Research interests of Uwe F. Mayer

While working in academia, mathematically I was interested in partial differential equations, evolution problems, free boundary problems, global analysis, differential geometry, and numerical simulations. My published work concentrates on geometric free boundary problems. For those problems, one has an initial curve or surface and a mathematical law which describes how the surface should evolve. The best known example is the one where the normal velocity is the mean curvature of the surface (possibly minus its average to force preservation of enclosed volume). However, there are many others, for example the Mullins-Sekerka flow, the surface diffusion flow, or the Willmore flow. Follow this link if you want to see a few numerical simulations. Besides on free boundary problems, I also previously worked on nonpositively curved metric spaces, in particular on questions concerning gradients.

For the last several years I focused my interest on data mining and machine learning. I have several publications and patent applications in these areas as well.

Research Publications

Clicking on a title will let you read an abstract and will give you download options.

One-sided Mullins-Sekerka flow does not preserve convexity. Electronic J. Diff. Equ., 1993 no. 08, pp. 1-7 (1993).
Two-sided Mullins-Sekerka flow does not preserve convexity, in Proceedings of the Third Mississippi State Conference on Difference Equations and Computational Simulations (Mississippi State, MS, 1997), J.Graef, R. Shivaji, B. Soni, J. Zhu (editors), Electronic J. Diff. Equ., Conference 01, 1997, pp. 171-179.
Gradient flows on nonpositively curved metric spaces and harmonic maps. Comm. Anal. Geom., 6, no. 2, pp. 199-253 (1998).
The surface diffusion flow for immersed hypersurfaces (with J. Escher and G. Simonett). SIAM J. Math. Anal., 29, no. 6, pp. 1419-1433 (1998).
On the surface diffusion flow (with J. Escher and G. Simonett), in Navier-Stokes equations and related nonlinear problems (Palanga, 1997), VSP, Utrecht, pp. 69-79 (1998).
Classical solutions for diffusion-induced grain-boundary motion (with G. Simonett). J. Math. Anal. Appl., 234, pp. 660-674 (1999).
On diffusion-induced grain-boundary motion (with G. Simonett), in Nonlinear Partial Differential Equations (Evanston, IL, 1998), Gui-Qiang Chen and Emmanuele DiBenedetto (editors). Contemporary Mathematics book series, Amer. Math. Soc., Providence, Rhode Island, pp. 231-240, 1999.
Self-intersections for the surface diffusion and the volume preserving mean curvature flow (with G. Simonett). Differential Integral Equations, 13, pp. 1189-1199 (2000).
A numerical scheme for free boundary problems that are gradient flows for the area functional. Europ. J. Appl. Math., 11, issue 2, pp. 61-80 (2000).
A singular example for the averaged mean curvature flow. Experimental Math., 10, no. 2, pp. 103-107 (2001).
Loss of convexity for a modified Mullins-Sekerka model arising in diblock copolymer melts (with J. Escher). Archiv der Mathematik, 77, issue 5, pp. 434-448 (2001).
Numerical solutions for the surface diffusion flow in three space dimensions. Comput. Appl. Math., 20, no. 3, pp. 361-379 (2001).
A numerical scheme for axisymmetric solutions of curvature driven free boundary problems, with applications to the Willmore Flow (with G. Simonett). Interfaces and Free Boundaries, 4, no. 1, pp. 89-109 (2002).
Self-intersections for the Willmore flow (with G. Simonett). Proceedings of the Seventh International Conference on Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics - EVEQ2000. Nonlinear Differential Equations Appl., 55, Birkhäuser, Basel, pp. 341--348 (2003).
Experimental Design for solicitation campaigns (with A. Sarkissian). Proceedings of KDD-2003, Washington, DC, pp. 717-722 (2003).
Data-Pattern Discovery Methods for Detection in Nongaussian High-dimensional Data Sets (with C. Levasseur, K. Kreutz-Delgado, and G. Gancarz). Conference Record of the Thirty-Ninth Asilomar Conference on Signals, Systems and Computers, pp. 545-549 (2005).
Generalized Statistical Methods for Unsupervised Minority Class Detection in Mixed Data Sets (with C. Levasseur, B. Burdge and K. Kreutz-Delgado). Proceedings of the 2008 IAPR Workshop on Cognitive Information Processing, Santorini, Greece, pp. 126-131 (2008).
A Unifying Viewpoint of some Clustering Techniques Using Bregman Divergences and Extensions to Mixed Data Sets (with C. Levasseur, B. Burdge and K. Kreutz-Delgado). Accepted for publication in the Proceedings of the 1st International Workshop on Data Mining and Artificial Intelligence (DMAI 2008) held in conjunction with the 11th IEEE International Conference on Computer and Information Technology, Khulna, Bangladesh (December 2008).

Patents

Comprehensive Identity Theft Protection (with M. Lazarus and T. Crooks). Utility patent application filed (2007).
Fast Accurate Fuzzy Matching (with M. Blume and V. Narayanan). Utility patent application filed (2007).
Adaptive Analytics for Fraud Detection (with J. Athwal, L. Peranich, Sajama and S. Zoldi). Utility patent application filed (2007).
Fraud Detection for Faster Payments System (with S. Zoldi). Provisional patent application filed (2008).

Other Publications

Clicking on a title will let you read an abstract and will give you download options.

The proof of Fermat's Last Theorem by R. Taylor and A. Wiles, written by Gerd Faltings, translated from German by Uwe F. Mayer. Notices of the AMS, 42 no. 7, pp. 743-746 (1995).
A proof that polynomials have roots. College Math Journal, 28 no. 1, p. 58 (1997).
Diploma thesis on the global existence of non-convex solutions for the averaged mean curvature flow, written by C. Kneisel, numerical simulations by Uwe F. Mayer, Universität Hannover, Germany (2003).

Acknowledged in Publications by Others

Analysis 2, 1st Edition, Verlag Springer, 1995, by Wolfgang Walter.
Linux Benchmarking: Part 1 - Concepts, Linux Gazette, October 1997, Issue 22, by André D. Balsa.
C++ by Dissection: The Essentials of C++ Programming, 1st Edition, Addison Wesley Publishers, 2002, by Ira Pohl.

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	Last updated: Tue Sep 23 13:01:21 MDT 2008