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UID:2019092110060820190916T15000020190916T1550005d869ed0d2dfc@uic.edu
CATEGORIES:MEETING
STATUS:TENTATIVE
DTSTAMP:20190920T075127
DTSTART:20190916T150000
DTEND:20190916T155000
SUMMARY:Geometry, Topology and Dynamics Seminar: Entropy, metrics and quasi-morphisms, by Michael Brandenbursky
DESCRIPTION:Michael Brandenbursky (Ben Gurion University): Entropy, metrics and quasi-morphisms One of the mainstream and modern tools in the study of non abelian groups are quasi-morphisms. These are functions from a group to the reals which satisfy homomorphism condition up to a bounded error. Nowadays they are used in many fields of mathematics. For instance, they are related to bounded cohomology, stable commutator length, metrics on diffeomorphism groups, displacement of sets in symplectic topology, dynamics, knot theory, orderability, and the study of mapping class groups and of concordance group of knots. Let $S$ be a compact oriented surface. In this talk I will discuss several invariant metrics and quasi-morphisms on the identity component ${\rm Diff}_0(S, {\rm area})$ of the group of area preserving diffeomorphisms of $S$. In particular, I will show that some quasi-morphisms on ${\rm Diff}_0(S, {\rm area})$ are related to the topological entropy. More precisely, I will discuss a construction of infinitely many linearly independent quasi-morphisms on ${\rm Diff}_0(S, {\rm area})$ whose absolute values bound from below the topological entropy. If time permits, I will define a bi-invariant metric on this group, called the entropy metric, and show that it is unbounded. Based on a joint work with M. Marcinkowski. Please click here to make changes to, or delete, this seminar announcement.
LOCATION:636 SEO Chicago IL
CLASS:PRIVATE
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