Jacek Szmigielski's Home Page

Position

Address

Research Interests

APPLIED MATHEMATICS/ MATHEMATICAL PHYSICS SEMINAR 2010-2011 (sponsored by MITACS and PIMS)

APPLIED MATHEMATICS/ MATHEMATICAL PHYSICS SEMINAR 2008-2009-2010 (sponsored by MITACS and PIMS)

APPLIED MATHEMATICS/ MATHEMATICAL PHYSICS SEMINAR 2006-2007 (sponsored by MITACS)

APPLIED MATHEMATICS/ MATHEMATICAL PHYSICS SEMINAR 2002-2003

Recent publications

• Cauchy biorthogonal polynomials
  M. Bertola, M. Gekhtman and J. Szmigielski .
  Download pdf version (local copy).
  Journal of Approximation theory, 2010
  • Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa-Holm type equation
    A.N.Hone, H. Lundmark and J. Szmigielski .
    Download pdf version (local copy).
    Dynamics of PDE, 2009
    • Cubic string boundary value problems and Cauchy biorthogonal polynomials
      M. Bertola, M. Gekhtman and J. Szmigielski .
      Download pdf version (local copy).
      Journal of Physics A, 2009
      • The Cauchy two-matrix model
        M. Bertola, M. Gekhtman and J. Szmigielski .
        Download pdf version (local copy).
        Communications in Mathematical Physics, 2009
      • Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Invicid Burgers Equation
        Hans Lundmark and Jacek Szmigielski.
        Journal of Nonlinear Mathematical Physics , Volume 15, Issue 3, pp. 264-276 doi:10.2991/jnmp.2008.15.s3.26
      • One-dimensional magnetotelluric inversion with radiation boundary conditions
        T. Helmuth, R. Spiteri and J. Szmigielski .
        Download pdf version (local copy).
        Canadian Applied Mathematics Quaterly, Winter 2007, Volume 15, Numb 4, pp. 419-444.
      • The String Density Problem and the Camassa-Holm equation
        R. Beals, D. Sattinger and J. Szmigielski .
        Download pdf version (local copy).
        Philosophical Transations-Royal Society of London Series A Mathematical Physical and Engineering Sciences, 2007, Volume 365, Numb 1858, pp. 2299-2312.
        • Degasperis-Procesi peakons and the discrete cubic string.
          Hans Lundmark and Jacek Szmigielski.
          International Mathematics Research Papers, Volume 2005, Issue 2, pp. 53-116. 64 pages.
          • Journal website (free access): IMRP, Volume 2005, Issue 2.
          • Preprint version at arXiv.org (58 pages): nlin.SI/0503036.
          
          
        • Multi-peakon solutions of the Degasperis-Procesi equation.
          Hans Lundmark and Jacek Szmigielski.
          Inverse Problems, 19 (December 2003): 1241-1245. 5 pages.
          • Journal website (subscription needed): Hans Lundmark and Jacek Szmigielski, Inv. Prob. 19 (Dec 2003): 1241-1245
          • Updated version at arXiv.org: nlin.SI/0503033. This version corrects a few minor errors; in particular, the denominators λ_i+λ_j should not be squared in the expression for m₃(t) (the paper's last equation).
        • R. Beals, D.H. Sattinger, J. Szmigielski, 2003.
          Periodic Peakons and Calogero-Francoise Flows.
          Download dvi version (local copy).
        • R.Beals, D.H. Sattinger, , J. Szmigielski, 2002.
          Two new applications of the Abel map to Integrable systems.
          Download pdf version (local copy).
        • R. Beals, D.H. Sattinger, J. Szmigielski, 2001.
          Peakons, Strings and the Finite Toda Lattice.
          Communication on Pure and Applied Mathematics, Vol. LIV, 91-106.
          Download DVI version (local copy).
          Journal web site with PDF version.
        • Beals, D.H. Sattinger, J. Szmigielski, 2001.
          Inverse Scattering and some finite-dimensional integrable systems.
          Contemporary Mathematics.
        • S. Berman, Y. Billig, J. Szmigielski, 2001.
          Vertex operator algebras and the representation theory of toroidal algebras.
          Contemporary Mathematics.
        • R. Beals, D.H. Sattinger and J. Szmigielski, 2000.
          Multipeakons and the Classical Moment Problem.
          Advances in Mathematics 154, 229-257.
          Journal web site with PDF version.
        • A.Z. Górski and J. Szmigielski, 2000.
          Representations of the Heisenberg algebra by difference operators.
          Acta Physica Polonica B 4, 31, 789-799.
          Journal web site with PS version.
        • S. Berman, J. Szmigielski, 1999.
          Principal Realization for the extended affine Lie algebra of type sl2 with coordinates in a simple quantum torus with two generators.
          Contemporary Mathematics 248, 39-67.
          Download DVI version (local copy).
          
        • R. Beals, D.H. Sattinger and J. Szmigielski, 1999.
          Multi-peakons and a theorem of Stieltjes.
          Inverse Problems 15, L1-L4.
          Journal web site with PDF, PS, and HTML versions.
        • J. Dorfmeister, H. Gradl and J. Szmigielski, 1998.
          Systems of PDEs obtained from factorization in loop groups.
          Acta Applicandae Mathematicae 53, 1-58.
          Journal web site with PDF version.
        • R.Beals, D.H. Sattinger and J. Szmigielski,1998.
          Acoustic Scattering and the Extended Korteweg deVries Hierarchy.
          Advances in Mathematics 140, 190-206.
          Journal web site with PDF version.
        • A.Z. Górski and J. Szmigielski, 1998.
          On pairs of difference operators satisfying [D, X] = Id.
          Journal Math. Phys 39(1), 545-568.
          Journal web site with PDF and PS versions.
        • Prezent dla A.Z. Górskiego
          Download pdf version (local copy).
          

          Teaching

          MATH 110
          MATH 238
          MATH 338
          Homework 13, due January 19, 2005
          Homework 15, due February 2, 2005
          Homework 16, due February 11, 2005
          Homework 17, due February 23, 2005
          Homework 18, due March 2, 2005
          Homework 19, due March 9, 2005
          Homework 20, due March 18, 2005
          Homework 21, due March 23, 2005

          Download pdf version of corrections to the book by M.Pinsky .
          MATH 379
          

        Other links

        Talks planned for BIRS Workshop: Orthogonal Polynomials; Interdisciplinary Aspects.

        Some of my research collaborators: Richard Beals, Stephen Berman, Yuli Billig, Joseph Dorfmeister, Andrzej Górski, Hans Gradl, Hans Lundmark, David Sattinger,

        My postdoc for the academic year 2002-2003: Hans Lundmark.

        Department of Mathematics & Statistics Page	People in the Department
        University of Saskatchewan