# Mathematics Colloquia and Seminars

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### Speakers: Michael Kapovich and Dev Sinha

**Geometry/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.