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

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 congurations 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. congurations),
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 congurations since the distance between two points can be
thought of as a 2-point conguration. Questions similar to the Erd}os distinct dis-
tance problem and the Falconer distance problem can also be posed for higher order
congurations. For example a triangle can be viewed as a 3-point conguration 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 congurations and then present recent Falconer type theorems for a wide class of
k-point congurations 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