Geometry Seminar

Organizers: Sema Salur, and Ibrahim Unal.

The seminar will generally be held on Thursdays from 2:00 P. M. to 3:00 P. M. in Hylan 1106A. Any exceptions will be noted below.

Fall 2009 Seminars:

November 19th: Mehmet Arikan, University of Rochester ; "An Upper Bound for the ''Support Genus Invariant'' of Contact Structures"

Time&Place : 2:00pm-3:00pm Hylan 1106A

Abstract: The algorithm given by Akbulut and Ozbagci constructs an explicit open book decomposition on a contact three-manifold described by a contact surgery on a link in the three-sphere. In this talk, we'll improve this algorithm by using Giroux's contact cell decomposition process. Our algo- rithm gives a better upper bound for the recently defined ''support genus invariant'' of contact structures.

November 6th: Mustafa Kalafat, University of Wisconsin-Madison ; "Scalar Curvature and Connected Sums Of Self-Dual 4-Manifolds"

Time&Place : 4:00pm-5:00pm Hylan 1106A

Abstract: Under a vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-Manifolds is again self-dual. We prove that the same result can be extended over to the positive scalar curvature case.

October 29th: Shuguang Wang, University of Missouri; "Gerbes, Objective B-fields and a Hitchin-Kobayashi Correspondence"

Abstract: The Hitchin-Kobayashi correspondence relates stable bundles to Hermitian-Einstein connections, linking algebraic objects to differential geomeric ones. This corner-stone result proved by Donaldson and Uhlenbeck-Yau has made it possible to compute the polynomial invariants using algebraic geomtery tools. In the current talk, we will state and prove a new correspondence between twisted stable bundles and H-E connections. It is based on recent work about gerbes and objective Chern classes.