| Time and Date | Speaker |
Title and Abstract |
September 14 1-2 pm Carney 309 |
Bill Menasco |
Rectangular
diagrams and Legendrian knots This is joint work with Hiroshi Matsuda (Hiroshima University). D. Bennquin established the classical result that any transversal knot in the standard contact stucture of S^3 can be transversally isotopied to a closed braid. We establish an analogous result for Legendrian knots in the standard S^3 contact structure. |
February 8 1-2 pm Carney 010 |
Genevieve Walsh (Tufts) |
Commensurability
classes of 2-bridge knots. Two three-manifolds are said to be commensurable if they share acommon finite-sheeted cover. We discuss commensurability classes of knot complements, and prove that every hyperbolic two-bridge knot is the unique knot complement in its commensurability class. This doesnot hold for a general knot complement. For example, if a knot complement admits a lens space filling, it is covered by another knotcomplement. We speculate on the general case. This is joint work with Alan Reid. |
Feb 15 1-2 pm Carney 010 |
Yunhi Cho (University of Seoul) |
The analytic
continuation of hyperbolic space We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives rise to a complex valued geometry consistent with both the hyperbolic and de Sitter space. Such a construction shed a light and inspires a new insight for the study of the hyperbolic geometry and Lorentzian geometry. We discuss the advantages of this new geometric model as well as some of its applications. |