Colloquium
Novel Data-driven Techniques in Reduced-Order Modeling of Fluid Flows
When
February 3, 2023 | 3:30 p.m. - 4:30 p.m.
Refreshments at 3:00 in Lobby
Where
University Hall 1005
Speaker
Dr. Muhammad Mohebujjaman
Abstract
In this talk, we present a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows. The novel DDF-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the nonlinear PDE and construct a filtered ROM. This filtered ROM is low-dimensional but is not closed. (ii) In the second step, we use data-driven modeling to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved modes. At the end, we enforce physical constraints in the data-driven modeling of the ROM closure term. The constrained data-driven ROM is significantly more accurate than its unconstrained counterpart. Finally, we present a novel high-order ROM differential filter and use it in conjunction with an evolve-filter-relax algorithm to attenuate the numerical oscillations of standard ROMs. We also examine how stochastic collocation methods can be combined with the EFR algorithm for efficient UQ of fluid flows.
Uniqueness and L2 stability of compressible Euler equations
When
December 2, 2022 | 2:30 p.m. - 3:30 p.m.
Refreshments to follow
Where
University Hall 4002
Speaker
Geng Chen
Abstract
Compressible Euler equations are a typical system of hyperbolic conservation laws, whose solution forms shock waves in general. It is well known that global BV solutions of system of hyperbolic conservation laws exist, when one considers small BV initial data. In this talk, we will present our recent proof on uniqueness of BV solution. This is a joint work with Sam Krupa and Alexis Vasseur.
How much further is it? A stroll through metric and length space
When
November 16, 2022 | 2:30 p.m. - 3:30 p.m.
Refreshments to follow
Where
University Hall 4002
Speaker
Peter Stollmann
Abstract
We review a simple dual characterization of length spaces, metric spaces in which points can be joined by a fairly short path.
On a conjecture by Erdoes, Pollack and Tuza
When
October 21, 2022 | 2:30 p.m. - 3:30 p.m.
Refreshments to follow
Where
University Hall 4002
Speaker
Eva Czabarka
Abstract
The Krein Extension: Basics and some concrete applications
When
October 12, 2022 | Reception: 3:30 p.m. | Lecture: 4:00 p.m.
Where
University Hall 1005
Speaker
Dr. Fritz Gesztesy, Baylor University
Description
2022 Roger T. Lewis Endowed Lectureship in Mathematics. Presented by the UAB Department of Mathematics.
Midrange crossing constants of certain graph classes
When
October 7, 2022 | 2:30 p.m. - 3:30 p.m.
Where
University Hall 4002
Speaker
Laszlo A. Szekely
Abstract
Southern Company Data Analytics & Optimization Coop/Intern Opportunities
When
September 16, 2022 | 2:30 PM. - 3:30 p.m.
Where
University Hall 4002
Speaker
Veronica Powell & Jeff Baker
Abstract
Southern Power, a subsidiary of Southern Company, is a leading U.S. wholesale energy provider meeting the electricity needs of municipalities, electric cooperatives, investor-owned utilities, and commercial and industrial customers. Southern Power and its subsidiaries own 54 solar, wind, natural gas generating facilities in 14 states with more than 12,500 megawatts of generating capacity. Veronica Powell, MS Applied Mathematics from UAB, and Jeff Baker, PhD in Applied Mathematics from UAB and will discuss coop/intern opportunities at Southern Company and data analytics and asset optimization in Commercial Optimization and Trading at Southern Power.
Evolution Flow and Ground States for Schrodinger Type Equation and Sytems
When
April 27, 2022 | 11:00 a.m. - 12:00 p.m.
Where
University Hall 4004
Speaker
Vladimir Georgiev
Abstract
The talk starts with an introduction to some basic models of Schrodinger type equations and their fractional generalizations. As an example the half - wave equation with nonlinear terms is considered.
We focus our study on the case of nonlinear half - wave equation. The results we present can be divided in the following main topics:
- existence, asymptotic properties of ground states and their linear stability/instability;
- existence or explosion phenomena of the evolution flow with large data below/above the ground state barrier for the corresponding Cauchy problem for the half – wave equation;
- blow - up for mass-critical half - wave equation.
Deep Learning of Conjugate Mappings
When
April 15, 2022 | 3:00 - 4:00 p.m.
Where
University Hall 1005
Speaker
Jason Bramburger
Abstract
Despite many of the most common chaotic dynamical systems being continuous in time, it is through discrete time mappings that much of the understanding of chaos is formed. Henri Poincaré first made this connection by tracking consecutive iterations of the continuous flow with a lower-dimensional, transverse subspace. The mapping that iterates the dynamics through consecutive intersections of the flow with the subspace is now referred to as a Poincaré map, and it is the primary method available for interpreting and classifying chaotic dynamics. Unfortunately, in all but the simplest systems, an explicit form for such a mapping remains outstanding.
In this talk I present a method of discovering explicit Poincaré mappings using deep learning to construct an invertible coordinate transformation into a conjugate representation where the dynamics are governed by a relatively simple chaotic mapping. The invertible change of variable is based on an autoencoder, which allows for dimensionality reduction, and has the advantage of classifying chaotic systems using the equivalence relation of topological conjugacies. We illustrate with low-dimensional systems such as the Rössler and Lorenz systems, while also demonstrating the utility of the method on the infinite-dimensional Kuramoto-Sivashinsky equation.
UAB Mathematics Open House and Alumni Forum
Featuring a presentation from:
Dr. Stephen Odaibo
March 25, 2022
University Hall, 2005
1402 10th Avenue South
Birmingham AL 35294-1241
Morning Session
9:15 - 9:30 a.m.: Welcome
9:30 - 11:10 a.m.: Faculty Presentations: research opportunities – Room 4004
11:15 a.m. - 12:30 p.m.: Lunch meeting with current graduate and fast track students – Room 4002
12:30 - 1:30 p.m.: Campus Tour
Alumni Forum
1:30 - 2:30 p.m.: Poster session and table second floor lobby
2:30 - 3:30 p.m.: Talk by Dr. Stephen Odaibo – Room 2005
3:30 - 4 p.m.: Reception"
Some recent results on regularity theory for linear parabolic equations with singular-degenerate coefficients
When
March 4th, 2022 | 2:30 – 3:30 p.m.
Where
University Hall 1005
Speaker
Dr. Tuoc Phan
Abstract
We discuss classes of linear parabolic equations in the upper-half space whose coefficients can be singular or degenerate as a power of the vertical variable. Two typical examples are the class of Caffarelli-Silvestre type extensional equations arising in the study of fractional Laplace equations or fractional heat equations, and a class of degenerate viscous Hamilton-Jacobi equations. The boundary conditions are either homogeneous Dirichlet or conormal one. Depending on the boundary conditions, generic weighted Sobolev spaces are found in which existence, uniqueness, and regularity estimates of solutions are proved. The main features in our results are that the coefficients may not be in the A_2 class of Muckenhoupt weights as previously studied in the available literature. The talk is based on several recent papers that are the joint work with Hongjie Dong (Brown University) and with Hung Vinh Tran (University of Wisconsin Madison).
Limiting absorption principle and virtual levels of operators in Banach spaces
When
November 12, 2021 | 3:30 - 4:30 p.m.
Where
University Hall 1005
Speaker
Andrew Comech
Abstract
Virtual levels, also known as threshold resonances, admit several equivalent characterizations:
- there are corresponding "virtual states" from a space "slightly weaker" than L^2;
- there is no limiting absorption principle in their vicinity (e.g. no weights such that the "sandwiched" resolvent is uniformly bounded);
- an arbitrarily small perturbation can produce an eigenvalue.
We develop a general approach to virtual levels in Banach spaces and provide applications to Schroedinger operators with nonselfadjoint potentials and in any dimension, deriving optimal estimates on the resolvent.
Renormalization in Conformal Dynamics
When
October 15, 2021 | 3:30 - 4:30 p.m.
Where
University Hall 1005
Speaker
Dr. Nikita Selinger
Abstract
Renormalization is a technique that allows us to study a dynamical system on small scales by restricting an iterate of the original system to a small part of the original domain. Successful renormalization theories produce rigidity statements: the geometry of an infinitely renormalizable system is completely determined by its combinatorial properties. Studying dynamics of the renormalization operator itself yields understanding of the structure not only of individual dynamical systems but of the parameter space of the class of dynamical systems considered.
I will discuss various renormalization schemes in real and complex discrete dynamical systems and their applications.
Siegel capture polynomials in parameter spaces
When
April 19, 2019 | 2:30 - 3:30 p.m.
Where
Campbell Hall 443
Speaker
Dr. Lex Oversteegen (joint with Alexander Blokh, Arnaud Cheritat, Toulouse, Lex Oversteegen, and Vladlen Timorin, Moscow)
Abstract
We consider the set of cubic polynomials $f$ with a marked fixed point. If $f$ has a Siegel disk at the marked fixed point, and if this disk contains an eventual image of a critical point, we call $f$ a \emph{IS-capture polynomial}. We study the location of IS-capture polynomials in the parameter space of all marked cubic polynomials modulo affine conjugacy. In particular, it is shown that any IS-capture is on the boundary of a unique bounded hyperbolic component determined by the rational lamination of the map. We also relate IS-captures to the cubic Principal Hyperbolic Domain and its closure (by definition, the \emph{cubic Principal Hyperbolic Domain} consists of cubic hyperbolic polynomials with Jordan curve Julia sets).
Slices of parameter space of cubic polynomials
When
April 12, 2019 | 2:30 - 3:30 p.m.
Where
Campbell Hall 443
Speaker
Dr. Alexander Blokh (joint with Lex Oversteegen and Vladlen Timorin, Moscow)
Abstract
In this paper, we study slices of the parameter space of cubic polynomials, up to affine conjugacy, given by a fixed value of the multiplier at a non-repelling fixed point. In particular, we study the location of the \emph{main cubioid} in this parameter space. The \emph{main cubioid} is the set of affine conjugacy classes of complex cubic polynomials that have certain dynamical properties generalizing those of polynomials $z^2+c$ for $c$ in the filled main cardioid.
A class of Schrodinger operators with convergent perturbation series
When
April 5, 2019 | 2:30 - 3:30 p.m.
Where
Campbell Hall 443
Speaker
Dr. Ilya Kachkovskiy, Michigan State University
Abstract
Rayleigh-Schrodinger perturbation series is one of the main tools of analyzing eigenvalues and eigenvectors of operators in quantum mechanics. The first part of the talk is expository and should be accessible to students with working knowledge of linear algebra: I will explain a way of representing all terms of the series in terms of graphs with certain structure (similar representations appear in physical literature in various forms). The second part of talk is based on joint work in progress with L. Parnovski and R. Shterenberg. We show that, for a class of lattice Schrodinger operators with unbounded quasiperiodic potentials, one can establish convergence of these series (which is surprising because the eigenvalues are not isolated). The proof is based on the careful analysis of the graphical structure of terms in order to identify cancellations between terms that contain small denominators. The result implies Anderson localization for a class of Maryland-type models on higher-dimensional lattices.
The story of the little ell one norm and its friends
When
March 29, 2019 | 2:30 - 3:30 p.m.
Where
Campbell Hall 443
Speaker
Dr. Carmeliza Navasca
Abstract
The popularity of sparse ell one norm optimization problem was due to Emmanuel Candes and Terrence Tao via compressed sensing. I will start by introducing the little ell one norm and its minimization. Then, I will describe how and why these sparse optimization problems are useful in solving today’s challenging problems in data science and machine learning. Numerical examples in foreground and background separation in surveillance videos, matrix and tensor completion as well as deep neural network for image classification are included. In this talk, one can observe the interplay of (multi)linear algebra, optimization and numerical analysis with applications in computer science.
This is joint work with Xiaofei Wang (former postdoc at UAB, now Prof at Normal University, China), Ramin Karim Goudarzi, Fatou Sanogo, Ali Fry (former Fast-Track) and Da Yan (CS Prof at UAB).
Probability bounds in classical and quantum statistical mechanics
When
March 22, 2019 | 2:30 - 3:30 p.m.
Where
Campbell Hall 443
Speaker
Dr. Shannon Star, UAB
Abstract
In the first half we will show that spectral gap bounds lead to concentration of measure bounds. Methods for the former were initiated by Lu and Yau, and further developed for quantum spin systems. This is joint with Michael Froehlich (UAB) a medical researcher pursuing a biostats PhD. In the second half of the talk, we will describe how probability bounds for the classical dimer model and six vertex model in 2d give bounds for quantum systems in 1d: general XY models, the XXZ model and the Hubbard model. This is joint work with Scott Williams (UAB) a former math major. The talk is accessible to students, and is particularly relevant to those interested in Markov chains.
Existence results for some classes of integrodifferential equations of Gurtin-Pipkin type
When
March 1, 2019 | 2:30 - 3:30 p.m.
Where
Campbell Hall 443
Speaker
Prof. Toka Diagana, The University of Alabama in Huntsville
Abstract
Integro-differential equations of Gurtin-Pipkin type play an important in studying various practical problems. In particular, they have been used to study the heat conduction in materials with memory, the sound propagation in viscoelastic media, or in homogenization problems in perforated media (Darcy’s Law).
To read the full abstract, view the PDF version.
Multiplicity One Conjecture in Min-max theory
When
February 18, 2019 | 2:30 - 3.30 p.m.
Where
Campbell Hall 443
Speaker
Dr. Xin Zhou, Institute for Advance Study (Princeton)/UC Santa Barbara
Abstract
I will present a recent proof of the Multiplicity One Conjecture in Min-max theory. This conjecture was raised by Marques and Neves as the key step to establish a Morse theory for the area functional. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves are all two-sided and have multiplicity one. As direct corollaries, it implies the generalized Yau's conjecture for such manifolds with positive Ricci curvature, which says that there exist a sequence of minimal hypersurfaces with area tending to infinity, and the Weighted Morse Index Bound Conjecture by Marques and Neves. The talk will be for general audience.