Please join the Department of Mathematics and Statistics on Thursday, January 20th at 4:30pm on Microsoft Teams for a fascinating colloquium featuring University of Rochester’s Alex Iosevich.
Analytic, Number-Theoretic, and Combinatorial Aspects of Finite Point Configurations, and Applications to Data Science
Alex Iosevich, University of Rochester
Thursday, January 20th, 4:30pm to 5:30pm, Microsoft Teams
Abstract: The basic question we are going to address is, does a sufficiently "large" subset of Euclidean space contain a point configuration of a given type, such as an equilateral triangle, a long chain, or an arbitrary angle? The notion of large can be measured in terms of Hausdorff dimension, Lebesgue density, or even the number of points in the discrete case. This simple-sounding question has attracted the attention of many mathematicians in the past 75 years or so, with the flagship problems being the Erdos distance conjecture in geometric combinatorics and the Falconer distance conjecture in geometric measure theory. We are going to discuss these problems, the variety of techniques and ideas that are used to approach them, and, towards the end of the talk, describe some ongoing efforts to apply the resulting technology to the study of dimensionality of large data sets.