name | Matthias Heymann | ||||||||||||||
date of birth | 1977 in Frankfurt/Main (Germany) | ||||||||||||||
education |
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interests | probability theory, functional analysis, numerical analysis, applications to biology, physics, chemistry, etc. |
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research area  | analytical and numerical aspects of large deviation theory |
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year |
title | area |
download |
2010 | Existence and Properties of Minimum Action Curves for Degenerate Finsler Metrics, M.Heymann | geometry / prob. theory | [monograph] |
Rare Transition Events in Nonequilibrium Systems with State-Dependent Noise: Application to Stochastic Current Switching in Semiconductor Superlattices, M. Heymann, S.J.Teitsworth, J.C.Mattingly | theo. phys. / num. math | [paper] | |
The sources of rare transitions in continuous-time Markov jump processes, M.Heymann, (in preparation) | prob. theory | ||
2008 | The geometric minimum action method for computing minimum energy paths, E.Vanden-Eijnden and M.Heymann, Jour. Chem. Phys. 128, 061103, 2008 | chem. phys. / num. math. |
[paper] |
The Geometric Minimum Action Method: A Least Action Principle on the Space of Curves, M.Heymann and E.Vanden-Eijnden, Comm. Pure Appl. Math. 61.8, 1052-1117, 2008 | prob. theory / num. math. |
[paper] | |
2007 | Pathways of maximum likelihood for rare events in non-equilibrium systems, Application to nucleation in the presence of shear, M.Heymann and E.Vanden-Eijnden, Phys. Rev. Letters 100.14, 140601, 2007 | physics / num. math. |
[paper] |
PhD Thesis: The Geometric Minimum Action Method: A Least Action Principle on the Space of Curves, M.Heymann, New York University, 2007 | prob. theory / num. math. |
[thesis] [talk] | |
2002 | A Model for the Online Time of Network Users, M.Heymann and M.Hansen, unpublished | statistics | [paper] |
A new set of sound commands for R; Sonification of the HMC algorithm, M.Heymann and M.Hansen, ASA Proceedings 2002, Statistical Computing Section, 1439-1443 | statistics | [paper] | |
The R sound package: A new set of commands for using sound under R, M.Heymann, available at http://cran.r-project.org | programming | [manual] [package] |
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The Stieltjes convolution and a functional calculus for non-negative operators, M.Heymann, unpublished | func. anal. | [paper] | |
2001 |
Diploma thesis: Fractional powers of operators, and their applications, M.Heymann, Leibniz Universität Hannover, Germany, 2001 | func. anal. | [paper] |
For more detailed descriptions of
the projects, please see the Abstracts section on my
Mathematics site.
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Please
download the poster of my exhibition for my students' linear
algebra semester project "3D graphics".
[pdf] In 2005 I was nominated for the NYU-wide "Dean's Outstanding Graduate Teaching Award". |
language |
skill level (1-10) | last used | projects |
---|---|---|---|
MatLab | 9 | 2010 | main language used for simulations in my research; also used for a graphical user interface in a semester project |
Java | 7 | 2006 | user interface for tablet PCs, combining simultaneous input by microphone and stylus pen |
R(SPLUS) | 7 | 2002 | main language for my data analysis project at Bell Labs, and for my sonification project at Bell Labs for which I programmed a new set of sound commands for R that is now available for download on the official R website. |
Pearl | 3 | 2004 | used for parsing my data files at Bell Labs, and for the student login and grade requests on my course websites |
C++ | 2 | 2006 | briefly used in my PhD thesis |
HTML | 7 | 2009 | several course websites and my private website; I edit about half of the HTML source code by hand |
LaTeX | 10 | 2010 | see "Papers & Publications" |
Further experience includes many years of experience in Commodore 64 Assembler as a teenager. |
In my diploma thesis and subsequent work in functional analysis
I developed a functional calculus for non-negative operators on a Banach
space, based on a distributional generalization of the classical Stieltjes
transform and a convolution operation on the space of Stieltjes-transformable
distributions that I defined.
I then spent one year in the Department of Statistics and Data Mining at Bell Labs, Murray Hill, NJ. Here I was introduced to the tools and methods commonly used by data analysts, including the programming language R that I used extensively throughout that year in a project in which I modeled and analyzed internet traffic data. As a separate project I developed a package of new commands for dealing with sound under R that is now downloadable on the official R developers website. The lectures that I attended as a graduate student at NYU were mostly related to various aspects of probability theory, and in the bioinformatics department at NYU I learned the basics of genetics. With my advisor Prof. Vanden-Eijnden I was working on numerical and analytical aspects of the theory of rare events. In particular, we characterized maximum likelihood transition curves as the minimizers of a geometric action, and based on this description we developed an algorithm for computing this minimum action curve. In my current research I develop criteria for the existence of minimizers of such geometric actions. I also prove that transition curves pass critical points as they cross from one basin of attraction to another. For details, see my research statement. |
classical piano, electronic music, Argentine Tango, Salsa, music theory (in particular composition techniques of Liszt and Chopin) |