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4:00pm to 5:00pm - RH 306 - Applied and Computational Mathematics Manuchehr Aminian - (Cal Poly Pomona) Manipulating transport properties of passive tracers in fluid channels via cross section Traditionally, theory developed for dispersion of asolute in a fluid flow has focused on predicting enhanced diffusion which can be observed, even with smooth fluid flow. A distribution will appear to spread much more rapidly than could be explained as the result of molecular diffusion alone, and decades of theory have been developed to successfully explain this. In our prior work, we developed asymptotic theory which predicts not only spread (variance), but also the sign differences in the distribution's skewness depending on cross section. This theory has had success matching with both experiment and numerical simulation. I will introduce the setting with these past results, then present a computational framework to extend this work past idealized cross sections and explore some questions in shape optimization towards more precise control of the tracer distribution, exploring the ability to design channels to match a given specification.
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3:00pm to 4:00pm - ISEB 1200 - Differential Geometry Malik Tuerkoen - (UC Santa Babara) Fundamental Gap Estimates on Positively Curved Surfaces The fundamental gap is the difference of the first two eigenvalues of the Laplace operator, which is important both in mathematics and physics and has been extensively studied. For the Dirichlet boundary condition, the log-concavity estimate of the first eigenfunction plays a crucial role, which was established for convex domains in the Euclidean space and the round sphere. Joint with G. Khan, H. Nguyen, and G. Wei, we obtain log-concavity estimates of the first eigenfunction for convex domains in surfaces of positive curvature and consequently establish fundamental gap estimates. In a subsequent work, together with G. Khan and G. Wei, we improve the log-concavity estimates and obtain stronger gap estimates which recover known results on the round sphere. |
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4:00pm - ISEB 1200 - Differential Geometry Xiaolong Li - (Wichita State University) The Curvature Operator of the Second Kind The Riemann curvature tensor on a Riemannian manifold induces two |
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9:00am to 9:50am - Zoom - Inverse Problems Jesse Railo - (University of Cambridge) Unique continuation of the fractional Laplacians, Radon transforms and nonlocal inverse problems |
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10:00am to 11:00am - RH 306 - Mathematical Physics Xiaowen Zhu - (U Washington) Cantor spectrum for a 1D moire model |
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1:00pm - RH 114 - Graduate Seminar Anna Ma - (UCI) TBA |
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1:00pm to 1:50pm - RH 306 - Inverse Problems Lili Yan - (University of Minnesota) Inverse boundary problems for elliptic operators on conformally transversally anisotropic manifolds In an inverse boundary problem, one seeks to determine the coefficients of a PDE inside a domain, describing internal properties, from the knowledge of boundary values of solutions of the PDE, encoding boundary measurements. Applications of such problems range from medical imaging to non-destructive testing. In this talk, starting with the fundamental Calderon inverse conductivity problem, we shall first discuss a partial data inverse boundary problem for the Magnetic Sch\"odinger operator on CTA manifolds. Next, we discuss first-order perturbations of biharmonic operators in the same geometric. Specifically, we shall present a global uniqueness result as well as a reconstruction procedure for the latter inverse boundary problem. |