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\noindent 12 October  2006

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\noindent Dear Hiring Committee:

%\noindent Kreso,

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\noindent I am applying for a tenure-track (lecturer) position in mathematics (dynamical systems) at University of Bristol.

%\noindent I am sending you this package of materials to apply for a tenure-track (assistant professor position in mathematics at University of Houston.  The rest of this e-mail includes my standard text for my more formal applications.  (I think you already know much of the information contained therein, but it's here anyway.)  Thanks very much for showing my application around!



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\noindent My research interests lie in applied mathematics and nonlinear dynamical systems. In particular, I use techniques from dynamical systems and perturbation theory to study phenomena in physics and other disciplines.


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\noindent During my postdoctoral career at Caltech and Georgia Tech, my main research thrust has been the study of nonlinear Schr\"odinger equations and their applications to Bose-Einstein condensation and optics.  I have also spent a lot of time investigating community-detection techniques in real-world networks.  In the past few years, I have also advised more than twenty undergraduate students in research projects, covering topics in theoretical ecology, billiard systems, quantum chaos, pattern formation, and complex networks (among other subjects). For my doctoral dissertation, which I completed in May 2002 in Cornell University's Center for Applied Mathematics, I studied quantum billiards with time-dependent boundaries, which provide a mixed quantum-classical description for the dynamics of small polyatomic molecules.

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%\noindent University of Washington's applied mathematics department would be an ideal fit for me.  Although my research is not in the primary target area of the present search, I am nevertheless applying in the hopes that some people outside that area will still be considered if they are a sufficiently good fit with the department.  (Additionally, I was discussing this with Bernard Deconinck at SIAM's nonlinear waves meeting in September and he indicated that it was possible that some people outside the target area might be considered.)  In general, my preference is (if possible) to be in an applied mathematics department that is separate from a math department and to be surrounded by colleagues who are very interested not only in mathematics but who also get their hands dirty with the applications they study.  This is how I was brought up academically in college and graduate school and is the way I like to do applied mathematics.  Additionally, because I study nonlinear waves, there is already a natural group of potential collaborators for me within Washington's applied math department (Bernard, Nathan Kutz, etc).  I also have common research interests with faculty in other departments (such as Bill Reinhardt from chemistry/physics, who studies Bose-Einstein condensates) and anticipate developing collaborations with them as well.  Finally, it is my understanding that Microsoft research (and some faculty on campus from various departments) conduct research in real-world networks, which is another of my areas of academic interests and another avenue of potential local collaboration.  

%\noindent My research plans include not only continuing my work in Bose-Einstein condensation (BEC), nonlinear optics, billiards, quantum chaos, and real-world networks, but also expanding into other areas of applied dynamical systems (such as spatio-temporally chaotic dynamics of the complex Ginzburg-Landau equation).  More specific current foci include the use of nonlinearity management to stabilize pulses in optics and BEC and the investigation of the quantization of mixed regular-chaotic dynamical systems (such as quantum mushroom billiards).

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%\noindent University of Bristol would be an ideal fit for me, as I share research interests with numerous members of the mathematics faculty (such as Jens Marklof, Carl Dettman, Jonathan Robbins, Andreas Winter, and others) as well as physics faculty (such as Michael Berry).



%\noindent University of Wisconsin would be a very good fit for me academically.  With my interests in dynamical systems, nonlinear waves, and real-world networks, I have common research interests with many faculty members, such as Gheorghe Craciun, Shi Jin, Paul Milewski, and Fabian Waleffe.  In fact, I had a chance to have some nice discussions with Prof. Waleffe at a recent conference last May and would be very interested in pursuing that further.



%\noindent University of Arizona would be an ideal fit for me academically, as I have research interests in common with numerous current faculty.  For example, Nick Ercolani, Joceline Lega, Alan Newell, and Vladimir Zhakarov (among others) share my interests in nonlinear waves.  In some cases, the shared interests are even more specific, as many of my studies have focused on nonlinear Schr\"odinger equations in optics and Bose-Einstein condensation.  In the past, I have had the chance to talk about my research on Bose-Einstein condensates a bit with Professors Lega and Newell.  (My work in optics is more recent, and I am very interested in collaborating with the professors in the nonlinear waves and optics groups as I continue pursuing it.)  Another major component of my work is dynamical systems.  My Ph.D. thesis was on a problem in quantum billiards, and I am still studying problems in classical and quantum billiards and would very much like to collaborate with University of Arizona faculty (such as Maciej Wojtkowski, who I met briefly many years ago as a graduate student, and Marek Rychlik) on these problems.


%\noindent While I realize that the primary focus of Colorado's search is probability and statistics, I am applying anyway because of how great a fit this department is for me.  Even though my primary area is nonlinear waves and dynamical systems rather than statistics, my work in complex networks has a very significant statistical component so that a large subset of my research program fits directly within the purview of this faculty search's primary focus.  This could lead to fruitful collaborative work with current Boulder faculty such as Manuel Lladser.  My work on the dynamics of Bose-Einstein condensates (BECs) and optics (and nonlinear waves in general) provides a large overlap in research interests with faculty such as Harvey Segur and Mark Ablowitz, and my work on Hamiltonian systems provides a similarly large overlap with faculty such as Jim Meiss.  Obviously, because I study BECs, being at a place with a strong nonlinear waves group and a local BEC lab with a strong group of experimental and theoretical physicists (at JILA) is absolutely ideal for me.  I would really love to become a faculty member at CU Boulder and hope to have the chance to interview for a tenure-track job.

%\noindent Because of my interests in both applied mathematics and dynamical systems, Montana State University would be a very good fit for me academically.  There are numerous faculty (such as Jack Dockery and Mark Pernarowski) with whom my research interests overlap quite substantially and many others (such as Tomas Gedeon) who, like me, are interested in applications of dynamical systems. 



%\noindent Texas A \& M University would be a very good fit for me academically.  Several faculty have research interests that overlap with mine; this includes Prabir Daripa, Peter Kuchment, and Steve Fulling.  Additionally, I have had the chance to talk to Sue Geller at some length about the math department's new honors program, and I would like to become deeply involved with this if I joined the faculty.


%\noindent University of Tennessee faculty with whom I have common research interests include Don Hinton, Ohannes Karakashian, and Grozdena Todorova. 


%\noindent Faculty at University of Pittsburgh with whom I share research interests include Xinfu Chen, Stuart Hastings, Jonathan Rubin, and William Troy.

%\noindent My research interests overlap with all four areas listed on the applied math research group's website.  In particular, my graduate and undergraduate education followed the tradition of physical applied mathematics, and my research per se has entailed a lot of work in dynamical systems and stability.  SUNY Buffalo faculty with whom I share research interests include Gino Biondini, Brian Hassard (who earned his doctorate from the same program I did), and Elaine Spiller. 

%\noindent I would fit in particularly well at University of Vienna.  Within the nonlinear PDEs and applications group, I fall directly within category 1. In terms of the PDEs and asymptotic analysis groups, my interests overlap with category 2.

%\noindent Becoming a faculty member in University of Massachusett's math department would be very beneficial to my career, as one of my primary collaborators (Panos Kevrekidis) is already a member of the department.  Other faculty members with whom I share research interests include Luc Rey-Bellet, Bruce Turkington, and Nathaniel Whitaker.

%\noindent Purdue's applied mathematics group would be a very good fit for me scientifically, as my research interests overlap with those of several of the faculty, such as Min Chen, Melvin Leok, and Daniel Phillips.  Additionally, my work fits in well with several of the research clusters in the COALESCE program---especially nanoscience and bioinformatics (as the methods that I have used to study social networks can also be applied to biological ones).

%\noindent ANU's Department of Mathematics would be an ideal fit for me, as my research interests overlap strongly with many of its faculty, such as Murray Batchelor, Ben Andrews, and Algy Howe.  Additionally, because my work is in applications of nonlinear dynamics and complex systems, I would also be able to forge collaborations with faculty in the Centre for Mathematics and its Applications and the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems.

%\noindent As I indicated above, I was a VIGRE postdoc in the Georgia Tech math department from August 2002-May 2005.  Accordingly, I have co-authored papers with several of the current faculty (such as Leonid Bunimovich, Shui-Nee Chow, and Yingfei Yi) and advised/co-advised several of the department's undergraduates (including Goldwater Fellows Thomas Callaghan and A.J. Friend).  I also had extensive interactions with many other members of the department (especially those in the mathematical physics and dynamical systems groups), as well as members of other departments (physics, electrical engineering, and biology) through my former affiliation with the Georgia Tech's Center for Nonlinear Science.  Among the faculty who have joined Georgia Tech since my departure, I have had several discussions with Howie Weiss and would be very interested in pursuing a collaboration with him.  As a postdoc, I found Georgia Tech to be a particularly good academic fit for me and would very much welcome the opportunity to return as an assistant professor.

%We (you, Eric Bollt, and I) discussed my application briefly two years ago at the Joint Mathematics Meetings and subsequently by e-mail.  Because the application process extended a long time, I was forced to commit to my present position (a postdoctoral position at Caltech) before I was invited for a campus interview.  When you contacted me concerning the interview, I mentioned that I would be back on the market in two years (that is, now) and that I remained very interested in Clarkson.  Thus, I am very pleased to see that you are seeking a new faculty member in applied dynamical systems, as that is my research area.  I look forward to renewing our discussion and hopefully visiting the campus for an interview.

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\noindent In addition to this letter, my application package includes a curriculum vitae, a list of publications, and discussions of my research program and teaching experience.  My online portfolio also includes several reprints and preprints, which are available at {\it http://www.its.caltech.edu/$\sim$mason/papers}.  I describe my research projects in further detail at {\it http://www.its.caltech.edu/$\sim$mason/research}.

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\noindent I will be attending the Joint Mathematics Meetings in 2007 and would be very interested in meeting up there to discussion my application.  

%(Perhaps we can continue our discussion from two years ago?)

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%\noindent Letters of recommendations from the following people are available as part of my online portfolio:

\noindent I have solicited letters of recommendation from the following mathematicians and physicists who know my work:

%\noindent The following mathematicians and physicists have agreed to be contacted as references on behalf of my application:

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\item{Leonid A. Bunimovich (bunimovh@math.gatech.edu, 404-894-4748 [office], 404-894-4409 [fax]), Regents' Professor, Mathematics; Member, Center for Nonlinear Science; and Director, Southeastern Applied Analysis Center, Georgia Tech}

\item{Predrag Cvitanovi\'c (predrag@cns.physics.gatech.edu, 404-385-2502 [office], 404-385-2506 [fax]), Professor, Physics and Director, Center for Nonlinear Science, Georgia Tech}

\item{Panayotis G. Kevrekidis (kevrekid@math.umass.edu, 413-577-1977 [office], 413-545-1801 [fax]), Associate Professor, Department of Mathematics \& Statistics, University of Massachusetts, Amherst}

\item{Peter J. Mucha (mucha@unc.edu, 919-843-2550 [office], 919-962-9345 [fax], Assistant Professor, Department of Mathematics and Institute for Advanced Materials, University of North Carolina, Chapel Hill}

\item{Mark E. J. Newman (mejn@umich.edu, 734-764-4223 [office], 734-763-9694 [fax]), Associate Professor, Physics and Complex Systems, University of Michigan and External Faculty, Santa Fe Institute}

\item{Michael T. Lacey (lacey@math.gatech.edu, 404-894-9237 [office], 404-894-4409 [fax]), Professor, Mathematics and former Undergraduate Coordinater, Mathematics, Georgia Tech [teaching reference]}

\end{itemize}


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\noindent Thank you very much for considering my application.  I look forward to hearing from you in the near future.

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\noindent Sincerely,

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\noindent Mason A. Porter

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\noindent Postdoctoral Scholar

\noindent Center for the Physics of Information

\noindent California Institute of Technology

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