Analysis Research Group

Function Theory Study Seminar (Fall 07) Tuesdays 1:30 - 2:20 pm Burt 204

Organizer: Xiang Fang Previous semesters: Fall 05,   Spring 06,  Fall 06,  Spring 07

The seminar where people are not allowed to speak about their own research, but instead relate on classic papers, or obscure old papers, or brand new preprints not yet checked ...

September 6 - Diego Maldonado "Xu-Jia Wang's approach to the Schauder estimates for elliptic equations." Abstract: It is a classical result (J.Schauder, 1934) that a solution u to the equation $\Delta u = f$ is in the class $C^{2,\alpha}$ whenever $f \in C^{\alpha}$ and $0 < \alpha < 1$. We will go over a recent short proof of this fact due to Xu-Jia Wang. This talk will be of elementary nature and grad students in Analysis should feel encouraged to attend. September  18 - Chuck Moore "Good lambda inequalities and Riesz potentials." September  25 - Ivan Blank "De Giorgi-Nash-Moser Theory and the solution to Hilbert's 19th problem." Abstract: I'll present the beginning of Jose Miguel Urbano's survey paper: Regularity for partial differential equations: From De Giorgi-Nash-Moser theory to intrinsic scaling. Although this gives the "lion's share" of the proof of Hilbert's 19th problem, the only real background assumed will be multivariable calculus. October 2 - Ivan Blank "De Giorgi-Nash-Moser Theory and the solution to Hilbert's 19th problem." (cont.) October 9 - Ivan Blank "De Giorgi-Nash-Moser Theory and the solution to Hilbert's 19th problem." (cont.) October 16 - Dave Auckly "A novel representation of $S^2$-valued maps " Abstract: This talk will finish the proof of a technical result about $S^2$-valued maps, and given time sketch some applications of the result. October 23 - Gabriel Nagy "The Infinite Dihedral Group and its Fourier Algebra. " October 30 - Gabriel Nagy "The Infinite Dihedral Group and its Fourier Algebra, " (cont.) November 6 - Olena Ostapyuk "Euclidean Quasiconvexity" Abstract: I will introduce quasiconvex spaces and describe some general properties. Then I will characterize plane quasiconvex domains. The talk will be based on paper by Hrant Hakobyan and David Herron. November 13 - Mukta Bhandari "Boundedness properties of Fractional Integral Operators Associated to Non-doubling Measure" November 27 - Dave Auckly "Degree theory " Abstract: If the boundary of a membrane is mapped around a hole, part of the membrane will have to cover the hole. This is a colloquial description of a generalization of the intermediate value theorem known as degree theory. In this talk we will introduce the basic ideas of degree theory and present applications to problems ranging from algebra to differential equations. December 4 - Ray Treinen " Liquid Bridges" Abstract: A fixed volume of fluid is between two plates. We prove existence and regularity of capillary surfaces, as well as some properites of minimizers of the functional related to the problem. This is work by Maria Athanassenas.