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Home » AT Postdoc Seminar: Mumford Conjecture, Characteristic Classes, Manifold Bundles, and the Tautological Ring

Seminar

AT Postdoc Seminar: Mumford Conjecture, Characteristic Classes, Manifold Bundles, and the Tautological Ring February 28, 2014 (01:00 PM PST - 02:00 PM PST)
Parent Program: Algebraic Topology
Location: Space Science Lab Conference Room
Speaker(s) Ilya Grigoriev (University of Chicago)
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I will describe a topologists' perspective on the history of the study of an object that Mumford called "the tautological ring" and its generalizations.

The tautological ring was originally defined as a subring of the cohomology of the moduli space of Riemann surfaces, but can also be studied as a ring of characteristic classes of topological bundles. This point of view led to a proof of Mumford's conjecture, stating that the tautological ring coincides with the entire cohomology of the moduli space in a "stable range", as well as to some generalizations of this result. If time permits, I will explain what we know about the tautological ring outside the stable range.

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