"Reason is immortal, all else mortal." - Pythagoras
Fall 2020
Organized by Mihaela B. Vajiac (director of CECHA).
The talks will be held online on Zoom or on campus at Keck Center of Science and Technology (no. 30 on the Campus map, at the intersection of Walnut Ave and Center St).
Schedule
Friday, October 2, 3pm - 4pm, Zoom
Ahmed Sebbar (Chapman University)
The Bernoulli Function
Abstract: pdf
Friday, October 16, 3pm - 4pm, Zoom
Daniel Alpay (Chapman University)
Generalized Fock Spaces and the Stirling Numbers
Abstract: The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. We imbed this space into a Gelfand triple. The spaces forming the Frechet part (i.e. the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced by the author and Guy Salomon. This is joint work with Motke Porat.
Friday, October 30, 3pm-4pm, Zoom
Polona Durcik (Chapman University)
A triangular Hilbert transform with curvature
Abstract: The triangular Hilbert transform is a two-dimensional bilinear singular integral originating in time-frequency analysis. No Lebesgue space bounds are currently known for this operator. In this talk, we discuss recent joint work with Michael Christ and Joris Roos on a variant of the triangular Hilbert transform involving curvature. As an application, we also discuss a quantitative nonlinear Roth type theorem on patterns in the Euclidean plane.
Friday, November 6, 3pm-4pm, Zoom
Xavier Ramos Olivé (Worchester Polytechnic Institute)
Eigenvalues of Manifolds with Integral Curvature Conditions
Abstract: pdf
Friday, November 13, 3pm-4pm, Zoom
Mihaela B. Vajiac (Chapman University)
Applications of Ternary Complex Analysis
Abstract: In recent years the theory of hypercomplex analysis has taken new directions towards more exotic examples such as the complex ternary case, in part due to possible applications in signal processing, physics, etc. The theory developed here is a particular case of the more general case of commutative hypercomplex analysis the author is working on and a continuation of the real ternary analysis case developed earlier.
Friday, November 19, 3pm-4pm, Zoom
Shoo Seto (CSUF)
On the first eigenvalue of the Laplacian on domains on spheres
Abstract: In this talk, we will give a brief overview of the Laplace eigenvalue problem on the sphere and present a recent result by the speaker in joint work with Guofang Wei and Xuwen Zhu.
Friday, December 4, 3pm-4pm, Zoom
Ahmed Sebbar (Chapman University)
Vieta Formula, Distributions, and Lemniscate
Abstract: pdf
Friday, December 11, 3pm-4pm, Zoom
Palle Jorgensen (University of Iowa, Iowa City)
Harmonic Analysis and Reproducing Kernel Properties of Singular Measures: Identification of Scales
Abstract: To better understand relationships and fractal structures in big datasets, neural networks, (and related structures), one is naturally led to a consideration of a harmonic analysis of non-smooth (singular) geometries. Examples where these types of geometries appear include large computer networks and other natural phenomena where dynamics of self-similar scales are present. Such a harmonic analysis will be presented. It still involves a choice of dual variables and associated RKHSs of analytic functions. The focus is on explicit transforms, algorithms, and expansions. This is combined with a use of multi-resolutions adapted to diverse fractal settings. The resulting harmonic analysis via Fourier duality is combined with reproducing kernels, frame expansions, and multi-resolution wavelet approaches. Our present focus here is L2 spaces derived from classes of singular measures.