Finite Point Configurations in Euclidean, Discrete, and Arithmetic Settings

Explore finite point configurations in Euclidean, discrete, and arithmetic settings through this comprehensive lecture by Alex Iosevich from the University of Rochester. Delve into the fundamental question of determining the necessary size of a subset within a given vector space to ensure it contains a congruent copy of a specific point configuration. Examine how size is measured using Hausdorff dimension in Euclidean space and counting measure in finite fields. Survey a range of recent and established results, uncovering the connections between them. Gain insights into emerging links with learning theory as the lecture progresses through its 1-hour and 5-minute duration. This talk, part of the Colloque des sciences mathématiques du Québec/CSMQ, offers a deep dive into advanced mathematical concepts for those interested in geometric measure theory and related fields.