Monday, May 14, 2012
Geometry Topology Seminar: Fractional powers of Dehn twists about nonseparating curves
Mon, 05/14/2012 - 2:05pm, Skiles 005
Kashyap Rajeevsarathy, IISER Bhopal Organizer: Dan Margalit
Let S_g be a closed orientable surface of genus g > 1 and C a simple closed nonseparating curve in S_g. Let t_C denote a left handed Dehn twist about C. A fractional power of t_C of exponent L/n is a h in Mod(S_g) such that h^n = t_C^L. Unlike a root of a t_C, a fractional power h can exchange the sides of C. We will derive necessary and sufficient conditions for the existence of both side-exchanging and side-preserving fractional powers. We will give some applications of the main result in both cases. Finally, we give a complete classification of a certain class of side-preserving and side-exchanging fractional powers on S_5.
Friday, May 18, 2012
Geometry Topology Seminar: Moduli spaces with no nonpositively curved metrics of bounded geometry
Fri, 05/18/2012 - 1:05pm, Skiles 006
Yunhui Wu, Brown University Organizer: Igor Belegradek
We prove the moduli space M_{g,n} of the surface of g genus with n punctures admits no complete, visible, nonpositively curved Riemannian metric, which will give a connection between conjectures from P.Eberlein and Brock-Farb. Motivated from this connection, we will prove that the translation length of a parabolic isometry of a proper visible CAT(0) space is zero. As an application of this zero property, we will give a detailed answer toP.Eberlein's conjecture.
Applied and Computational Mathematics Seminar: On Some Variational Models and Their Algorithms from Image Segmentation and Registration
Fri, 05/18/2012 - 2:05pm, 006 Skiles
Ke Chen, University of Liverpool Organizer: Hao Min Zhou
Both segmentation and registration are important image processing tasks in a number of real life applications. While there exist powerful and effective models,many scientific challenges remain open. In this talk, I shall first present some image segmentation work of modelsand algorithms in two and three dimensions, followed by some recent works of selective segmentationThen I introduce some new work on multimodality image registration modelling.Numerical experiments will demonstrate the advantages of our new models and algorithms over existing results. Collaborators related to this work include Noor Badshah (Peshawar, Pakistan), Jian-ping Zhang and Bo Yu (Dalian, China),Lavdie Rada (Liverpool), C Brito (Mexico) and N Chumchob (Thailand).