Title: Measuring combinatorial complexity via regularity lemmas
Many tools have been developed in combinatorics to study global structure in finite graphs. One such tool is called Szemer\'{e}di’s regularity lemma, which gives a structural decomposition for any large finite graph. Beginning with work of Alon-Fischer-Newman, Lov\'{a}sz-Szegedy, and Malliaris-Shelah, it has been shown over the last 15 years that regularity lemmas can be used to detect structural dichotomies in graphs, and that these dichotomies have deep connections to model theory. In this talk, I present extensions of this type of result to arithmetic regularity lemmas, which are analogues of graph regularity lemmas, tailored to the study of combinatorial problems in finite groups. This work uncovered tight connections between tools from additive combinatorics, and ideas from the model theoretic study of infinite groups.
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https://illinois.zoom.us/j/87806108905?pwd=bWwzN0tnSWdyY1RUSTdybitQVi80QT09
Meeting ID: 878 0610 8905
Password: 668040
