Colloquia
Department of Mathematics and Statistics
Texas Tech University
See pdf for abstract
Seven 15-minute talks — see pdf for abstracts
The SIAM Departmental Colloquium may be attended at 3:00 PM CDT (UT-5) via this Zoom link.
The shapes of soap bubbles and soap films are fascinating because of their beauty and elegance. In this talk, we give an approach to the mathematics that explains these shapes through experiments with soapy water and wires.
This is a Bilingual Colloquium. The slides will be in English and the speaker will deliver the talk in Spanish.
The Fourier transform is one of the most fundamental tools in classical analysis. It plays a pervasive role in several branches of theoretical mathematics and of the applied sciences. The theorem of Hausdorff-Young states that, when p is an exponent in the interval [1,2], the Fourier transform of a function in the Lebesgue class L^p belongs to the dual Lebesgue space L^p’. As such, it is only defined almost everywhere and therefore it is a priori all but clear why it should be possible to restrict it to a lower dimensional manifold, such for instance the unit sphere, which has zero Lebesgue measure. The restriction conjecture states that this is in fact possible, provided that p stays in a certain optimal subinterval of the Hausdorff-Young range [1,2]. I will give a completely self-contained presentation of such conjecture, and hint at the role that the curvature (of the sphere) plays in it. I will also highlight the celebrated Tomas-Stein theorem which completely solves the restriction problem when the target is L^2 of the unit sphere. If time permits, some notable applications will be given. Disclaimer: although it is helpful to know a bit of Lebesgue spaces, to enjoy this talk you do not need to know much about them. I will tell you the very basics.