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Geometry-Topology Seminar

Thursday, October 21, 2021 - 5:15pm

Yakov Eliashberg & Tarik Aougab

Stanford University & Haverford College


University of Pennsylvania

via Zoom

This double-header seminar is sponsored jointly with Bryn Mawr, Haverford and Temple. The zoom link will be e-mailed to faculty and graduate students at Penn, and is otherwise available by e-mailing

ELIASHBERG:  I will prove that the space of positive tight contact structures on the 3-sphere is homotopy equivalent to the real projective plane.  The talk is based on a joint work with N. Mishachev.
AOUGAB: Choose a homotopically non-trivial curve “at random” on a compact orientable surface- what properties is it likely to have? We address this when, by “choose at random”, one means running a random walk on the Cayley graph for the fundamental group with respect to the standard generating set. In particular, we focus on self-intersection number and the location of the metric in Teichmuller space minimizing the geodesic length of the curve. As an application, we show how to improve bounds (due to Dowdall) on dilatation of a point-pushing pseudo-Anosov homeomorphism in terms of the self-intersection number of the defining curve, for a “random” point-pushing map. This represents joint work with Jonah Gaster.