Algebra and Number Theory Seminar
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Posted March 1, 2018

LSU Spring Break

Applied Analysis Seminar
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Posted March 18, 2018

3:30 pm - 4:30 pm Lockett 233
Stephen Shipman, Mathematics Department, LSU

Reducibility of the Fermi surface for periodic quantum-graph operators

The Fermi, or Floquet, surface for a periodic operator at a given energy level is an algebraic variety that describes all complex wave vectors admissible by the periodic operator at that energy. Its reducibility is intimately related to the construction of embedded eigenvalues supported by local defects. The rarity of reducibility is reflected in the fact that a generic polynomial in several variables cannot be factored. The "easy" mechanism for reducibility is symmetry. However, reducibility ensues in much more general and interesting situations. This work constructs a class of non-symmetric periodic Schrodinger operators on metric graphs (quantum graphs) whose Floquet surface is reducible. The graphs in this study are obtained by coupling two identical copies of a periodic quantum graph by edges to form a bilayer graph. Reducibility of the Floquet surface for all energies ensues when the coupling edges have potentials belonging to the same asymmetry class, that is, when their "spectral A-functions" are identical. If the potentials of the connecting edges belong to different asymmetry classes, then typically the Floquet surface is not reducible. Bilayer graphene is a notable exception--its Floquet surface is always reducible.

Posted March 23, 2018

6:00 pm - 7:00 pm Keiser Math Lounge Room 321
Rod Friedy, Director of Life Actuarial Services, Louisiana Department of Insurance

ASA Club Meeting

Rod Friedy, FSA, MAAA will be presenting on the life actuarial profession.

Posted March 19, 2018

8:30 am - 9:30 am Keisler Lounge, Room 321A Conversation with Prof. Irene Fonseca

(sponsored by the LSU SIAM and AWM Student Chapters)

Informal Topology Seminar
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Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233
Sudipta Ghosh, Louisiana State University

TBD

Pasquale Porcelli Lecture Series
Special Lecture Series

Posted November 7, 2017

Last modified March 13, 2018

Irene Fonseca, Carnegie Mellon University

Porcelli Lecture 1: Mathematics and Imaging Science

(The talk is intended to be accessible to High School Students.) In this talk, we will address the mathematical treatment of image processing, including inpainting, recolorization, denoising, and machine learning schemes.

Pasquale Porcelli Lecture Series
Special Lecture Series

Posted November 7, 2017

Last modified March 13, 2018

Irene Fonseca, Carnegie Mellon University

Porcelli Lecture 2: Mathematics and Materials Science

(Intended to be accessible to Undergraduate Students.) Abstract: Quantum dots are man-made nanocrystals of semiconducting materials. Their formation and assembly patterns play a central role in nanotechnology, and in particular in the optoelectronic properties of semiconductors. Changing the dots' size and shape gives rise to many applications that permeate our daily lives, such as the new Samsung QLED TV monitor that uses quantum dots to turn "light into perfect color"! Quantum dots are obtained via the deposition of a crystalline overlayer (epitaxial film) on a crystalline substrate. When the thickness of the film reaches a critical value, the profile of the film becomes corrugated and islands (quantum dots) form. As the creation of quantum dots evolves with time, materials defects appear. Their modeling is of great interest in materials science since material properties, including rigidity and conductivity, can be strongly influenced by the presence of defects such as dislocations. In this talk, we will use methods from the calculus of variations and partial differential equations to model and mathematically analyze the onset of quantum dots, the regularity and evolution of their shapes, and the nucleation and motion of dislocations.

Pasquale Porcelli Lecture Series
Special Lecture Series

Posted November 7, 2017

Last modified March 13, 2018

Irene Fonseca, Carnegie Mellon University

Porcelli Lecture 3: Homogenization of Integral Energies Under Periodically Oscillating Differential Constraints

(The talk is intended to be accessible to Graduate Students.) Abstract: A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. We will give an example that illustrates that, in general, when the operators differential operators have non constant coefficients then the homogenized functional maybe be nonlocal, even when the energy density is convex. This work is based on the theory of A-quasiconvexity with variable coefficients and on two-scale convergence techniques.

Algebra and Number Theory Seminar
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Posted January 15, 2018

Last modified March 23, 2018

Li Guo, Rutgers University at Newark

Rota's Classification Problem, Rewriting Systems and Groebner-Shirshov Bases

Throughout the history, mathematical objects are often understood through studying operators defined on them. Well-known examples include Galois theory where a field is studied by its automorphisms (the Galois group), and analysis and geometry where functions and manifolds are studied through their derivations, integrals and related vector fields. A long time ago, Rota raised the question of identifying all the identities that could be satisfied by a linear operator defined on algebras. We will discuss some recent progress on understanding and solving Rota's Problem by the methods of rewriting systems and Groebner-Shirshov bases. This is joint work with Xing Gao, William Sit, Ronghua Zhang and Shanghua Zheng.

Computational Mathematics Seminar

Posted March 5, 2018

3:30 pm - 4:30 pm 1034 Digital Media Center
Shu Lu, Univeristy of North Carolina at Chapel Hill

Statistical inference for sample average approximation of constrained optimization and variational inequalities

Abstract: The sample average approximation is widely used as a substitute for the true expectation function in optimization and equilibrium problems. We study how to provide a confidence region or confidence intervals for the true solution, once the SAA solution is obtained. Our method is based on the asymptotic distribution of the SAA solution, and we handle polyhedral constraints by examining the nonsmooth structure of the asymptotic distribution.

Informal Topology Seminar
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Posted March 19, 2018

10:30 am - 12:00 pm Lockett 233
Kent Vashaw, Louisiana State University

TBD

Harmonic Analysis Seminar
Abstract and additional information

Posted March 21, 2018

3:30 pm - 4:20 pm Lockett 243
Joseph Grenier, Louisiana State University

Constructive and Topological Reflection Positivities

In the 1970''s, Osterwalder and Schrader introduced an axiom for Constructive Quantum Field Theories called Reflection Positivity. The uses and consequence of Reflection Positivity have been explored by Jaffe, Neeb, Olafsson, and more with numerous interesting results. It was only recently, in 2016, that Reflection Positivity was adapted to Topological Quantum Field Theory through the use of bordisms and categories. This talk will briefly introduce the constructive form of Reflection Positivity before discussing the categorical approach taken by Freed and Hopkins. The talk will be suitable for graduate students in algebra, analysis and topology.

Colloquium
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Posted December 26, 2017

3:30 pm - 4:20 pm TBD
Stefan Kolb, Newcastle University

TBD

Algebra and Number Theory Seminar
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Posted January 16, 2018

3:10 pm - 4:00 pmTBA

Computational Mathematics Seminar

Posted March 5, 2018

Last modified March 19, 2018

Longfei Li, Univerisity of Louisiana at Lafayette

Overcoming the added-mass instability for coupling incompressible flows and elastic beams

Abstract: A new partitioned algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with elastic structures undergoing finite deformations. The new algorithm, referred to as the Added-Mass Partitioned (AMP) scheme, overcomes the added-mass instability that has for decades plagued partitioned FSI simulations of incompressible flows coupled to light structures. Within a Finite-Difference framework, the AMP scheme achieves fully second-order accuracy and remains stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The stability and accuracy of the AMP scheme is validated through mode analysis and numerical experiments. Aiming to extend the AMP scheme to an Finite-Element framework, we also develop an accurate and efficient Finite-Element Method for solving the incompressible Navier-Stokes Equations with high-order accuracy up-to the boundary.

Informal Topology Seminar
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Posted January 24, 2018

Last modified March 19, 2018

Nurdin Takenov, Louisiana State University

TBD

Colloquium
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Posted January 12, 2018

3:30 pm - 4:20 pm TBD
Birge Huisgen-Zimmermann, University of California, Santa Barbara

TBD

Algebra and Number Theory Seminar
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Posted February 27, 2018

3:10 pm - 4:00 pmTBA