Speaker
Description
The topic of finding point configurations in large subsets of the Euclidean space lies at the intersection of combinatorics, geometry, and analysis. Euclidean Ramsey theory tries to identify patterns that are present in every finite coloring of the space, while a part of geometric measure theory studies patterns in sets of positive measure or positive density (as opposed to lower-dimensional sets or fractals). The two mathematical branches share many ideas, and they often successfully apply techniques from Fourier analysis and its generalizations. Consequently, many questions that have been posed in the 1980s, can now be fully or partially resolved using analytical tools that have been developed in the meantime. We will give a brief overview of the topic and then present some recent results and open problems.
