Mathematics Colloquia and Seminars
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Speakers: Michael Kapovich and Dev SinhaGeometry/Topology
|Speaker: ||BATS (Bay Area Topology Seminar), Fall Meeting at UC Berkeley|
|Location: ||939 Evans Hall,|
|Start time: ||Tue, Oct 21 2003, 2:30PM|
2:30pm Dev Sinha (Univ. of Oregon)
Title: Homotopy methods in knot theory.
Abstract: Bott and Taubes first indicated that what finite-type knot
invariants are measuring for a knot K : S^1 -> R^3 are homotopy
invariants of the induced map on compactified configuration spaces
C_n[K] : C_n[S^1] -> C_n[R^3]. By combining results with those of
Volic, we now know a precise way in which this is the case rationally.
Working integrally sheds new light on finite-type invariants, leading
in lowest degree to a formula for the z^2 coefficient of the Conway
polynomial involving instances in which a knot intersects a line in
four points. Attempts to extend these results to higher degrees lead
to refined understanding of topics ranging from compactifications of
configuration spaces to Hopf invariants and Whitehead products.
4:10pm Michael Kapovich (UC Davis)
Title: "Geometrization conjecture and Ricci flow, after Hamilton and Perelman".
Abstract: The goal of this talk is to state Thurston's Geometrization
Conjecture for 3-manifolds and outline the Ricci flow approach to this
conjecture following Hamilton and Perelman.