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Texas A&M University

Events for 09/08/2023 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

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Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Yi Sheng Lim, University of Bath

Title: An operator-asymptotic approach to periodic homogenization applied to equations of linearized elasticity

Abstract: We explain an operator-asymptotic approach to homogenization for periodic composite media. This approach was developed by Cherednichenko and Velčić in the context of thin elastic plates, and here we demonstrate the approach under the simpler setting of equations of linearized elasticity.

As a consequence, we obtain L2 → L2, L2 → H1, and higher-order L2 → L2 norm-resolvent estimates. The correctors for the L2 → H1, and higher-order L2 → L2 results are constructed from boundary value problems that arise during the asymptotic procedure.

This is joint work with Josip Žubrinić (University of Zagreb).

Geometry Seminar

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Time: 4:00PM - 4:50PM

Location: BLOC 302

Speaker: Georgy Scholten, Sorbonne Université

Title: Global Optimization of Analytic Functions over Compact Domains

Abstract: In this talk, we introduce a new method for minimizing analytic Morse functions over compact domains through the use of polynomial approximations. This is, in essence, an effective application of the Stone-Weierstrass Theorem, as we seek to extend a local method to a global setting, through the construction of polynomial approximants satisfying an arbitrary set precision in L-infty norm. The critical points of the polynomial approximant are computed exactly, using methods from computer algebra.

Our Main Theorem states probabilistic conditions for capturing all local minima of the objective function $f$ over the compact domain. We present a probabilistic method, iterative on the degree, to construct the lowest degree possible least-squares polynomial approximants of f which attains a desired precision over the domain. We then compute the critical points of the approximant and initialize local minimization methods on the objective function f at these points, in order to recover the totality of the local minima of f over the domain.