: | November 14, 2017 |
Time: | 5:00PM - 6:00PM |
Location: | BLOC 628 |
Speaker: | P. Sarin, TAMU |
Title: | Tensor surgery and tensor rank after Christiandl and Zuiddam |
Date: | November 15, 2017 |
Time: | 1:45PM - 2:45PM |
Location: | BLOC 220 |
Speaker: | Riad Masri, Texas A&M University |
Title: | TBA |
Date: | November 15, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Paul Hand, Rice University |
Date: | November 15, 2017 |
Time: | 6:00PM - 00:00AM |
Location: | BLOC 220 |
Speaker: | Rana Soltani, PhD Student, Texas A&M University, Department of Mechanical Engineering |
Title: | TBA |
Date: | November 15, 2017 |
Time: | 7:00PM - 7:15PM |
Location: | BLOC 220 |
Speaker: | Angelique Morvant, Undergraduate Student, Texas A&M University, Department of Mathematics |
Title: | TBA |
Date: | November 17, 2017 |
Time: | 1:50PM - 2:50PM |
Location: | BLOC 628 |
Speaker: | Fritz Gesztesy, Baylor University |
Title: | On factorizations of differential operators and Hardy-Rellich-type inequalities |
Abstract: | We will illustrate how factorizations of singular, even-order partial differential operators yield an elementary approach to classical inequalities of Hardy-Rellich-type. More precisely, using this factorization method, we will derive a general (and, apparently, new) inequality and demonstrate how particular choices of the parameters contained in this inequality yield well-known inequalities, such as the classical Hardy and Rellich inequalities as special cases. Actually, other special cases yield additional and apparently less well-known inequalities. We will indicate that our method, in addition to being elementary, is quite flexible when it comes to a variety of generalized situations involving the inclusion of remainder terms and higher-order operators. This is based on various joint work with Lance Littlejohn, I. Michael, M. Pang, and R. Wellman. |
Date: | November 17, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 117 |
Speaker: | X. Shawn Cui, Stanford University |
Title: | TBA |
Abstract: | TBA |
Date: | November 17, 2017 |
Time: | 3:00PM - 3:50PM |
Location: | BLOC 628 |
Speaker: | Maxim Zinchenko, University of New Mexico |
Title: | TBA |
Date: | November 17, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 628 |
Speaker: | Taylor Brysiewicz, TAMU |
Title: | TBA |
Date: | November 17, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 220 |
Speaker: | Anna Skripka, University of New Mexico |
Title: | TBA |
Abstract: | TBA |
Date: | November 20, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Zheng Zhang, TAMU |
Title: | TBA |