**Jacek Szmigielski's
Home Page**

Needs2012.jpg

**Position**

Professor

**Address**

Department of Mathematics and Statistics

Room 223 McLean Hall

University of Saskatchewan

106 Wiggins Road

Saskatoon, SK

S7N 5E6

Canada

Phone Number: (306) 966-6093

E-mail address: __szmigiel@math.usask.ca__

*Mahmood
Khoshkam (1951-2003) in memoriam*

**Research Interests**

Integrable Systems, Inverse Problems, Mathematical Physics, Lie Theory

*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*

*Search
MathSciNet for all of Jacek Szmigielski's publications.*

**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 *m*_{3}(*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__.