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Archive : Inverse Problems and Analysis

 

 

Prof. Philip Gressman, University of Pennsylvania Prof. Philip Gressman, University of Pennsylvania Title: Geometric Averages in Harmonic Analysis Abstract: I will present recent results relating to the problem of quantifying L^p-improving properties of convolutions with singular measures. This theory is much more complete for measures supported on curves and hypersurfaces than it is for submanifolds of intermediate dimension. This relative lack of positive results is due in part to the problem that the Phong-Stein rotational curvature condition (which governs nondegeneracy in many important cases) is frequently impossible to satisfy for surprisingly deep algebraic reasons. I will focus primarily on the case of 2-surfaces in R^5, which does not fit nicely into previously-existing combinatorial strategies, and will present a new approach with the potential to apply in a broad range of new situations. 4/21/2017 5:00:00 PM4/21/2017 6:00:00 PMFalse
Dr. Javier Garcia-Frias, University of Delaware, Department of Electrical and Computer EngineeringDr. Javier Garcia-Frias, University of Delaware, Department of Electrical and Computer EngineeringEWG 205Title: Graphical models for source and channel coding Abstract: This talk presents an introduction to the use of graphical models in communications, specifically for channel and source coding. We will review some codes defined on graphs, and discuss how the source and channel statistics can also be incorporated into the graphical model representing these codes to improve the end-to-end performance. 3/10/2017 6:00:00 PM3/10/2017 7:00:00 PMFalse
Eyvindur Ari Palsson, Virgina TechEyvindur Ari Palsson, Virgina TechEWG205Title: Falconer type theorems for simplices Abstract: Finding and understanding patterns in data sets is of significant importance in many applications. One example of a simple pattern is the distance between data points, which can be thought of as a 2-point configuration. Two classic questions, the Erdos distinct distance problem, which asks about the least number of distinct distances determined by N points in the plane, and its continuous analog, the Falconer distance problem, explore that simple pattern. Questions similar to the Erdos distinct distance problem and the Falconer distance problem can also be posed for more complicated patterns such as triangles, which can be viewed as 3-point configurations. In this talk I will present recent progress on Falconer type problems for simplices. The main techniques used come from analysis and geometric measure theory. 3/3/2017 6:00:00 PM3/3/2017 7:00:00 PMFalse
Jens Christensen, Colgate University Jens Christensen, Colgate University EWG 336 <div dir="LTR"><font face="Arial">Title: Mean Value Operators</font> </div> <div dir="LTR"><font color="#282828" face="Arial">Abstract: Mean value operators have many uses</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">in mathematics. They can be used to characterize</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">harmonic functions, and several generalizations have</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">been found in the theory of PDEs.</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">The operators are a special type of Radon transforms,</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">and they show up in thermo and photo acoustic tomography.</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">We will start with a survey of mean value operators, and then start</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">studying the mapping properties of these operators.</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">Our main result is that any smooth function (on a non-compact symmetric</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">space of rank one) can be written as the spherical mean</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">value of another smooth function. The work builds on</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">results by Ehrenpreis regarding division in Paley-Wiener space.</font><font color="#282828" face="Arial"> </font><br> <font color="#282828" face="Arial">The result will be demonstrated with an example.</font><font color="#282828" face="Arial"> </font></div> 12/2/2016 3:00:00 PM12/2/2016 4:00:00 PMFalse

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