Welcome to my professional Web page

Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: shamseddine_June13-08

 

Currently, I am an Associate Professor in the Department of Physics and Astronomy and an Adjunct Professor in the Department of Mathematics at the University of Manitoba. I am also a member of the Winnipeg Institute for Theoretical Physics and an associate at the Center for Advanced Mathematical Sciences at the American University of Beirut.

 

Contact Information

Education

Professional Experience

  • May 15, 2008- : Associate Professor in the Department of Physics and Astronomy at the University of Manitoba
  • July 1, 2011- : Adjunct Professor in the Department of Mathematics at the University of Manitoba
  • August 15, 2007- May 14, 2008: Tenured Associate Professor in the Department of Mathematics at Western Illinois University.
  • August, 2004- May 14, 2008: Graduate Program Director in the Department of Mathematics at Western Illinois University.
  • August 18, 2003- August 15, 2007: Assistant Professor (tenure-track) in the Department of Mathematics at Western Illinois University.
  • August 4, 2000- Present: Associate at the Center for Advanced Mathematical Sciences at the American University of Beirut.
  • May 29-July 23, 2007: Visiting Professor in the Department of Mathematics at the University of Wisconsin- Eau Claire.
  • July 1-July 31, 2006: Visiting Assistant Professor in the Department of Physics and Astronomy at Michigan State University.
  • July 1-July 31, 2005: Visiting Assistant Professor in the Department of Physics and Astronomy at Michigan State University.
  • June 1-June 30, 2005: Visiting Research Scientist in the Department of Mathematics at the University of Wisconsin- Eau Claire.
  • Summer 2002: Visiting Assistant Professor in the Department of Physics and Astronomy at Michigan State University.
  • January 1, 2001- August 15, 2003: Full-time Visiting Research Instructor in the Department of Mathematics at Michigan State University.
  • January 1, 2000- December 31, 2000: Half-time Visiting Research Instructor in the Department of Mathematics and half-time Research Associate at the National Superconducting Cyclotron Laboratory at Michigan State University.
  • Spring 1994: Teaching Assistant, Chemistry Department, Michigan State University.
  • September 1993-December 1999: Research assistant, Beam Physics Theory group, National Superconducting Cyclotron Laboratory, Michigan State University.
  • Summer 1989: Research assistant, Department of Physics and Astronomy, Michigan State University.
  • 1988-1990: Teaching Assistant, Department of Physics and Astronomy, Michigan State University.
  • Academic year 1987-1988: Teaching Assistant, Department of Physics, American University of Beirut.

Refereed Publications

I.                 Books

  • Advances in p-Adic and Non-Archimedean Analysis, Proceedings of the 10th International Conference on p-Adic and Non-Archimedean Analysis, Martin Berz and Khodr Shamseddine, editors, Contemporary Mathematics, American Mathematical Society, Volume 508, 2010, ISBN 978-0-8218-4740-4.

II.            Papers

Invited Talks at Conferences

  • Absolute and relative extrema, the mean value theorem and the inverse function theorem for analytic functions on a Levi-Civita field, 11th International Conference on P-adic Functional Analysis, Université Blaise Pascal, Clermont-Ferrand, France, July 5-9, 2010.
  • Analysis on a non-Archimedean field extension of the real numbers and applications, The Sixth Conference on Function Spaces, Southern Illinois University- Edwardsville, Illinois, USA, May 18-22, 2010.
  • Analysis on the Levi-Civita field, a brief overview, Tenth International Conference on P-Adic and Non-Archimedean Analysis, Michigan State University, East Lansing, Michigan, USA, June 30- July 3, 2008.
  • Intermediate value theorem for analytic functions on a Levi-Civita field, Ninth International Conference on P-adic Functional Analysis, University of Concepcion, Concepcion, Chile, July 10-14, 2006.
  • Analytical properties of power series on Levi-Civita fields, Eighth International Conference on P-adic Functional Analysis, Clermont-Ferrand, France, July 5-9, 2004.
  • Measure theory and integration on the Levi-Civita field, Seventh International Conference on P-adic Functional Analysis, Nijmegen, The Netherlands, June 17-21, 2002.
  • The differential algebraic structure of the Levi-Civita field and applications, Ninth International Colloquium on Numerical Analysis and Computer Science with Applications, Plovdiv, Bulgaria, August 12-17, 2000.
  • Convergence on the Levi-Civita field and study of power series, Sixth International Conference on P-adic Functional Analysis, Ioannina, Greece, July 2-9, 2000.
  • Power series on the Levi-Civita field, Eighth International Colloquium on Numerical Analysis and Computer Science with Applications, Plovdiv, Bulgaria, August 13-18, 1999.

Contributed Talks at Conferences

  • The Non-Archimedean Field R-script, Overview and Applications, International Conference on Scientific Computations, LAU, Beirut, Lebanon, March 1999.
  • Non-Archimedean Structures as Differentiation Tools, Second LAAS International Conference on Computer Simulation, AUB, Beirut, Lebanon, September 1997.
  • Exception Handling in Derivative Computation with Non-Archimedean Calculus, SIAM 96: Second International Workshop on Industrial and Applied Mathematics, Santa Fe, New Mexico, February 1996.

Invited Talks, Seminars and Colloquia at Universities

  • Departments of Mathematics (Joint Mathematics Colloquium), Universidad del Bio-Bio and Universidad de Concepcion, Concepcion, Chile, December 5, 2011.
  • Department of Mathematics, American University of Beirut, Beirut, Lebanon, July 21, 2011.
  • Department of Mathematics, University of Wisconsin- Eau Claire, December 17, 2008.
  • Winnipeg Institute of Theoretical Physics, November 5, 2008.
  • Winnipeg Institute of Theoretical Physics, October 22, 2008.
  • Department of Mathematics, University of Wisconsin- Eau Claire, July 7, 2007.
  • Department of Mathematics, University of Wisconsin- Eau Claire, June 21, 2007.
  • Department of Physics & Astronomy, University of Manitoba, November 24, 2006.
  • Department of Mathematics, University of Manitoba, November 24, 2005.
  • Center for Advanced Mathematical Sciences (CAMS), American University of Beirut, Beirut, Lebanon, August 12, 2005.
  • Center for Research in Applied Mathematics & Statistics (CRAMS), Business and Computer University College, Beirut, Lebanon, January 7, 2005.
  • Center for Advanced Mathematical Sciences (CAMS), American University of Beirut, Beirut, Lebanon, January 5, 2005.
  • Department of Mathematics, Western Illinois University, November 11, 2004.
  • Department of Mathematics, University of Wisconsin- Eau Claire, July 13, 2004.
  • Department of Physics and Astronomy, Michigan State University, June 18, 2004.
  • Department of Mathematics, University of Wisconsin- Eau Claire, April 30, 2004.
  • Department of Mathematics, Western Illinois University, February 5, 2004.
  • Department of Mathematics, Western Illinois University, February 14, 2003.
  • Department of Mathematics and Computer Science, Lawrence Technological University, May 14, 2002.
  • Department of Mathematics, Michigan State University, October 8, 2001.
  • Center for Advanced Mathematical Sciences (CAMS), American University of Beirut, Beirut, Lebanon, July 19, 2000.
  • National Superconducting Cyclotron Laboratory, Michigan State University, November 24, 1999.
  • Department of Mathematics, American University of Beirut, Beirut, Lebanon, March 24, 1999.

Research Interests

My research interests and activities include various areas of non-Archimedean Analysis: power series and analytic functions, measure theory and integration, optimization, existence and uniqueness of solutions of differential equations, complex analysis and multivariable analysis. The focus of my research has been on the Levi-Civita fields which were first introduced by the Italian mathematician Tullio Levi-Civita at the end of the nineteenth century. Of those Levi-Civita fields, one (which we denote by R-script) is of particular interest; it is shown to be the smallest non-Archimedean field extension of the real numbers that is complete in the order topology and real closed. In fact, R-script is small enough so that the numbers of the field can be implemented on a computer; and this allows for many useful applications, one of which is the fast and accurate computation of the derivatives of real-valued functions up to high orders.

We have studied convergence of sequences and series in two different topologies, which led to an exhaustive study of power series. A handful of people had investigated power series on the Levi-Civita fields before, but all the previous studies had been restricted to the special case of power series with real coefficients. We have dropped that restriction and showed that power series on Levi-Civita fields have all the nice smoothness properties that real power series have. In particular, they satisfy the intermediate value theorem, the extreme value theorem, the mean value theorem and the inverse function theorem; they are infinitely often differentiable; and they are re-expandable around any point within their domain of convergence.

While it is a known fact that conventional continuity or differentiability are not sufficient to guarantee that a function on a closed interval of a non-Archimedean field be bounded or satisfy any of the common theorems of real calculus, we have shown that under mild conditions, differentiability is sufficient for the function to assume all intermediate values and a differentiable inverse function. We also showed that conventional differentiability is not the right one to study optimization questions on non-Archimedean fields in general; and based on a stronger concept of differentiability, we studied finite-dimensional optimization both with and without constraints. In both cases, we derived necessary and sufficient conditions of first and second order for a function to have a local minimum at a point of its domain.

We developed a measure theory and integration on the Levi-Civita field R-script. We introduced a measure that proved to be a natural generalization of the Lebesgue measure on the field of the real numbers and have similar properties. Then we introduced a family of simple functions from which we obtained a larger family of measurable functions and derived a simple characterization of such functions. We studied the properties of measurable functions, we showed how to integrate them over measurable sets, and we showed that the resulting integral satisfies similar properties to those of the Lebesgue integral of Real Analysis.

We studied two topologies on R-script: the valuation topology induced by the order on the field, and another weaker topology induced by a family of semi-norms, which we call weak topology. We showed that each of the two topologies results from a metric on R-script, that the valuation topology is not a vector topology while the weak topology is, and that R-script is complete in the valuation topology while it is not in the weak topology. Then we studied the properties of both topologies in detail; in particular, we gave simple characterizations of open, closed, and compact sets in both topologies. Finally, we showed that the metric which induces the weak topology is translation invariant.

Building on my previous research and benefiting from new collaborations with colleagues in the Department of Physics and Astronomy (in particular, theoretical physicists) and in the Department of Mathematics (in particular, analysts), I am establishing a research program in Non-Archimedean Analysis at the University of Manitoba. The long term aim of my research program is to develop a complete analysis which holds for any real closed Cauchy-complete non-Archimedean field extension F of the field of real numbers R. The theorem of Hahn entails that any such field F is isomorphic to a subfield of a field of generalized power series with coefficients in R and exponents forming a well-ordered subset of some ordered abelian group G. As a part of my research program, I have designed several research projects, any one of which (or, in some cases, a combination thereof) could also be a suitable topic for an interested student's M.Sc. or Ph.D. thesis.

 

Teaching at University of Manitoba

 

 

  • Fall 2011: on sabbatical leave

 

  • Winter 2011:
    • PHYS 2490, Theoretical Physics II
    • PHYS 3640, Electro- and Magnetodynamics and Special Relativity

 

  • Fall 2010: PHYS 7590, Electromagnetic Theory

 

  • Winter 2010:
    • PHYS 2490, Theoretical Physics II
    • PHYS 3640, Electro- and Magnetodynamics and Special Relativity

 

  • Fall 2009: PHYS 7590, Electromagnetic Theory

 

  • Winter 2009:
    • PHYS 2490, Theoretical Physics II
    • PHYS 3640, Electro- and Magnetodynamics and Special Relativity

Honor Societies and Awards

  • Nominated for the J. S. Frame Teaching Excellence Award for Faculty, Spring 2003, Department of Mathematics, Michigan State University.
  • Nominated for the J. S. Frame Teaching Excellence Award for Faculty, Spring 2002, Department of Mathematics, Michigan State University.
  • Hariri Foundation alumnus.
  • Member of The Honor Society of Phi Kappa Phi.
  • Member of Phi Beta Delta, the Honor Society for International Scholars.
  • BS in Physics with High Distinction, American University of Beirut, June 1988.
  • Philip Hitti Award, American University of Beirut, June 1988, for graduating with the highest average in the Faculty of Arts and Sciences.
  • Dean's Honor List, faculty of Arts and Sciences, American University of Beirut, 1986-1988.
  • Malcolm Kerr Award, American University of Beirut, 1986-1988.

Professional Societies

Languages

  • Arabic: fluent (reading, speaking and writing).
  • English: fluent (reading, speaking and writing).
  • French: good (reading, speaking and writing).

Maintained by K. Shamseddine (last updated July 6, 2011). Top of home page.