PhD Fredrik Strömberg

Office: S2|15 426
Phone: 06151 / 16-4681
Fax: 06151 / 16-6030
Email: stroemberg [at] mathematik.tu-darmstadt.de


Current contact information

I am currently a temporary lecturer at the Department of Mathematical SciencesDurham University, UK. 

See my official homepage in Durham for more information. 

 

Research

Research interests (amongst other things):

  • Computational aspects of automorphic forms:

    • Maass waveforms (non-holomorphic automorphic forms)
    • Harmonic weak Maass forms
    • Weak modular forms
    • Vector-valued modular forms 
    • Non-congruence modular forms

  • Weil representations 
  • Computational spectral theory for Fuchsian groups
  • Mathematical aspects of Quantum Chaos
  • Dynamical systems,  transfer operators and zeta functions 

Detailed research statement

undefinedDownload research statement.

Other research activities

I am  a senior member of the NSF FRG (Focused Research Group) project "L-functions and Modular Forms" which is large project in the computational aspects of modular forms (holomorphic as well as Maass) and L-functions. The PI of the FRG is William Stein and co-PI's are: A. Booker, B. Conrey, N. Elkies, M. Rubinstein and P. Sarnak.

I am an editor of the L-functions and modular forms database project (www.lmfdb.org). This project is a joint effort of a large number of researchers in modular forms and L-functions. The goal is to make information (theoretical and numerically computed) related to modular forms and L-functions available to a larger mathematical audience (i.e. not only to experts).  The website is also meant to serve as a platform to make new data   available.

Master projects

If you are interested in number theory, modular forms or related topics (in particular involving computations) and want a topic for for a Bachelor, Master or Diploma thesis please contact me and describe your interest and background.

  • Recent projects:

    • On statistics of Hecke eigenvalues, Diploma thesis by J.-L. Landvogt. 2010.

Previous Positions  

04/2008--03/2012
 Research assistant (Wissenschaftlicher Mitarbeiter) with Prof. Jan-Hendrik Bruinier at TU-Darmstadt.
06/2005--03/2008
 Research assistant (Wissenschaftlicher Mitarbeiter) with Prof. Dieter Mayer at TU-Clausthal.
02/2005--05/2005
Researcher (50%) at the Department of Mathematics, Uppsala University.
09/2002--12/2004
Lecturer (50%) at the Department of MathematicsUppsala University.
01/1999--09/2002
PhD student with a position at the Department of MathematicsUppsala University.
01/1999--09/2002
PhD student with stipend at the Department of MathematicsUppsala University.

    My Phd was obtained at Uppsala University (Sweden) and my advisor was prof. Dennis A. Hejhal (U. Uppsala and U. Minnesota MN.). Other members of the research group there are Andreas Strömbergsson, Pierre Bäcklund, Andreas Juhl and Andreas Södergren. A former member is Helen Avelin. See also the research group in analytic number theory. The research group in Uppsala was (is) a member of the EC-funded Research Training Network Mathematical Aspects of Quantum Chaos.  

Publications

Book Chapter

 

  • Maass waveforms on (Γ0(N),χ) (Computational aspects), Ch. 6 in Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology, LMS Lecture Notes Series, No. 397. 2011. (preprint version: pdf ps)

 

Theses

 If requested I can also send out copies by email (in pdf-format) or paper.    

Preprints

(If any mistakes are found in the preprints, please let me know.) 

       

      Invited Lecture Series

       

      • “Arithmetic Quantum Chaos” (4 lectures) at the “Expository Quantum Lecture Series 5”, January 2012, Universiti Putra Malaysia, Serdang, Selangor, Malaysia. 
      • “Maass waveforms for SL(2,Z)  and subgroups, from a computational point of view” (4 lectures) at the 2009 SMS Summerschool “Automorphic Forms and L-functions: Computational Aspects”, CRM, Montreal, Canada.
      • “Spectral theory and automorphic forms for modular groups” (4 lectures) at “A Workshop on Modular Forms and Related Topics”, February 2012, American University of Beirut, Beirut, Lebanon. 

       

      Invited Talks

      A selection of invited talks. There is usually slides available for at least one talk on a given topic.

      Pictures

       

      • Figures of zeros of Holomorphic cusp forms (computed by me) appear in 

        • Dana McKenzie, What's Happening in the Mathematical Sciences, Volume 8
        •  Peter Sarnak, Recent progress on the quantum unique ergodicity conjecture. Bull. Amer. Math. Soc. (N.S.) 48 (2011).
        • Amit Ghosh and Peter Sarnak, Real zeros of holomorphic Hecke cusp forms. Preprint. arXiv:1103.3262v1.

      • Plots of Maass waveforms appear in:

        • Front page of: Nicolas Bergeron, Le Spectre des Surfaces Hyperbolique, CNRS Éditions, EDP Sciences, 2011.

      • Misc. Figures:

      Programs

      As is the nature of these kind of things, most programs listed as available available are also under (perpetual) development. 

      • Ongoing projects in Sage/Page: 

        • Efficient algorithms for non-congruence subgroups (enumerate, classify up to conjugacy etc.)
        • Holomorphic modular forms for non-congruence subgroups.
        • Maass forms for subgroups of the modular group.
        • Harmonic weak Maass forms for subgroups of the modular group.
        • Vector-valued modular forms and harmonic weak Maass forms for the Weil representation.
        • The Selberg zeta function (is currently available for Hecke triangle groups)

      • My current Sage projects (most) are available from my psage clone: http://code.google.com/r/fredrik314-psage/
      • A Sage program for the Weil representation associated to arbitrary finite quadratic modules (over the rationals) is included in the fqm package of Nils Skoruppa et. al and can be obtained from: http://hg.countnumber.de/fqm-devel
      • Available for separate download: 

      • Previous projects in Fortran. These are no longer being developed but the code is available by request:

        • Computation of Harmonic weak Maass forms for the Weil representation.
        • Computation of Harmonic weak Maass forms for congruence subgroups.

      • Fourier coefficients for Gamma_0(229) and R=0.

      Address

      Fachbereich Mathematik
      Technische Universität Darmstadt

      Schloßgartenstr. 7
      64289 Darmstadt

      Germany

       

      Office

      Ute Fahrholz
      Gerlinde Gehring
      Zimmer: S2|15 K414

       +49 6151 / 16-2089

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