COLLOQUIA         2014 -- 2015

Colloquia are held on Fridays in Parker Hall, Room 250, from 4:00-4:50 (unless otherwise advised).
Refreshments are served in Parker Hall, Room 244, beginning at 3:30.

February 6, 2015

Speaker:  R. N. Mohapatra  (University of Central Florida, Orlando, FL)

Title:  Optimal Frames for Erasers with Spectral Measure

Abstract:  In this talk we will talk about Riesz bases, Frames and Erasers. I shall present some  results on optimal frames for Erasers with spectral radius as the measure. Some open problems will be mentioned. If time permits, then I shall make some remarks on Frames in Fock spaces and Triebel Lizorkin spaces and in Hilbert C* modules.


January 23, 2015

Speaker: Jessica McDonald

Title: Colouring and Structure in Graphs

Abstract: I will give a general overview of my research program as part of my third-year review (mid-P&T evaluation). As such I will be talking about colouring and structure in graphs -- in particular, edge and list-edge-colouring,  packing and covering, and the immersion containment relation.

January 26, 2015 (MONDAY) Parker Hall 249

Speaker: Dr. Li Wang, Department of Mathematics, UCLA

Title: Asymptotic-Preserving schemes for multi-scale semiconductor Boltzmann equation 

Abstract: Kinetic equations often contain multiple scales that lead to various asymptotic regimes, in which classical numerical methods become prohibitively expensive. Asymptotic-Preserving (AP) scheme is one efficient way to treat such multiscale problems. It is a unified kinetic solver that automatically solves the macroscopic equations in the small scale regime by preserving the asymptotic limit at the discrete level. In this talk, I will present AP schemes for the semiconductor Boltzmann equation in a diffusive scaling with two-scale collisions that leads to an energy-transport system for electron mass and internal energy as mean free path goes to zero. Our scheme is based on a BGK (Bhatnagar-Gross-Krook) penalization together with a spatially dependent threshold on the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level. An alternative approach via a splitting strategy will also be presented which can systematically treat the collisions at different scales separately. Formal asymptotic analysis and numerical results confirm the efficiency and accuracy of the schemes. In the end, I will illustrate the promise of these ideas in treating the hierarchy of macroscopic models in semiconductors and other applications.

Faculty host: Yanzhao Cao

January 28, 2015 (WEDNESDAY) Parker Hall 249

Speaker: Dr. David Seal, Department of Mathematics, Michigan State University

Title: Flux modifications for hyperbolic conservation laws: Beyond the method of lines formulation

Abstract: Hyperbolic conservation laws describe a large class of problems including applications in astrophysics, aerospace engineering, storm surge modeling and electromagnetics. Difficulties in developing numerical methods for these problems include the ability of the scheme to capture shocks, the necessity to satisfy a discrete conservation of physical quantities such as mass, momentum and energy, and for plasmas, the ability to retain divergent free magnetic fields. High-order methods for hyperbolic conservation laws have seen an increasing amount of attention for over the past several decades given their ability to obtain high-order accuracy with far fewer unknowns. 

High-order methods require high-order time stepping that have traditionally been classified into two disparate categories: i) the method of lines formulation which starts by discretizing the spatial variables, and then evolves a system of ODEs with an appropriate time-integrator, or ii) Lax-Wendroff discretizations that immediately convert temporal Taylor series into discrete spatial derivatives. In this talk, we resolve this false dichotomy by introducing multiderivative methods as a unifying class. Our methods are constructed through a flux modification, and therefore are automatically mass conservative and have the capacity to reduce computational complexity, including i) a reduction in the number of characteristic variable projections, ii) the number of applications of expensive limiters, and iii) a reduction in the effective stencil size. We present multidimensional results that include positivity preservation for Euler and MHD equations, as well as highlight our flux modifications by demonstrating a new limiter.

Faculty host: Yanzhao Cao

January 30, 2015 Parker Hall 249

Speaker: Dr. Hans-Werner van Wyk, Department of Scientific Computing, Florida State University

Title: Modeling, Simulation, and Design of Distributed Parameter Systems under Uncertainty

Abstract: While physical systems involving sound, heat, electrostatics, electrodynamics, fluid flow, or elasticity are generally modeled and understood in the deterministic language of partial differential equations, they often operate within complex environments that cannot be described, or even observed directly, in full deterministic detail. As simulation plays an increasingly central role in modern science and engineering research, by supplementing experiments, aiding in the prototyping of engineering systems or informing decisions on safety and reliability, the need to quantify uncertainty in model outputs due to uncertainties in the model parameters becomes critical. In this talk, we discuss some of the mathematical and computational challenges of uncertainty quantification for distributed parameter systems, and present our contributions to this field. These include: 1) the statistical identification of spatially varying model parameters from measurements of related observable quantities, 2) the numerical simulation of scale-invariant noisefields over arbitrary spatial regions and on general grids, 3) the development of multilevel sampling methods to improve the efficiency of stochastic simulations through the dynamic incorporation of the model's numerical discretization, and 4) an examination of the interplay between parameter uncertainty and model sensitivity.

Faculty host: Yanzhao Cao

February 6, 2015

Speaker: Professor Ram Mohapatra, University of Central Florida

Title: TBA

Faculty host: Pete Johnson and Narendra Govil

February 13, 2015

Speaker: Guanqun Cao

Title: TBA 

February 27, 2015 SPECIAL TIME: 2:30 - 3:30

Speaker: Prof. Shari Moskow, Drexel University

Faculty host: Junshan Lin

Refreshments will be served between the two presentations, at the regular time, 3:30

February 27, 2015

Speaker: Roger Howe, Yale University

Title: TBA

Faculty host: Huajun Huang

March 13, 2015

Speaker: Asuman Turkmen, The Ohio State University

Title: TBA

Faculty host: Nedret Billor

April 3, 2015

Speaker: Norou Diawara, Old Dominion University

Title: TBA

Faculty host: Nedret Billor

April 10, 2015

Speaker: Chi-Kwong Li, Ferguson Professor of Mathematics, 
              College of William and Mary 
Editor-in-chief of Linear and Multilinear Algebra, and Operators and Matrices.

Title: TBA

Faculty host: T.-Y. Tam 

April 24, 2015

Speaker: Dr. David Todem, Michigan State University

Title: TBA

Faculty host: Guanqun Cao

Past Colloquia

January 16, 2015 PLEASE NOTE CHANGE IN TIME: 3:00 for presentation; 4:00 for refreshments

Speaker:  Ferenc Fodor (University of Szeged, Hungary)

Title: Approximation and extremal properties of round convex bodies

Abstract: We will consider convex bodies that slide freely in a ball. Such bodies can be approximated not only by polytopes but also by intersections of certain congruent balls. We will review recent results about best and random approximations of such bodies. We will also consider analogues of some classical inequalities for convex bodies that slide freely in a ball.

Faculty host:  Andras Bezdek

November 14, 2014

Speaker: Dr. Huaihou Chen, University of Florida

Title: Optimally weighted L² distance for functional data

For abstract, click here

Faculty host: Guanqun Cao

November 7, 2014

Speaker: Dr. Kumer Pial Das ('05), Associate Professor of Mathematics, Lamar University (Beaumont, Texas)

Dr. Das is one of three people from the U.S. and Canada to receive the 2013 Mathematical Association of America's (MAA) Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member.

Title: The modeling of extreme events

Faculty host: Ming Liao

MONDAY, NOVEMBER 3, 2014 in honor of Andrew Lelek, who is turning 80

This colloquium will be held in Parker Hall 236

Speaker 1:  Prof. Lex Oversteegen, University of Alabama at Birmingham, 3:00 - 4:00 pm Title: A complete classification of homogeneous plane continua

For abstract, click here

Speaker 2:  Prof. Thelma West,  University of Louisiana at Lafayette, 4:00 - 5:00 pm Title: An introduction to span

For abstract, click here

Refreshments will be served at 2:30 in Parker Hall 244

Faculty host: Krystyna Kuperberg

October 31, 2014

Speaker: Prof. Jie Shen, Purdue University

Title: Phase-field models for multiphase complex fluids: Modeling, numerical analysis and simulations

Abstract: I shall present some recent work on phase-field model for multiphase incompressible flows. We shall pay particular attention to situations with large density ratios as they lead to formidable challenges in both analysis and simulation.

I shall present efficient and accurate numerical schemes for solving this coupled nonlinear system, in many case prove that they are energy stable, and show ample numerical results which not only demonstrate the effectiveness of the numerical schemes, but also validate the flexibility and robustness of the phase-field model.

Faculty host: Junshan Lin

October 3, 2014

Speaker: Max Pitz, Mathematical Institute, University of Oxford

Title: Reconstruction problems in graph theory and topology

Abstract: In graph theory, the Reconstruction Conjecture is an influential open problem, remaining unsolved now for well over 70 years. It conjectures that every finite graph with at least 3 vertices can be identified ("reconstructed") from the collection of those unlabelled subgraphs that can be obtained by deleting single vertices.

In this colloquium talk I will briefly explain general background and results for the graph theoretic reconstruction problem, and then continue with the corresponding topological reconstruction problem: When can topological spaces be identified from its point-complement subspaces? I will explain some of my recent results, and I will also provide some surprising examples demonstrating that reconstructability is an exciting new topological concept.

Faculty host: Ziqin Feng


October 10, 2014

Speaker: Frank Uhlig

Topic: Francis Algorithm, the mathematics, uses, and history

Abstract: Click here


September 26, 2014

Speaker: Tomas Caraballo, University of Seville, Spain

Title: Random and Non-autonomous Dynamics of Chemostats

Abstract: Click here

Faculty host: Georg Hetzer

September 19, 2014

Speaker: Dr. Habib Najm, Sandia National Laboratories, Livermore, California

Title: Uncertainty Quantification in Computational Models

Abstract: Models of physical systems typically involve inputs/parameters that are determined from empirical measurements, and therefore exhibit a certain degree of uncertainty. Estimating the propagation of this uncertainty into computational model output predictions is crucial for purposes of model validation, design optimization, and decision support.

Recent years have seen significant developments in probabilistic methods for efficient uncertainty quantification (UQ) in computational models. These methods are grounded in the use of functional representations for random variables. In particular, Polynomial Chaos (PC) expansions have seen significant use in this context. The utility of PC methods has been demonstrated in a range of physical models, including structural mechanics, porous media, fluid dynamics, aeronautics, heat transfer, and chemically reacting flow. While high-dimensionality remains a challenge, great strides have been made in dealing with moderate dimensionality along with non-linearity and oscillatory dynamics.

In this talk, I will give an overview of UQ in computational models. I will cover the two key classes of UQ activities, namely: estimation of uncertain input parameters from empirical data, and forward propagation of parametric uncertainty to model outputs. I will cover the basics of PC UQ methods with examples of their use in both forward and inverse UQ problems.

Faculty host: Xiaoying Han


September 5, 2014

Speaker: Jim Gleason, Department of Mathematics, University of Alabama, Tuscaloosa

Title: Math Tests: What are we measuring and how well?

Abstract: We will examine and reflect on our goals and objectives for giving math tests and describe how educational research techniques can help us to determine how well we are meeting those goals.

Faculty host: T.-Y. Tam

THURSDAY, August 28, 2014, 2:00 in Parker 328 

Speaker: Saad El-Zanati, Illinois State University (Professor Zanati received his Ph.D. from Auburn in 1991; Dr. Rodger was his advisor.)

Title: On Decomposing Regular Graphs and Multigraphs into Isomorphic Trees and Forests

Abstract: Click here

Faculty host: Chris Rodge

Last updated: 01/30/2015