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.

- Thursday, February 22, 2024, 3:15pm, Physics 119, Probability Seminar
*Non-asymptotic Random Matrix Theory for Unitarily Invariant Matrices*

Jorge Garza Vargas (Caltech)- Classical random matrix theory focuses on the study of highly structured models (e.g. Wigner and Wishart matrices) which are presented as a sequence of random matrices defined for every dimension, whose asymptotic (i.e. as the dimension goes to infinity) spectral properties must be understood in detail. However, modern problems in data and computer science require only a coarser understanding of the random matrices in question, but necessitate nonasymptotic results in settings where the models are less structured and do not necessarily belong to a prescribed sequence of matrices. In this work we provide tools for analyzing the spectral distribution of any self-adjoint noncommutative polynomial evaluated in arbitrary independent unitarily invariant Hermitian random matrices of a fixed dimension. Our results can be interpreted as a quantitative version of Voiculescu's celebrated asymptotic freeness result. This is joint work with Chi-Fang Chen and Joel Tropp.

- Monday, February 26, 2024, 12:00pm, Physics 119, Probability Seminar
*Non-reversible Markov processes in particle systems*

Manon Michel- Recently, Markov-chain Monte Carlo methods based on non-reversible piecewise deterministic Markov processes (PDMP) are under growing attention, thanks to the increase in performance they usually bring. Beyond their numerical efficacy, the non-reversible and piecewise deterministic characteristics of these processes prompt interesting questions, regarding for instance ergodicity proof and convergence bounds. During this talk, I will particularly focus on the obtained results and open problems left while considering PDMP evolution of particle systems, both in an equilibrium and out-of-equilibrium setting. Hardcore particle systems have embodied a testbed of choice since the first implementations of Markov chain Monte Carlo in the 50’s. Even today, the entropic barriers they exhibit are still resisting to the state-of-the-art MCMC sampling methods. During this talk, I will review the recent developments regarding sampling such systems and discuss the dynamical bottlenecks that are yet to be solved.

- Tuesday, February 27, 2024, 3:15pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Vakhtang Poutkaradze (University of Alberta) - Tuesday, March 19, 2024, 3:15pm, Physics 119, Applied Math And Analysis Seminar
*TBD*

Patrick Guidotti (UC Irvine, Mathematics) - Tuesday, March 26, 2024, 3:15pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Sanchit Chaturvedi (Courant Institute) - Tuesday, April 9, 2024, 3:15pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Samuel Punshon-Smith (Tulane) - Tuesday, April 16, 2024, 3:15pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Jaemin Park (University of Basel) - Tuesday, April 23, 2024, 3:15pm, Physics 119, Applied Math And Analysis Seminar
*TBA*

Ayman Said (University of Cambridge)

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+)

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