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15 Geometry and Topology
Geometry and Topology Speaker: "No lecture" Time: 15:30 Room: MC 108 |
16 Noncommutative Geometry
Noncommutative Geometry Speaker: Enxin Wu (Western) "Chern-Weil's approach to Chern classes for vector bundles II" Time: 14:00 Room: MC 106 I will start from the definition of vector bundles over a manifold, basic operations on vector bundles, connections and curvature, Chern-Weil's approach to Chern classes of vector bundles, and basic properties of Chern classes. Analysis Seminar
Analysis Seminar Speaker: Debraj Chakrabarti (Notre Dame) "The Cauchy-Riemann equations on Product Domains" Time: 14:30 Room: MC 108 It is well-known that the $\overline{\partial}$--Neumann operator on a product domain does not preserve smoothness up to the boundary; however, the canonical solution operator does preserve smoothness up to the boundary. We try to understand this phenomenon, and derive some estimates for the canonical solution in Sobolev spaces.
(Joint work with Mei-Chi Shaw.)
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18 Noncommutative Geometry
Noncommutative Geometry Speaker: Ali Moatadelro (Western) "Metric aspects of noncommutative geometry VI" Time: 14:00 Room: MC 106 My aim was to explain four formulas of Riemannian geometry due to Alain Connes which have analogues in NCG. So far we discussed a dual version formula of geodesic distance on a manifold which is stated in terms of algebra of smooth functions, Dirac operator in the Hilbert space of spinors. We also talked about Weyl's formula which gives us the integration against the volume form in this set up. Next we introduced Connes' differential forms and their inner product to bring in Yang-Mills action.
In the upcoming talk, I shall try to reach the third formula which states the relation between Connes differential graded algebra and de Rham algebra of differential forms on the manifold. |
19 Algebra Seminar
Algebra Seminar Speaker: READING WEEK "(NO TALK SCHEDULED) " Time: 14:30 Room: MC 108 |
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Mathematics Calendar 
Week of February 14, 2010
