Catherine M. Kublik

Assistant Professor of Computational Mathematics University of Dayton Department of Mathematics 300 College Park Dayton, OH 45469 Phone: (937) 229-2374 Email: ckublik1 at udayton dot edu |

I am an Assistant Professor of Computational Mathematics at the University of Dayton. My research is in computational methods with a focus on level set techniques, non parametric interfaces, boundary integral methods and image processing. My primary research interest is in designing computational tools in the context of implicit/non parametric interfaces. Specifically, I aim at providing elegant and simple algorithms for computing certain desired quantities, such as surface integrals, solutions of a PDE or geometric motions. Why implicit/non parametric interfaces?

1. Having an interface defined implicitly allows us to use the level set method, a computational framework of algorithms that track the motion of an interface moving with a certain normal velocity. Unlike explicit methods, the level set technique handles topological changes and is simple to implement on a fixed uniform grid.

2. Non parametric interfaces refer to manifolds described by a set of unstructured sample points. Such data sets of dense and unorganized point sets can be acquired from an imaging device (e.g. LIDAR).

My research aims at further exploiting and exploring the computations that can be done in these two settings.

My secondary research interest is in image processing, more precisely denoting and segmentation. In this context, my goal is to understand previous methods from an analytical standpoint, and build robust algorithms for extracting the desired information from an image with the minimum manual intervention.

Previously, I was a Bing Instructor at the University of Texas at Austin. I received my Ph.D. in Applied and Interdisciplinary Mathematics from the University of Michigan in 2010. My advisors were Selim Esedoglu and Jeffrey Fessler. I obtained a M.Sc. in Applied Mathematics from the University of British Columbia and an Engineering Degree (Diplôme d'Ingénieur) from the Ecole Nationale Supérieure de Techniques Advancées (ENSTA) in 2005.