Department of Mathematics,
University of California San Diego
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Group Actions and Friends Seminar
Zoltán Vidnyánszky
Eötvös Loránd University
Measurable Complexity
Abstract:
We investigate the question of complexity of deciding the existence of measurable colorings of Borel graphs. With a new and relatively easy argument we show that deciding the existence of measurable 3 coloring is maximally complicated, (i.e., analytic complete), even for the nicest possible class of graphs: acyclic, regular and measure preserving ones. This also yields a new, significantly simpler proof of most of the complexity results about graph colorings in the Borel context, and relies on proving complexity results for countable hypergraph colorings and on the notion of measurable primitive positive definability, which are interesting on their own. If time permits, we will also discuss where the dividing line between hard and easy coloring problems lies, and how it seems to be different from any characterization result proposed so far. The talk will not assume familiarity with descriptive set theory. Joint work with Jan Grebík.
October 14, 2026
1:00 PM
APM 6402
Research Areas
Combinatorics Ergodic Theory and Dynamical Systems Logic and Computational Complexity****************************

