The Hele Shaw Flow and the Moduli of Holomorphic Discs
Freitag, 11.1.13, 10:00-11:00, Raum 404, Eckerstr. 1
The Hele-Shaw Flow is a model for describing the propagation of\nfluid in a cell consisting of two parallel places separated by a small\ngap. This model has been intensely studied for over a century, and is a\nparadigm for understanding more complicated systems such as the flow of\nwater in porous media, melting of ice and models of tumor growth.\n\nIn this talk I will discuss how this flow fits into the more general\nframework of "inverse potential theory" through the idea of complex\nmoments. I will then discuss joint work with David Witt Nystrom that\nconnects to the moduli space of holomorphic discs with boundary in a\ntotally real manifold. Using this we prove a number of short time\nexistence/uniqueness results for the flow, including the case of the Hele\nShaw flow with varying permeability starting from a smooth Jordan domain,\nand for the Hele Shaw flow starting from a single point.
Modified surgery theory - Application to Bott manifolds
Freitag, 18.1.13, 10:00-11:00, Raum 404, Eckerstr. 1
One of the fundamental questions in geometric topology is the question whether two manifolds are diffeomorphic. Surgery theory translated that question as follows: Assuming they are simply connected it now reads: Are our manifolds h-cobordant? But for certain settings yet another transformation of our question is useful leading to modified surgery theory. The key idea here is to compare controlled bordism classes of manifolds.\n\nIn my talk I will explain how one can apply this theory to problems related to Bott manifolds. Bott manifolds are a very nice and explicite class of manifolds given as iterated CP^1-fiber bundles. They are of special interest since, conjecturally, they are diffeomorphic if and only if their cohomology rings are isomorphic.
Canonical degree of curves on varieties of general type
Freitag, 25.1.13, 10:00-11:00, Raum 404, Eckerstr. 1