Type: Seminar

Distribution: World

CalTitle1: Joint Colloquium: Palsson -- k-point configurations and multilinear generalized Radon transforms

Auth: afish@p617.pc (assumed)

Speaker: Dr. Eyvindur Ari Palsson http://www.math.rochester.edu/people/faculty/palsson/ Time: Friday, May 31, 2:30--3:30PM Room: Chemistry Lecture Theatre 2, the University of Sydney Lunch plan: we meet near Level 2 entrance to Carslaw Building around 1PM. The lunch would be at Law Annex Cafe with reservation at 1:10PM. ----------------------------------------------- Title: k-point congurations and multilinear generalized Radon transforms Abstract: As big data sets have become more common the interest in nding and understand- ing patterns in them has grown. A classical question on patterns (i.e. congurations), known as the Erd}os distinct distance problem, asks what is the least number of dis- tinct distances determined by N points in the plane. A continuous analog of this is the Falconer distance problem. Although originally formulated around distance, both problems also relate to congurations since the distance between two points can be thought of as a 2-point conguration. Questions similar to the Erd}os distinct dis- tance problem and the Falconer distance problem can also be posed for higher order congurations. For example a triangle can be viewed as a 3-point conguration which then naturally leads to the question of what is the least number of distinct triangles determined by N points in the plane. In this talk we will give a brief history of Erd}os and Falconer type questions for k- point congurations and then present recent Falconer type theorems for a wide class of k-point congurations in any dimension. Techniques from geometric measure theory and analysis are used to establish these recent theorems. The key step is to obtain bounds on multilinear analogs of the generalized Radon transforms introduced by Phong and Stein. In the talk we will also present these operators and their estimates. ----------------------------------------------- Joint Colloquium web site: http://www.maths.usyd.edu.au/u/SemConf/JointColloquium/index.html