Dalhousie-AARMS AAMP Seminar: Chamsol Park (Johns Hopkins University)
2023-01-20 16:00 - 17:00 (America/Halifax) | Dalhousie University, Halifax, Nova Scotia, Canada
Title: Eigenfunction restriction estimates on curves with nonvanishing geodesic curvatures

Abstract: Studying eigenfunctions of the Laplace-Beltrami operator on compact Riemannian manifolds (without boundary) is one of the interesting topics in Harmonic Analysis. One way to study them is to consider the L^p estimates of the eigenfunctions restricted to submanifolds. In this talk, we briefly summarize previous results and would like to talk about the logarithmic improved analogue for the restriction to curves with nonvanishing geodesic curvatures, in the presence of nonpositive sectional curvatures in the manifolds. If time permits, we will discuss some applications and open problems for the Schrodinger counterparts.

The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom and in Chase 227. If you would like to attend, please email the organizers for connection details.

Dalhousie-AARMS AAMP Seminar: Alex Barnett (Flatiron Institute, NYC)
2023-01-27 16:00 - 17:00
Title: Equispaced Fourier representations for efficient Gaussian process regression from a billion data pointsAbstract: Gaussian process regression is widely used in geostatistics, time-series analysis, and machine learning. It infers an unknown continuous function in a principled fashion from noisy measurements at $N$ scattered data points. The prior on the function is Gaussian, with covariance given by some user-chosen translationally invariantkernel. Yet $N$ has been limited to about $10^6$, even with modern low-rank methods. Focusing on low spatial dimension (1–3), we present a GP regression method using kernel approximation by an equispaced quadrature grid in the Fourier domain. This enables the iterative solution of a smaller Toeplitz linear system, exploiting both the FFT and the nonuniform FFT to give ${mathcal O}(N)$ cost. The result is often one to two orders of magnitude faster than state of the art methods, and enables cheap massive-scale regressions. For example, for a 2D Mat’ern-3/2 kernel and $N = 10^9$ points, the posterior mean function is found to 3-digit accuracy in two minutes on a desktop.Joint work with Philip Greengard (Columbia) and Manas Rachh (Flatiron Institute)
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over either Zoom and/or in Chase 227 depending on the speaker. If you would like to attend, please email the organizers for connection details.

Dalhousie-AARMS AAMP Seminar: Victor Ivrii (U. Toronto)
2023-02-10 16:00 - 17:00
Title + Abstract: TBD
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over either Zoom and/or in Chase 227 depending on the speaker. If you would like to attend, please email the organizers for connection details.

Dalhousie-AARMS AAMP Seminar: Katrina Morgan (Northwestern University)
2023-03-10 16:00 - 17:00

Dalhousie-AARMS AAMP Seminar: Milivoje Lukic (Rice U.)
2023-03-17 16:00 - 17:00
Title: Universality limits for orthogonal polynomialsAbstract: It is often expected that the local statistical behavior ofeigenvalues of some system depends only on its local properties; forinstance, the local distribution of zeros of orthogonal polynomials shoulddepend only on the local properties of the measure of orthogonality. Thisphenomenon is studied using an object called the Christoffel-Darbouxkernel. The most commonly studied case is known as bulk universality,where the rescaled limit of Christoffel-Darboux kernels converges to thesine kernel.In this talk, we will survey this subject, prior results, and a recentresult which gives for the first time a completely local sufficientcondition for bulk universality. The new approach is based on a matrixversion of the Christoffel-Darboux kernel and the de Branges theory ofcanonical systems, and it applies to other self-adjoint systems with 2×2transfer matrices such as continuum Schrodinger and Dirac operators.The talk is based on joint work with Benjamin Eichinger (TechnicalUniversity Wien) and Brian Simanek (Baylor University).
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over either Zoom and/or in Chase 227 depending on the speaker. If you would like to attend, please email the organizers for connection details.

Dalhousie-AARMS AAMP Seminar: Erick Schulz (ETH Zürich)
2023-03-31 16:00 - 17:00
