Alex Kasman's Publications
Research Articles:
Most of the articles listed below are available online as PDF files or
on the arXiv of math/physics preprints. If you would like a printed copy
of any of these articles, please write to me at the address
above and I would be happy to send you one.

Bispectral KP Solutions and Linearization of CalogeroMoser Particle
Systems was published in Communications in Mathematical Physics
172 (1995).
Journal or
PDF or
arXiv.

Orthogonal Polynomials and Finite Toda Lattices appeared
in The Journal of Mathematical Physics, 38 (1) 1997 pp. 247254.
PDF.

Bispectral Darboux Transformations: the Generalized Airy Case
by Mitchell Rothstein and myself was published in Physica D 102
(1997), no. 34 pp. 159176.
PDF
or
arXiv.

Darboux Transformations from nKdV to KP appeared in Acta
Applicandae Mathematicae 49 no. 2 (1997) pp. 179197.
PDF.

The Bispectral Involution as a Linearizing Map in "CalogerMoserSutherlandModels",
CRM
Series in Mathematical Physics, JF van Diejen and L Vinet, eds. Springer
(2000) pp. 221230.

Darboux Transformations and the Bispectral Problem in CRM
Proceedings and Lecture Notes 14 American Mathematical Society
(1998) pp.8191.

Integrable Systems with Singular Rational Spectral Varieties
was my talk at the Workshop on Supersymmetry and Integrable Models, University
of Illinois  Chicago, April 1997. Published as Lecture Notes in Physics502
SpringerVerlag (1998) pp. 7790

Dmodules and Darboux Transformations written jointly with
Yuri Berest appeared in Letters in Mathematical Physics 43 (1998)
pp. 279294.
PDF or
arXiv.

Duality and Construction of Quantum Integrable Systems (with
E. Horozov)
Trends in mathematical physics (Knoxville, TN, 1998),
289297, AMS/IP Stud. Adv. Math., 13, Amer. Math. Soc., Providence, RI,
1999

Spectral Difference Equations Satisfied by KP Soliton Wavefunctions
was published as Inverse Problems 14 (1998) pp.14811487.
PDF
or
arXiv.

Kernel Inspired Factorizations of Partial Differential Operators appeared as The
Journal of Mathematical Analysis and Applications 234/2 (1999) pp.
580591.
PDF.

Grassmannians, Nonlinear Waves and Generalized Schur Functions was published in Contemporary
Mathematics 246 (1999) pp. 163174.
PDF.
Note: I liked my first draft of this article better than the one which
was published. That version was longer and did a better job of introducing
ideas (like Grasmmannian manifolds) which were cut out of the final version
at the editor's request. It is available from the arXiv as http://arXiv.org/abs/mathph/9811008v2.

Darboux Transformations of Bispectral Quantum Integrable Systems
written jointly with Emil Horozov, was published as
Letters in Mathematical
Physics 49: 131143, 1999.
PDF or
arXiv.

Finite Canonical Commutation Relations and Rational Nested Bethe
Ansatz was published as Regular and Chaotic Dynamics 6 (2), 211214 (2001).
PDF or
arXiv or journal.

Commutative Partial Differential Operators written with Emma
Previato was published as Physica D 152153 (2001) 6677
PDF.

Solitons and AlmostIntertwining Matrices with Michael Gekhtman
appeared in the Journal of Mathematical Physics 42 8 (2001) 35403553.
PDF
or arXiv
or
journal.

On the Quantization of a SelfDual Integrable System was published as Journal of Physics A 23 (2001) 63076312.
PDF.
 Overcoming the Phage Replication Threshold: A mathematical model
with implications for phage therapy with Laura M. Kasman, Caroline
Westwater, Joseph Dolan, Michael G. Schmidt, and James S. Norris was
published in The Journal of Virology.
76 11, (2002) 5575564.
PDF.
 Integrable
Systems and Rank One Conditions for Rectangular Matrices with
Michael Gekhtman was published as Theoretical and Mathematical
Physics 133(2): 14981503 (2002) [and in Russian as
Teoreticheskaya i Matematicheskaya Fizika Vol. 133 No. 2
pp. 211217, November 2002].
arXiv or PDF
(Funny Note: I wrote this paper in English and submitted it to this
Russian journal which translated it into Russian for the original
edition of the journal. Interestingly, when the American Mathematical
Society summarized the paper in Math Reviews, they translated the Russian title back into English and ended up with something just slightly different than our original title!)
 On KP Generators and the Geometry of the HBDE with
Michael Gekhtman was published in The Journal of Geometry and
Physics 56 (2006) 282309.
Journal or
arXiv
 On Decompositions of the KdV 2Soliton with Nicholas Benes and Kevin Young was published as The Journal of Nonlinear Science Volume 16 Number 2 (2006) pages 179200.
PDF or Journal or Slides from a Talk
 When is negativity not a problem for the ultradiscrete limit? with Stéphane Lafortune was published as Journal of Mathematical Physics 47, 103510 (2006).
Journal or arXiv
 TauFunctions, Grassmannians and Rank One
Conditions with Michael Gekhtman was published as The
Journal of Computational and Applied Mathematics 202 (2007) 8087.
Journal
 Universality of Rank 6 Plücker Relations and Grassmann
Cone Preserving Maps with Takahiro Shiota, Kathryn Pedings and Amy
Reiszl was published as The Proceedings of the American Mathematical Society 136 (2008) 7787.
arXiv
or
Journal
 Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy with Maarten Bergvelt and Michael Gekhtman was published as Mathematical Physics, Analysis and Geometry 12 (2009) 181200.
arXiv or Journal
 Factorization and Resultants of Partial Differential Operators with Emma Previato was published as Mathematics in Computer Science 4 (2010) 169184.
(The Mathematica notebook containing the commands for multiplying, conjugating and taking resultants of partial differential operators described in the paper is available here for download.)
 Duality and Collisions of Harmonically Constrained Calogero Particles was published as Contemporary Mathematics (2013) 593 pp. 109123.
PDF
 Bispectrality of NComponent KP Wave Functions: A Study in NonCommutativity
was published as SIGMA 11 (2015), 087, 22 pages
Journal or arXiv
 Factorization of a Matrix Differential Operator Using Functions in its Kernel (to appear in The American Mathematical Monthly)
arXiv
 Recurrence Relations for Exceptional Hermite Polynomials with D. GomezUllate, A. Kuijlaars and R. Milson The Journal of Approximation Theory (2016), pp. 116
arXiv
Journal
 On Factoring an Operator Using Elements of its Kernel (under review)
arXiv
Books
Other Mathematics Related Publications:

Student Answer Manual to accompany "Calculus" by HughesHallett,
Gleason, et al. John Wiley & Sons, 1993 (with S.A. Mallozzi,
A.H. Wang and G. Zhang).

Book Review: Imaginary
Numbers in the Notices of the AMS, Volume 47 Number 7, August 2000.

Book Review: Cryptonomicon
in the Notices of the AMS, Volume 46 Number 11, December 1999.

Letter to the Editor
in the Notices of the AMS, Volume 44 Number 6. (On Calculus Education.)

Letter to the Editor
in the Notices of the AMS, Volume 42 Number 10. (On typesetting preferences
of mathematicians.)

Letter to the Editor
in the Notices of the AMS, Volume 43 Number 5. (On the need for mathematical
exposition to nonmathematicians.)
 Letter to
the Editor in the Notices of the AMS, Volume 49 Number 6. (On the
connection between mathematics and insanity implicit in works of fiction
such as the film A Beautiful Mind.)
 Unreasonable
Effectiveness, a short story was published in Math Horizons
magazine.
 "Mathematics in Fiction: An Interdisciplinary Course" appeared in
PRIMUS Volume XIII Number 1, March 2003, Pages 116.
 Book Review: "It Must Be Beautiful" in the American Mathematical
Monthly, October 2003.
 Book Review: "After Math, The Fractal Murders and Other
Mathematical Murder Mysteries" in the AMS Notices, October 2003,
10871092.
 "Mathematics in Science Fiction" in Math Horizons, April 2004,
57.
 Book Review: "PopCo" published in the AMS Notices, February 2006.
 Book Review: "Pythagorean Crimes" published in the AMS Notices, January 2009.
 My short story On the Quantum Theoretic Implications of Newton's Alchemy has been published in Analog (October 2007), Esli (February 2008) and the book The Shape of Content (AK Peters Publishing, 2008).
 Book Review: "After Genius" in the December 2010 issue of the Mathematical Intelligencer.
 My essay "Fictional Women in Mathematics" appeared in the January 2011 newletter of the AWM.
 Bispectrality and Duality: A PDF copy of the talk I gave at the 2012 Joint Mathematics Meeting in Boston reviewing progress on my "research program" aiming to demonstrate a correspondence between the actionangle duality of integrable particle systems and the bispectral property. The talk mentions a bit about the quantum correspondence, but focuses especially on the classical case.
 "A Survey of Fictional Mathematics in Literature" in Mathematics and Popular Culture: Essays on Appearances in Film, Fiction, Games, Television and Other Media (Sklar and Sklar, Eds.), McFarland 2012.
(Return to the top of the page)
Faculty List for Math Department
Department of Mathematics Homepage
College of Charleston Homepage
