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 mathematical 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.

Research Publications

Data Mining / Machine Learning

• Canary in the e-Commerce Coal Mine: Detecting and Predicting Poor Experiences Using Buyer-to-Seller Messages (with D. Masterov and S. Tadelis). Proceedings of ec'15, Portland, Oregon, USA (June 2015).

• Bootstrapped Language Identification For Multi-Site Internet Domains. Proceedings of KDD'12, Beijing, China (August 2012).

• Classifying non-Gaussian and Mixed Data Sets in their Natural Parameter Space (with C. Levasseur and K. Kreutz-Delgado). Proceedings of the Nineteenth IEEE Int'l Workshop on Machine Learning for Signal Processing, Grenoble, France (September 2009).

• 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). 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).

• 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).

• 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).

• Experimental Design for solicitation campaigns (with A. Sarkissian). Proceedings of KDD-2003, Washington, DC, pp. 717-722 (2003).

Mathematics

• 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).

• 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).

• Numerical solutions for the surface diffusion flow in three space dimensions. Comput. Appl. Math., 20, no. 3, pp. 361-379 (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).

• A singular example for the averaged mean curvature flow. Experimental Math., 10, no. 2, pp. 103-107 (2001).

• 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).

• Self-intersections for the surface diffusion and the volume preserving mean curvature flow (with G. Simonett). Differential Integral Equations, 13, pp. 1189-1199 (2000).

• 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.

• Classical solutions for diffusion-induced grain-boundary motion (with G. Simonett). J. Math. Anal. Appl., 234, pp. 660-674 (1999).

• 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).

• The surface diffusion flow for immersed hypersurfaces (with J. Escher and G. Simonett). SIAM J. Math. Anal., 29, no. 6, pp. 1419-1433 (1998).

• Gradient flows on nonpositively curved metric spaces and harmonic maps. Comm. Anal. Geom., 6, no. 2, pp. 199-253 (1998).

• 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.

• One-sided Mullins-Sekerka flow does not preserve convexity. Electronic J. Diff. Equ., 1993 no. 08, pp. 1-7 (1993).

Graduate Students

• Cécile Levasseur, Ph.D. (Electical Engineering), University of California, San Diego (2009). Thesis: Generalized Statistical Methods for Mixed Exponential Families, jointly advised with Prof. Kenneth Kreutz-Delgado.

• Carl-Heinz Kneisel, Diploma (Mathematics), Universität Hannover, Germany (2003). Thesis: On the global existence of non-convex solutions for the averaged mean curvature flow, advisor: Prof. Joachim Escher, numerical simulations provided by Uwe F. Mayer.

Patents

• Enhanced Supply And Demand Tool (with W. Pang, J. Lane, J. Colmenares, G. Singh, R. Tiwari, P. Coles, D. Coey).
  United States Patent Application 15/149,964 (Filed 2016/05/09, provisional application 62/159,052 filed 2015/05/08).

• Fraud Detection System For The Faster Payments System (with S. Zoldi).
  United States Patent 11,037,229 (Granted 2021/06/15, application 20090222369 filed 2008/05/13).

• Automated entity identification for efficient profiling in an event probability prediction system (with A. Vaiciulis, L. Peranich, S. Zoldi and S. De Zilwa).
  United States Patent 8,645,301 (Granted 2014/02/04, continuation application 13/710,423 filed 2012/12/10).
  United States Patent 8,332,338 (Granted 2012/12/11, continuation application 13/399,067 filed 2012/02/17).
  United States Patent 8,121,962 (Granted 2012/02/21, application 12/110,261 filed 2008/04/25).

• Adaptive Fraud Detection (with S. Zoldi, L. Peranich, J. Athwal and Sajama).
  United States Patent 10,510,025 (Granted 2019/12/17, application 20090222243 filed 2008/02/29 titled Adaptive Analytics).

• Fast Accurate Fuzzy Matching (with V. Narayanan and M. Blume).
  United States Patent 7,870,151 (Granted 2011/01/11, application 20080189279 filed 2007/06/13).

• Comprehensive Identity Theft Protection System (with T. Crooks and M. Lazarus).
  United States Patent 8,296,250 (Granted 2012/10/23, continuation application 13/195,328 filed 2011/08/01).
  United States Patent 7,991,716 (Granted 2011/08/02, continuation application 12/961,478 filed 2010/12/06).
  United States Patent 7,849,029 (Granted 2010/12/07, application 11/421,896 filed 2006/06/02).

Other Publications

• A proof that polynomials have roots. College Math Journal, 28 no. 1, p. 58 (1997).

Contributed to Publications by Others

• Level Set Method: For Motion by Mean Curvature, Notices of the AMS, November 2016, by Tobias Holck Colding and William P. Minicozzi II. (Uwe F. Mayer contributed some of the figures.)

• Mean Curvature Flow, Bulletin (New Series) of the American Mathematical Society 52 no. 2 (2015), by Tobias Holck Colding, William P. Minicozzi II, and Erik Kjær Pedersen. (Uwe F. Mayer contributed some of the figures.)

• C++ by Dissection: The Essentials of C++ Programming, 1st Edition, Addison Wesley Publishers, 2002, by Ira Pohl. (Uwe F. Mayer contributed some of the exercises.)

• Carl-Heinz Kneisel, Diploma (Mathematics), Universität Hannover, Germany (2003). Thesis: On the global existence of non-convex solutions for the averaged mean curvature flow advisor: Prof. Joachim Escher. (Uwe F. Mayer contributed the numerical simulations.)

Acknowledged in Publications by Others

• Optimizing Similar Item Recommendations in a Semi-structured Marketplace to Maximize Conversion, 10th ACM Conference on Recommender Systems, Boston, MA, USA, ISBN 978-1-4503-2138-9 DOI: 10.1145/1235 (2016), by Yuri M. Brovman, Marie Jacob, Natraj Srinivasan, Stephen Neola, Daniel Galron, and Ryan Snyder.

• Linux Benchmarking: Part 3 - Interpreting Benchmark Results, Linux Gazette, January 1998, Issue 24, by André D. Balsa.

• Linux Benchmarking: Part 1 - Concepts, Linux Gazette, October 1997, Issue 22, by André D. Balsa.

• 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).

• Analysis 2, 1st Edition, Verlag Springer, 1995, by Wolfgang Walter.

Connectivity

• Erdös Number: 5
  Paul Erdös [0] -> Svante Janson [1] -> Jie Xiao1 [2] -> Xuan Thinh Duong [3] -> Gieri Simonett [4] -> Uwe F. Mayer [5]
  Paul Erdös [0] -> Daniel Grieser [1] -> Isamu Ohnishi [2] -> Yasumasa Nishiura [3] -> Joachim Escher [4] -> Uwe F. Mayer [5]
  Find your Erdös Number using the collaboration distance tool of MathSciNet.
• Chomsky Number: 6
  Noam Chomsky [0] -> Marcel-Paul Schützenberger [1] -> Alain Connes [2] -> Don Bernard Zagier [3] -> Jonatan Lenells [4] -> Joachim Escher [5] -> Uwe F. Mayer [6]

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	Last updated: Thu Jul 8 12:57:16 PDT 2021