All Mathematical Sciences colloquium events will be held in Fisher Hall. Talks are from 1:00–2:00 p.m., followed by light refreshments. All events are open to the public.

Colloquium Archives

Cafer Caliskan

Some Open Problems in Finite Geometry

Abstract: The study of Finite Geometries deals with some combinatorial structures such as projective planes which have many fruitful connections with other fields in mathematics. This talk will give an introduction to some elements of Finite Geometry. Although there have been many attempts, some problems in the area of Finite Geometry have remained unsettled for decades. I will have an overview of some of these challenging problems.

Weizhong Dai

New Accurate Finite Difference Schemes for Neumann Boundary Condition of Heat Conduction

Abstract: The Neumann (or insulated) boundary condition is often encountered in engineering applications. The conventional finite difference schemes are either first-order accurate or second-order accurate but need a ghost point outside the boundary. In this talk, I will present a kind of new and accurate finite difference schemes for the Neumann boundary condition in Cartesian, cylindrical, and spherical coordinates, respectively. Combined with the Crank-Nicholson finite difference method or other higher-order methods, the overall scheme is proved to be unconditionally stable and provides much more accurate numerical solutions. The numerical errors and convergence rates of the solution are tested by several examples.

Dr. Weizhong Dai is a McDermott International Professor of Mathematics at Louisiana Tech University. His research interests include numerical solutions of partial differential equations, numerical heat transfer and bioheat transfer, numerical simulations for bioeffect of electromagnetics, and numerical methods for microfabrication systems, such as LCVD, melt crystallization, and X-ray lithography. Currently, he is working on the development of numerical simulations for hydrogen storage, which is supported by an NSF-EPSCOR grant. He has published one book and over 100 research articles in refereed journals. He is a member of the editorial board for The Open Applied Mathematics Journal, The Open Numerical Methods Journal, The Open Thermodynamics Journal, ISRN Mechanical Engineering, and Advances in Differential Equations and Control Processes, and is a reviewer for various international journals and conferences.

David Field

Manufacturing, Robotics, and Computational Geometry

Abstract: This lecture features examples of geometry’s dominating influence in the automotive manufacturing process. The lecture begins with the design and manufacture of sheet metal components that motivated advances in mathematical applications for computer-aided design. Many examples of the manufacturing process motivate a discussion of the mathematics developed for the describing automotive components. The discussion includes applying the same mathematics to robotics. The lecture also relates the previous geometric constructions with computational geometric aspects of generating finite element meshes for three dimensional analysis of automotive components. The lecture ends with the award winning video “Ballet Robotique.”

Durdu Guney

Quantum Computing and Communications with Optical Materials

Abstract: Quantum computing and communications is the field of processing information, based on quantum mechanical nature of information carriers, such as photons and atoms. Quantum superposition and entanglement provide new resources to solve the intractable problems outright, and to communicate more efficiently and securely. Quantum algorithms, quantum teleportation, and quantum cryptography are anticipated to change our lives dramatically, once they are reliably implemented. I will give an overview of this challenging information technology. Then I will propose engineered optical materials such as photonic crystals and metamaterials for scalable digital and analog quantum computing and high-speed long-distance quantum communications.

Daniel Kaplan

Toward a Calculus for our Era: Remodeling Math Education in Today’s University

Abstract: Calculus remains at the center of university math education, but problematically. Students in many areas see little applicability for the techniques that are covered in differentially and integral calculus. Calculus was developed for studying problems of physical motion and growth, not for the analysis of data, the evaluation of trade-offs, or the untangling of multiple contributing factors in complex systems. But just as Newton and his successors invented the technology of calculus and modern algebraic notation to solve physics problems of their era, so new “mathematical technologies” have been invented over the last century to deal with new problems.

I will argue that in most areas students will be better served by a university math education that incorporates these new mathematical technologies. I’ll describe the progress we have made at Macalester College in remodeling the introductory math curriculum to do so.

Seung Hyun Kim

Computational Reacting Flows in Energy Applications

Abstract: Chemically reacting flows are central to energy applications such as combustors, catalytic reactors, and fuel cells. Such flows typically involve several physical and chemical processes interacting with each other over a wide range of scales. Computation of those multiscale and multiphysics phenomena poses a great scientific challenge and is crucial to enhancing the development of advanced energy systems that meet future standards. In this talk, I will discuss the computational modeling of reacting flows observed in two important energy conversion devices, combustors and fuel cells. The modeling of turbulence-chemistry interactions in turbulent nonpremixed flames will be presented in the context of the conditional moment closure method and the large eddy simulation. The emphasis will be given to the effects of multiscale turbulent mixing on pollutant formation. The multiscale modeling of proton exchange membrane (PEM) fuel cells will then be presented with emphasis on interactions of surface reactions, nanoscale reactant transport, and liquid water dynamics in porous electrodes.

Bing Li

Sparse estimation of conditional graphical models with applications to gene networks (Bing Li, Hyonho Chun, and Hongyu Zhao)

Abstract: In many applications the graph structure in a network arises from two sources: intrinsic connections and connections due to external effects. We introduce a sparse estimation procedure for graphical models that is capable of isolating the intrinsic connections by removing the external effects. Technically, this is formulated as a {\em conditional} graphical model, in which the external effects are modeled as predictors, and the graph is determined by the nonzero entries of the conditional precision matrix. We introduce two sparse estimators of the conditional precision matrix using reproducing kernel Hilbert space combined with lasso and adaptive lasso. We establish the sparse property, variable selection consistency, oracle property, and derive the explicit asymptotic distributions of the proposed estimators for a specific type of reproducing kernel. The methods are compared with sparse estimators for unconditional graphical models, and with the constrained maximum likelihood estimate that assumes a known graph structure. Finally, the methods are applied to a genetic data set to construct a gene network after removing the effects from single-nucleotide polymorphisms.

Alex Rosa

Designs, graph decompositions and quasigroups

Abstract: The relationship between designs and graph decompositions on one hand, and quasigroups on the other, has been explored by many researchers. We survey the historical development, and discuss various characterizations, both old and new, for several varieties of “graphical” quasigroups.

Celine Vachon

  • Associate Professor of Epidemiology, Mayo Clinic
  • Genetic Epidemiology of Mammographic Density, A Strong Risk Factor for Breast Cancer

Xiaobo Zhou

Computational Systems Bioinformatics for Pathway Analysis and Drug Optimization

Computational Systems Bioinformatics for Pathway Analysis and Drug Optimization

Abstract: In this talk, I will first talk about the gene regulation and gene signature discovery using next-generation transcriptome sequencing technology. And then dug effects and drug combination synergy prediction will be discussed based on signal pathway map. Signal pathway inference from extracellular scale to cell nuecleus will be further discussed based on newly developed high-throughput technology, Reverse Phase Protein Array (RPPA). Finally I will talk about multiscale tumor in-silico modeling, and drug effect prediction in tumor microenvironment.

Mathematics Grad Student