Analysis and Geometry Seminar

Fall 2025 Seminar Information

28 October 2025

Boya Liu: Stability in an inverse spectral problem for the magnetic Schrödinger operator (Part 2)

21 October 2025

Boya Liu: Stability in an inverse spectral problem for the magnetic Schrödinger operator

Abstract: In this talk we discuss Hölder-type stability estimates of the magnetic field and the electric potential of the magnetic Schrödinger operator from the knowledge boundary spectral data. This data contains eigenvalues and Neumann traces of the corresponding sequence of eigenfunctions of the magnetic Schrödinger operator. We show that this data is enclosed in the hyperbolic Dirichlet-to-Neumann map associated with solutions to the electro-magnetic wave equation. Our geometric setting is on a simple manifold of dimension two or higher. This talk is based on a joint work with Hadrian Quan (UC Santa Cruz), Teemu Saksala (NC State), and Lili Yan (NC State).

14 October 2025

Mulue Gebreslasie: Oil Price Movement Estimation: Machine Learning on Original vs. Gaussian Process–Densified Data

Abstract: This study applies Gaussian process (GP) regression to an empirical oil price dataset to address data sparsity and noise. Using a Gaussian kernel with data-dependent initialization, GP regression is used to generate predictions at densely interpolated time points, while also producing confidence intervals. This process yields a denoised, augmented dataset from which a procedure is developed to estimate impending crash-like price behavior. We conclude by demonstrating that this GP-driven data densification significantly improves the performance of machine learning algorithms in detecting future large fluctuations within the commodity data.

7 October 2025

Nikita Barabanov: Absolute stability and Joint Spectral Radius (Part 3)

30 September 2025

Nikita Barabanov: Absolute stability and Joint Spectral Radius (Part 2)

23 September 2025

Nikita Barabanov: Absolute stability and Joint Spectral Radius

Abstract: We introduce the concept of joint spectral radius of a family of matrices and analyze its properties. Then we discuss a connection between this concept and absolute stability of automatic control systems with one sector nonlinearity. The necessary and sufficient conditions for absolute stability will be given in terms of Fourier transform, linear matrix inequalities, Kronecker products, Pontryagin maximum principle. Open problems will be also discussed.

Mathematics

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