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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.