**COLLOQUIA 2014 -- 2015**

Refreshments are served in Parker Hall, Room 244, beginning at 3:30.

**WEDNESDAY July 1, 2015**

Speaker: Quansen Jiu, Capital Normal University, Beijing & Princeton University, NJ

Title: On Liouville Type of Theorems to the Three-dimensional Incompressible Axisymmetric Navier-Stokes Equations

Abstract: The Liouville type of theorem plays a key role in the blow-up approach to study the global regularity of the three-dimensional Navier-Stokes equations. In this talk, we will present Liouville type of theorems to the 3-D axisymmetric Navier-Stokes equations with swirls under some suitable assumptions on swirl component velocity $u_\theta$, which are scaling invariant. It is known that $ru_\theta$ satisfies the maximum principle. The assumptions on $u_\theta$ will be natural and useful to make further studies on the global regularity to the three-dimensional incompressible axisymmetric Navier-Stokes equations.

Faculty host: Yongsheng Han

**May 1, 2015**

Speaker: Guantao Chen, Georgia State University

Title: Long cycles and spanning trees in planar graphs and beyond

Abstract: Click here

**April 24, 2015 time (1 pm) and place (224), and refreshment time (2pm)**

Speaker: Dr. Wei-wen Hsu, Kansas State University

Title: A Sup-Score Test for the Cure Fraction in Mixture Models for Long-Term Survivors

Abstract: Score tests are often used to assess the cure proportion in the population under interesting two-component mixture models for censored survival data with long term follow-up. But the existing test procedures often rely on restrictive assumptions, particularly on the form of the alternative. One common restriction is that constant cure proportions are often assumed. In this paper, we adopt a general formulation where these proportions are allowed to depend on covariates via a regression model. The hypothesis then translates into testing infinitely large intercepts in the mixing proportions while holding fixed the other regression terms. The implied hypotheses are not typical and standard regularity conditions to conduct the test may not even hold. Using empirical processes arguments, we construct a score-based test statistic under this general formulation and establish its limiting null distribution as a functional of chi-square processes. In practice, we suggest a simple resampling procedure to approximate this limiting null distribution. Our simulation results show that the proposed test can greatly improve efficiency over tests based on constant cure proportions under the alternative. The practical utility of the methodology is illustrated using ovarian cancer survival data with long-term follow-up from the SEER registry.

Faculty host: Guanqun Cao

**April 17, 2015**

Speaker: Dr. Vladimir Tkachuk, Universidad Autónoma Metropolitana de México

Title: Properties of $C_p(X)$ determined by its discrete subspaces

Abstract: Given a topological property $P$, say that a space $Z$ is discretely $P$ if the closure of $D$ in $Z$ has $P$ whenever $D$ is a discrete subspace of $Z$. We study the properties $P$ in $C_p(X)$ that are equivalent to $C_p(X)$ being discretely $P$. We will show that it is independent of ZFC whether discrete metrizability of $C_p(X)$ implies its metrizability for a compact space X. We also establish that it is consistent with ZFC that countable tightness and Lindelof $\Sigma$-property are not discretely reflexive in spaces $C_p(X)$. However, if $C_p(X)$ is discretely Cech-complete, then $X$ is countable and discrete. If $C_p(X)$ is discretely $\sigma$- compact, then $X$ has to be finite.

Faculty host: Ziqin Feng

**April 10, 2015 **Parker Hall 249

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*. See http://people.wm.edu/~cklixx/

Title: Decomposition of unitary gates

Abstract: In quantum computation, one has to manipulate quantum states using unitary operators. In this talk, we discuss some results and questions concerning the decomposition of unitary gates in the context of quantum computing. (No quantum mechanics background is needed).

Faculty host: T.-Y. Tam

**April 3, 2015**

Speaker: Norou Diawara, Old Dominion University

Title: Statistical Pattern Recognition using Gaussian Copula

For abstract, click here

Faculty host: Nedret Billor

**March 13, 2015**

Speaker: Asuman Turkmen, The Ohio State University

Title: The Hunt for Missing Heritability: Discovering Rare Variant Effects in Association Studies

Abstract: Genome-wide association studies (GWAS) have led to discovery of numerous common genetic variants linked to complex traits such as heart disease, diabetes, and auto-immune diseases. Despite these successes, the genetic variants identified so far can only account for a small proportion of the presumed phenotypic variation. The inability to find the complete genetic causes for complex traits has been called the "missing heritability" problem. With the ability to sequence genomic regions deeply, researchers have been looking beyond common sequence differences and interrogating rare variants that might solve the mystery of missing heritability. In this talk, I will introduce Kullback-Leibler distance based Tests (KLTs) to reveal possible genetic effects related to rare as well as common variants in case-control studies. The proposed tests are based on the idea of measuring the differences between distributions using Kullback-Leibler distance so that one can capture significant features of cases and controls. Extensive simulation studies and an application to the Dallas Heart Study data are utilized to compare our newly proposed tests with other promising methods in the literature. The numerical results show that the proposed tests are attractive alternatives for association studies involving rare variants.

This talk is based on a joint work with Zhifei Yan, Yueqing Hu and Shili Lin.

Faculty host: Nedret Billor

**March 30, 2015 MONDAY ROOM 250**

Speaker: Bjoern Schmalfuss, Friedrich-Schiler-Universitat Jena of Germany

Title: Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise

For abstract, click here

Faculty host: Xiaoying Han

**MONDAY ROOM 249**

Speaker: Jan Boronski, National Supercomputing Center IT4 Innovations Institute for Research and Applications of Fuzzy Modeling, Ostrava, Czech Republic

Title: More on constructions of R.H. Bing’s pseudo-circle in surface dynamics

Abstract: Motivated by the results in [1], we study circle maps f that give the pseudo-circle as the inverse limit space. We show that any such map exhibits the following properties: (1) there exists an entropy set for f with infinite topological entropy, (2) the rotation set is a nondegenerate interval. This shows that the Anosov-Katok type constructions of the pseudo-circle as a minimal set in volume-preserving smooth dynamical systems, or in complex dynamics, obtained previously by Handel, Herman and Chéritat cannot be modeled on inverse limits. This also relates to a known fact for Hénon-type attractors: R.F. Williams showed that every hyperbolic, one-dimensional, expanding attractor for a discrete dynamical system is topologically conjugate to the induced map on an inverse limit space based on a branched one-manifold, but M. Barge proved that certain dynamical systems with Hénon-type attractors cannot be modeled on inverse limits.

[1] Boronski J.P.; Oprocha P., Rotational chaos and strange attractors on the 2-torus, Mathematische Zeitschrift, (2015) 279:689--702, DOI10.1007/s00209-014-1388-1

Faculty hosts: Krystyna Kuperberg and Michel Smith

**March 11, 2015** (WEDNESDAY) regular time

Speaker: Tony Hilton, The University of Reading and Queen Mary’s College of the University of London

Title: Some theorems and conjectures about extremal finite set structures

Abstract available here

Faculty host: Peter Johnson

**February 27, 2015 SPECIAL TIME: 2:30 - 3:30 ROOM 249**

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 ROOM 249**

Speaker: Professor Roger Howe, Yale University

Title: Four stages of classical invariant theory

Abstract: "Classical" invariant theory, as described by Hermann Weyl in his book, *The Classical Groups*, has seen very substantial progress since Weyl wrote. This talk will survey four stages of development in the theory, of which the fourth stage is currently unfolding. A key role is played by the Weyl algebra, which was introduced by Weyl in his discussions of quantum mechanics, but not used by him in invariant theory. The main ideas used are from representation theory, The talk will include a summary of relevant notions from representation theory.

For PDF of presentation, click here

Dr. Howe is a renowned mathematician with a long history of interest in mathematics education. He is a member of the National Academy of Sciences and American Academy of Arts and Sciences. There will be a conference in honor of Professor Howe on the occasion of his 70th birthday http://math.mit.edu/conferences/howe/ in June 1-5, 2015 at Yale University, New Haven, with funding support from Yale, NSF, and Number Theory Foundation.

Faculty host: Huajun Huang

**February 13, 2015**

Speaker: Guanqun Cao

Title: Statistical Inference for Complex Data

Abstract: In this talk, I will give a general overview of my research program as part of my third-year review (mid-P&T evaluation). I will be talking about simultaneous inference for functional data and statistical inference in zero-inflated models -- in particular, covariance functions, repeated functional data and score-type test.

**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.

Faculty hosts: Narendra Govil and Peter Johnson

**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

**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 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 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 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 *L*² 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

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