# Applied Mathematics and Analysis Seminar

As part of the Duke University Department of Mathematics, the Program in Applied Mathematics hosts this ongoing series of seminars. The presentations cover a broad range of topics including numerical analysis, ordinary and partial differential equations, nonlinear systems, scientific computing, dynamical systems theory, mathematical biology, pattern formation, and complex physical systems.

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As a convenience, some selected seminars and presentations can be viewed live via the web. Further, we have video archives of past talks, which are also publicly available for you to view at any time.

Upcoming Seminars:
• Tuesday, March 3, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Jun Kitagawa (Michigan State University)

• Tuesday, March 17, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Xiangxiong Zhang (Purdue)

• Tuesday, March 24, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Daryl Deford (MIT, CSAIL)

• Wednesday, March 25, 2020, 12:00pm, Gross 330, Applied Math And Analysis Seminar
TBA
Wotao Yin (UCLA)

• Tuesday, March 31, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Pedro Aceves Sanchez (NC State)

• Wednesday, April 1, 2020, 12:00pm, 119 Physics, Applied Math And Analysis Seminar
Vortex stretching and a modified zeroth law for the incompressible 3D Navier-Stokes equations
Tsuyoshi Yoneda (The University of Tokyo)

By DNS of Navier-Stokes turbulence, Goto-Saito-Kawahara (2017) showed that turbulence consists of a self-similar hierarchy of anti-parallel pairs of vortex tubes, in particular, stretching in larger-scale strain fields creates smaller-scale vortices. Inspired by their numerical result, we examine the Goto-Saito-Kawahara type of vortex-tubes behavior using the incompressible 3D Navier-Stokes equations. More precisely, we consider the NS equations under the following $2+\frac{1}{2}$-dimensional situation: small-scale horizontal vortex blob being stretched by large-scale, anti-parallel pairs of vertical vortex tubes. We prove a modified version of the zeroth law (but very close to the actual zeroth-law) induced by such vortex-stretching. This is a joint work with In-Jee Jeong.

• Wednesday, April 15, 2020, 12:00pm, TBA, Colloquium
An improvement of Liouville’s theorem for discrete harmonic functions
Eugenia Malinnikova (Stanford University)

The classical Liouville theorem tells us that a bounded harmonic function on the plane is a constant. At the same time for any (arbitrarily small) angle on the plane there exist non-constant harmonic functions that are bounded everywhere outside this angle. The situation is completely different for discrete harmonic functions on the standard square lattices. The following strong version of the Liouville theorem holds on the two-dimensional lattice. If a discrete harmonic function is bounded on 99% of the lattice then it is constant. A simple counter-example shows that in higher dimensions such improvement is no longer true.

The talk is based on a joint work with L. Buhovsky, A. Logunov and M. Sodin.

• Tuesday, April 21, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
Prediction of random and chaotic dynamics in nonlinear optics
Amir Sagiv (Columbia)

The prediction of interactions between nonlinear laser beams is a longstanding open problem. A traditional assumption is that these interactions are deterministic. We have shown, however, that in the nonlinear Schrodinger equation (NLS) model of laser propagation, beams lose their initial phase information in the presence of input noise. Thus, the interactions between beams become unpredictable as well. Not all is lost, however. The statistics of many interactions are predictable by a universal model. Computationally, the universal model is efficiently solved using a novel spline-based stochastic computational method. Our algorithm efficiently estimates probability density functions (PDF) that result from differential equations with random input. This is a new and general problem in numerical uncertainty-quantification (UQ), which leads to surprising results and analysis at the intersection of probability and approximation theory.

• Tuesday, April 28, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Jongchon Kim (UBC)

• Tuesday, May 12, 2020, 3:15pm, 119 Physics, Applied Math And Analysis Seminar
TBA
Xiaoping Wang (USTHK)

• Wednesday, September 9, 2020, 12:00pm, Physics 119, Frontiers In Mathematics Distinguished Lecture Series
Lecture 1 (Frontiers in Mathematics)
Hong Wang (IAS)

(This is the first talk in the Frontiers in Mathematics Distinguished Lecture Series. See also the second talk in the series, on Friday September 11 at noon.)

• Friday, September 11, 2020, 12:00pm, Physics 119, Frontiers In Mathematics Seminar (second of 2 lectures)
Lecture 2 (Frontiers in Mathematics)
Hong Wang (IAS)

(This is the second talk in the Frontiers in Mathematics Distinguished Lecture Series. See also the first talk on Wednesday September 9 at noon.)

All seminars take place on Mondays at 4:30 pm in Room 119 Physics Building unless otherwise noted.

Tea and refreshments are served before the seminars at 4:00 pm in Physics 101.

Related Seminars

Past speakers in the Duke Applied Mathematics seminars (1997+)