• Contact Information
• About the classes I teach
• About my Area of Research
• Publications
• Personal Information and Links

Contact Information for Alex Kasman

Phone: 843-953-8018
Fax: 843-953-1410

e-mail: kasmana@cofc.edu

Office: My office is in room 336 RSS. (That's the Robert Scott Small Building, directly across from Maybank Hall.)

Office Hours: This semester I can be found in my office at the following times: Monday 10-11 and Wednesday 2-3..

(If you would like to meet with me at another time, please write or call 843-953-8018 and I would be happy to set up an appointment.)

Alex Kasman's Teaching

In Fall 2024, I am teaching MATH 120 (Introductory Calculus) and MATH 221 (Multivariable Calculus).

Office Hours: This semester I can be found in my office at the following times: Monday 10-11 and Wednesday 2-3..

(If you would like to meet with me at another time, please write or call 843-953-8018 and I would be happy to set up an appointment.)

Faculty List for Math Department
Department of Mathematics Homepage
College of Charleston Homepage

Alex Kasman's Research

My own research is done on this `boundary' between mathematical physics and algebraic geometry.   Among the things I have written about are:

• The particle-like waves called `solitons'.
• The symmetry of linear wave equations known as `bispectrality'
• Algebro-geometric constructions for producing quantum integrable systems
• Rank one perturbations of operator identities and their connections to discrete integrable systems including the Bethe Ansatz and the Hirota Bilinear Difference Equation.
• The geometry of Grassmannian manifolds and associated functions which satisfy nonlinear partial differential equations of mathematical physics
• Classical and quantum integrable particle systems
• The geometry (spectral varieties) of commutative rings of partial differential operators.
• Solutions to the KP hierarchy associated to higher rank vector bundles over singular rational curves.

Faculty List for Math Department
Department of Mathematics Homepage
College of Charleston Homepage

Alex Kasman's Publications

Research Articles:

1. Bispectral KP Solutions and Linearization of Calogero-Moser Particle Systems was published in Communications in Mathematical Physics 172 (1995). 
   Journal or PDF or arXiv. 
2. Orthogonal Polynomials and Finite Toda Lattices appeared in The Journal of Mathematical Physics, 38 (1) 1997 pp. 247-254.
   PDF. 
3. Bispectral Darboux Transformations: the Generalized Airy Case by Mitchell Rothstein and myself was published in Physica D 102 (1997), no. 3-4 pp. 159-176.
   PDF or arXiv. 
4. Darboux Transformations from n-KdV to KP appeared in Acta Applicandae Mathematicae 49 no. 2 (1997) pp. 179-197.
   PDF. 
5. The Bispectral Involution as a Linearizing Map in "Caloger-Moser-Sutherland-Models", CRM Series in Mathematical Physics, JF van Diejen and L Vinet, eds. Springer (2000) pp. 221--230. 
6. Darboux Transformations and the Bispectral Problem in CRM Proceedings and Lecture Notes 14 American Mathematical Society (1998) pp.81-91. 
7. 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 Springer-Verlag (1998) pp. 77-90
8. D-modules and Darboux Transformations written jointly with Yuri Berest appeared in Letters in Mathematical Physics 43 (1998) pp. 279-294.
   PDF or arXiv.
9. Duality and Construction of Quantum Integrable Systems (with E. Horozov) Trends in mathematical physics (Knoxville, TN, 1998), 289--297, AMS/IP Stud. Adv. Math., 13, Amer. Math. Soc., Providence, RI, 1999
10. Spectral Difference Equations Satisfied by KP Soliton Wavefunctions was published as Inverse Problems 14 (1998) pp.1481-1487.
    PDF or arXiv. 
11. Kernel Inspired Factorizations of Partial Differential Operators appeared as The Journal of Mathematical Analysis and Applications 234/2 (1999) pp. 580-591.
    PDF. 
12. Grassmannians, Nonlinear Waves and Generalized Schur Functions was published in Contemporary Mathematics 246 (1999) pp. 163-174.
    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 https://arXiv.org/abs/math-ph/9811008v2.
13. Darboux Transformations of Bispectral Quantum Integrable Systems written jointly with Emil Horozov, was published as Letters in Mathematical Physics 49: 131-143, 1999.
    PDF or arXiv.
14. Finite Canonical Commutation Relations and Rational Nested Bethe Ansatz was published as Regular and Chaotic Dynamics 6 (2), 211-214 (2001).
    PDF or arXiv or journal. 
15. Commutative Partial Differential Operators written with Emma Previato was published as Physica D 152-153 (2001) 66-77
    PDF. 
16. Solitons and Almost-Intertwining Matrices with Michael Gekhtman appeared in the Journal of Mathematical Physics 42 8 (2001) 3540-3553.
    PDF or arXiv or journal. 
17. On the Quantization of a Self-Dual Integrable System was published as Journal of Physics A 23 (2001) 6307-6312.
    PDF.
18. 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) 557-5564.
    PDF.
19. Integrable Systems and Rank One Conditions for Rectangular Matrices with Michael Gekhtman was published as Theoretical and Mathematical Physics 133(2): 1498-1503 (2002) [and in Russian as Teoreticheskaya i Matematicheskaya Fizika Vol. 133 No. 2 pp. 211-217, 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!)
20. On KP Generators and the Geometry of the HBDE with Michael Gekhtman was published in The Journal of Geometry and Physics 56 (2006) 282-309.
    Journal or arXiv
21. On Decompositions of the KdV 2-Soliton with Nicholas Benes and Kevin Young was published as The Journal of Nonlinear Science Volume 16 Number 2 (2006) pages 179-200.
    PDF or Journal or Slides from a Talk
22. When is negativity not a problem for the ultra-discrete limit? with Stéphane Lafortune was published as Journal of Mathematical Physics 47, 103510 (2006).
    Journal or arXiv
23. Tau-Functions, Grassmannians and Rank One Conditions with Michael Gekhtman was published as The Journal of Computational and Applied Mathematics 202 (2007) 80--87.
    Journal
24. 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) 77-87.
    arXiv or Journal
25. 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) 181-200.
    arXiv or Journal
26. Factorization and Resultants of Partial Differential Operators with Emma Previato was published as Mathematics in Computer Science 4 (2010) 169-184.
    (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.)
27. Duality and Collisions of Harmonically Constrained Calogero Particles was published as Contemporary Mathematics (2013) 593 pp. 109--123.
    PDF
28. Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity was published as SIGMA 11 (2015), 087, 22 pages
    Journal or arXiv
29. Factorization of a Matrix Differential Operator Using Functions in its Kernel was published as The American Mathematical Monthly Vol. 123, No. 7 (August-September 2016), pp. 704-709
    arXiv Journal
30. Recurrence Relations for Exceptional Hermite Polynomials with D. Gomez-Ullate, A. Kuijlaars and R. Milson The Journal of Approximation Theory (2016), pp. 1-16
    arXiv or Journal
31. On Factoring an Operator Using Elements of its Kernel Communications in Algebra (2017) 45 pp. 1443-1451.
    arXiv or Journal
32. The Duplexing of the Genetic Code and Sequence-Dependent DNA Geometry Bulletin of Mathematical Biology 80 (10), 2734-2760 (2018).
    Journal or Downloadable Mathematica Notebook or Springer Nature Sharing
33. Quaternion-Valued Breather Soliton, Rational, and Periodic KdV Solutions (with John Cobb, Albert Serna, and Monique Sparkman) The Journal of Nonlinear Mathematical Physics 27:3, 429-452 (2020).
    arXiv or Journal
34. Did Sequence Dependent Geometry Influence the Evolution of the Genetic Code? (with Brenton LeMesurier) Contemporary Mathematics 746 pp.41-56 (2020).
    arXiv or Journal
35. The Adelic Grassmannian and Exceptional Hermite Polynomials (with Robert Milson) Mathematical Physics, Analysis and Geometry (2020) 23:40
    arXiv or Journal or Springer Nature Sharing

Books

• The Bispectral Problem CRM Proceedings and Lecture Notes Volume 14 (1999) Edited by John Harnad and Alex Kasman is available from the American Mathematical Society.
• Reality Conditions: Short Mathematical Fiction (2005), a collection of mathematically themed short stories was published by the Mathematical Association of America.
• Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs (2010) is part of the Student Mathematical Library Series of the American Mathematical Society.
• A second edition of Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs (2023) was published by the American Mathematical Society with many updates and improvements, including a completely new approach to KdV n-soliton interactions.

Other Mathematics Related Publications:

• Student Answer Manual to accompany "Calculus" by Hughes-Hallett, 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 non-mathematicians.)
• 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 1-16.
• 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, 1087-1092.
• "Mathematics in Science Fiction" in Math Horizons, April 2004, 5-7.
• Book Review: "PopCo" published in the AMS Notices, February 2006.
• DNA Solitons and Codon Bias: A PDF copy of a poster that I presented at Mathematics of DNA Structure, Function and Interactions (Institute of Mathematics and its Applications, September 2007).
• 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 action-angle 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.
• Book Review: "Machines Like Me / A Universe of Sufficient Size". Notices of the American Mathematical Society, 68, 1786-1789.
• "Uses of Chaos Theory and Fractal Geometry in Fiction" In Robert Tubbs and Alice Jenkins (Eds.), The Palgrave Handbook of Literature and Mathematics (pp. 129-147). Palgrave Macmillan, Cham. (2021)
• "Hidden Figures, Hidden Messages: The Construction of Mathematical Identities with Children’s Picturebooks" (with O. Fellus, D. Low, L. Guzmán, and R. Mason) For the Learning of Mathematics, 42(2), 2--8 (2022).

Faculty List for Math Department
Department of Mathematics Homepage
College of Charleston Homepage

Alex Kasman's Links

Check out these sites that I (in theory) maintain:

• The Mathematical Fiction Homepage: A continuously updated, searchable, browsable list of all of the works of fiction (novels, comic books, TV Shows, films, plays, etc.) I know which involve mathematics and/or mathematicians. Each entry includes a brief review of the mathematical content, ratings and comments from site visitors, as well as links to similar works.
• The Amanda Museum: This site was first created when my daughter was little and we wanted to share her drawings with relatives and friends far away. But, we stopped updating it when she finished high school. To see what she's doing now (as an art conservator) visit her Wix page.
• Square Root Farm in Denmark SC (a hobby of my wife and I which we hope will be a major part of our "retirement plan").

Faculty List for Math Department
Department of Mathematics Homepage
College of Charleston Homepage