Applied Analysis Seminar
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Posted September 12, 2018

Last modified September 21, 2018

Aynur Bulut, LSU

Logarithmically energy-supercritical Nonlinear Wave Equations: axial symmetry and global well-posedness

In nonlinear dispersive PDE, radial symmetry often plays a key role in allowing for more refined analysis of the nonlinear interactions which could lead to possible blowup. We will describe recent work where we have recently introduced a mechanism for relaxing assumptions of radiality by considering symmetry in a subset of the variables (for instance, assuming that the initial data is axially symmetric). We applied this philosophy to show global well-posedness and scattering in for the nonlinear wave equation in the logarithmically energy-supercritical setting, generalizing a result of Tao which was established for the radial case. The uses Morawetz and Strichartz estimates that have been adapted to the new symmetry assumption. These methods in fact bring a new perspective to sharp estimates for the energy-critical problem, along the lines of the influential work of Ginibre, Soffer, and Velo. This is joint work with B. Dodson

Harmonic Analysis Seminar
Abstract and additional information

Posted September 18, 2018

3:20 pm Lockett 232This event has been rescheduled for 3:30 pm, Wednesday, September 26, 2018

Jiuyi Zhu, LSU

Quantitative unique continuation of partial differential equations

Abstract: Motivated by the study of eigenfunctions, we consider the quantitative unique continuation (or quantitative uniqueness) of partial differential equations. The quantitative unique continuation is characterized by the order of vanishing of solutions, which describes quantitative behavior of strong unique continuation property. Strong unique continuation property states that if a solution that vanishes of infinite order at a point vanishes identically. It is interesting to know how the norms of the potential functions and gradient potentials control the order of vanishing. We will report some recent progresses about quantitative unique continuation in different Lebesgue spaces for semilinear elliptic equations, parabolic equations and higher order elliptic equations.

Informal Geometry and Topology Seminar
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Posted August 27, 2018

1:30 pm - 12:00 am Saturday, September 15, 2018 Lockett 233
Yilong Wang, Louisiana State University

TBA

Geometry and Topology Seminar
Seminar website

Posted August 16, 2018

3:30 pm - 4:30 pm Lockett 233
Yilong Wang, Louisiana State University

TBA

Harmonic Analysis Seminar
Abstract and additional information

Posted September 12, 2018

Last modified September 18, 2018

Jiuyi Zhu, LSU

Quantitative unique continuation of partial differential equations

Abstract: Motivated by the study of eigenfunctions, we consider the quantitative unique continuation (or quantitative uniqueness) of partial differential equations. The quantitative unique continuation is characterized by the order of vanishing of solutions, which describes quantitative behavior of strong unique continuation property. Strong unique continuation property states that if a solution that vanishes of infinite order at a point vanishes identically. It is interesting to know how the norms of the potential functions and gradient potentials control the order of vanishing. We will report some recent progresses about quantitative unique continuation in different Lebesgue spaces for semilinear elliptic equations, parabolic equations and higher order elliptic equations.

Applied Analysis Seminar
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Posted August 28, 2018

Last modified September 10, 2018

Prashant Kumar Jha, LSU

TBA

Posted August 30, 2018

5:00 pm - 6:00 pm Math Lounge
Shea Vela-Vick, Louisiana State University

TBA

Frontiers of Scientific Computing Lecture Series

Posted August 19, 2018

Last modified September 5, 2018

Nicholas Zabaras, University of Notre Dame

Bayesian Deep Learning for Predictive Scientific Computing

Abstract: We will briefly review recent advances in the solution of stochastic PDEs using Bayesian deep encoder-decoder networks. These models have been shown to work remarkably well for uncertainty quantification tasks in very-high dimensions. In this talk through examples in computational physics and chemistry, we will address their potential impact for modeling dynamic multiphase flow problems, accounting for model form uncertainty in coarse grained RANS simulations and providing the means to coarse graining in atomistic models. Emphasis will be given to the small data domain using Bayesian approaches. The training of the network is performed using Stein variational gradient descent. We will show both the predictive nature of these models as well as their ability to capture output uncertainties induced by the random input, limited data and model error. In closing, we will outline the integration of these surrogate models with generative adversarial networks for the solution of inverse problems. NOTE: Reception in 1034 DMC at 3pm. Additional details at: https://www.cct.lsu.edu/lectures/bayesian-deep-learning-predictive-scientific-computing

Informal Geometry and Topology Seminar
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Posted August 27, 2018

Last modified September 17, 2018

Kent Vashaw, Louisiana State University

TBA

Harmonic Analysis Seminar
Abstract and additional information

Posted September 12, 2018

3:30 pm - 4:20 pm Lockett 232
Gestur Olafsson, Mathematics Department, LSU

Commuting Families of Toeplitz operators and representation theory

Abstract coming later

Applied Analysis Seminar
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Posted August 31, 2018

Last modified September 12, 2018

Karthik Adimurthi, Seoul National University

Partial existence result for Homogeneous Quasilinear parabolic problems beyond the duality pairing

Algebra and Number Theory Seminar
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Posted September 10, 2018

3:10 pmThis event has been rescheduled for 3:10 pm, Monday, January 21, 2019

Sharon Frechette, College of the Holy Cross

TBA

The talk is rescheduled to be given in Spring. The date will be announced later.

Computational Mathematics Seminar

Posted August 19, 2018

Last modified September 2, 2018

Minah Oh, James Madison University

The Hodge Laplacian on Axisymmetric Domains

Abstract: An axisymmetric problem is a problem defined on a three-dimensional (3D) axisymmetric domain, and it appears in numerous applications. An axisymmetric problem can be reduced to a sequence of two-dimensional (2D) problems by using cylindrical coordinates and a Fourier series decomposition. A discrete problem corresponding to the 2D problem is significantly smaller than that corresponding to the 3D one, so such dimension reduction is an attractive feature considering computation time. Due to the Jacobian arising from change of variables, however, the resulting 2D problems are posed in weighted function spaces where the weight function is the radial component r. Furthermore, formulas of the grad, curl, and div operators resulting from the so-called Fourier finite element methods are quite different from the standard ones, and it is well-known that these operators do not map the standard polynomial spaces into the next one. In this talk, I will present stability and convergence results of the mixed formulations arising from the axisymmetric Hodge Laplacian by using a relatively new family of finite element spaces that forms an exact sequence and that satisfies the abstract Hilbert space framework developed by Arnold, Falk, and Winther.

Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233
Federico Salmoiraghi, Department of Mathematics, LSU

TBA

Geometry and Topology Seminar
Seminar website

Posted September 14, 2018

3:30 pm - 4:30 pm Lockett 233
Scott Baldridge, LSU

TBA

Colloquium
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Posted August 29, 2018

3:30 pm - 4:20 pm TBD
Guillermo Goldsztein , School of Mathematics, Georgia Institute of Technology

TBD

Applied Analysis Seminar
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Posted August 25, 2018

Last modified August 29, 2018

Jiuyi Zhu, LSU

Nodal sets for Robin and Neumann eigenfunctions

We investigate the measure of nodal sets for Robin and Neumann eigenfunctions in the domain and on the boundary of the domain. A polynomial upper bound for the nodal sets is obtained for the Robin eigenfunctions. For the analytic domains, we show a sharp upper bound for the nodal sets on the boundary of the Robin and Neumann eigenfunctions. Furthermore, the sharp doubling inequality and vanishing order are obtained.

Informal Geometry and Topology Seminar
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Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233
Lucas Meyers, Louisiana State University

TBA

Geometry and Topology Seminar
Seminar website

Posted August 14, 2018

Last modified September 17, 2018

Joshua Sabloff, Haverford College

Length and Width of Lagrangian Cobordisms

Abstract: In this talk, I will discuss two measurements of Lagrangian cobordisms between Legendrian submanifolds in symplectizations: their length and their relative Gromov width. The Gromov width, in particular, is a fundamental global invariant of symplectic manifolds, and a relative version of that width helps understand the geometry of Lagrangian submanifolds of a symplectic manifold. Lower bounds on both the length and the width may be produced by explicit constructions; this talk will concentrate on upper bounds that arise from a filtered version of Legendrian contact homology, a Floer-type invariant. This is joint work with Lisa Traynor.

Algebra and Number Theory Seminar
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Posted September 7, 2018

3:10 pm - 4:00 pm 232 Lockett
Armin Straub, University of South Alabama

TBA

Applied Analysis Seminar
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Posted September 13, 2018

3:30 pm - 4:30 pm Lockett 233
Blaise Bourdin, Department of Mathematics, Louisiana State University

Variational phase-field models of fracture

Informal Geometry and Topology Seminar
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Posted August 27, 2018

1:30 pm - 3:00 pm Lockett 233
Sudipta Ghosh, Louisiana State University

TBA