Welcome to my professional Web page |
Currently,
I am a tenured (full) 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 former Ian C. P. Smith
Integrated Science Faculty Scholar (July1, 2017- December 31, 2021), a former
Associate Head for Undergraduate Studies in the Department of Physics and
Astronomy (July 1, 2018- June 30, 2021), a former Director of the Winnipeg Institute for Theoretical
Physics (January 1, 2015- December 31, 2016), and an
associate at the Center
for Advanced Mathematical Sciences at the American
University of Beirut. Prior to arriving at the University of Manitoba, I
was a tenured associate professor in the Department of Mathematics
at Western Illinois University.
I.
Books
II.
Papers
1. On the Complex Levi-Civita field: Algebraic and Topological Structures, and Foundations for Analysis, Khodr Shamseddine, Khayyam Journal of Mathematics, accepted.
2. On a new measure on the Levi-Civita field ℜ,
Mateo Restrepo Borrero, Vatsal Srivastava, and Khodr Shamseddine, p-Adic Numbers, Ultrametric
Analysis, and Applications, Volume 15 # 1, 2023, pp. 1-22.
3. A weaker smoothness criterion for the
inverse function theorem, intermediate value theorem, and mean value theorem in
a non-Archimedean setting, Khodr Shamseddine and Aaron Shalev, p-Adic Numbers, Ultrametric
Analysis, and Applications, Volume 14, Suppl. # 1, 2022, pp. S45-S58.
4. On the analyticity of WLUD^{∞}
functions of one variable and WLUD^{∞} functions of several
variables in a complete non-Archimedean valued field, Khodr Shamseddine,
Proceedings of the Edinburgh Mathematical Society, Volume 65, 2022, pp.
691-704.
5. On
non-Archimedean valued fields: a survey of algebraic, topological
and metric structures, analysis and applications, Khodr Shamseddine
and Angel Barria Comicheo, Advances in Non-Archimedean Analysis and
Applications - The p-adic Methodology, a
special volume in STEAM-H: Science, Technology, Engineering, Agriculture,
Mathematics & Health, 2021, pp. 209-254.
6. Taylor's theorem, the inverse function theorem and the implicit function theorem for weakly locally uniformly differentiable functions on non-Archimedean spaces, Khodr Shamseddine, p-Adic Numbers, Ultrametric Analysis, and Applications, Volume 13 # 2, 2021, pp. 148-165.
7. On computational applications of the Levi-Civita field, Darren Flynn and Khodr Shamseddine, Journal of Computational and Applied Mathematics, Volume 382, 2021.
8. On the topological structure of the Hahn field and convergence of power series, Darren Flynn and Khodr Shamseddine, Indagationes Mathematicae, Volume 30 # 5, 2019, pp. 773-795.
9. On an operator theory on a Banach space of countable type over a Hahn field, Khodr Shamseddine and Changying Ding, Proceedings of the 11th ISAAC Congress (Växjö, Sweden, August 2017), Analysis, Probability, Applications, and Computation, April 2019, pp. 267-282.
10. Summary on non-Archimedean valued fields, Angel Barria Comicheo and Khodr Shamseddine, Contemporary Mathematics, American Mathematical Society, Volume 704 (Advances in Ultrametric Analysis), 2018, pp. 1-36.
11. Calculus on a non-Archimedean field extension of the real numbers: inverse function theorem, intermediate value theorem and mean value theorem, Gidon Bookatz and Khodr Shamseddine, Contemporary Mathematics, American Mathematical Society, Volume 704 (Advances in Ultrametric Analysis), 2018, pp. 49-67.
12. On Integrable Delta Functions on the Levi-Civita Field, Darren Flynn and Khodr Shamseddine, p-Adic Numbers, Ultrametric Analysis, and Applications, Volume 10 # 1, 2018, pp. 32-56.
13. Positive operators on a free Banach space over the Levi-Civita field, Jose Aguayo, Miguel Nova and Khodr Shamseddine, p-Adic Numbers, Ultrametric Analysis, and Applications, Volume 9 # 2, 2017, pp. 122-137.
14. A local mean value theorem for functions on non-Archimedean field extensions of the real numbers, Khodr Shamseddine and Gidon Bookatz, p-Adic Numbers, Ultrametric Analysis, and Applications, Volume 8 # 2, 2016, pp. 160-175.
15. Measure theory and Lebesgue-like integration in two and three dimensions over the Levi-Civita field, Khodr Shamseddine and Darren Flynn, Proceedings of the 13^{th} International Conference on p-Adic Functional Analysis, Contemporary Mathematics, American Mathematical Society, Volume 665 (Advances in Non-Archimedean Analysis), 2016, pp. 289- 325.
16. On the solutions of linear ordinary differential equations and Bessel-type special functions on the Levi-Civita field, Alpar Meszaros and Khodr Shamseddine, Journal of Contemporary Mathematical Analysis, Volume 50 # 2, 2015, pp. 53-62.
17. Analysis on the Levi-Civita field and computational applications, Khodr Shamseddine, Applied Mathematics and Computation, Volume # 255, 2015, pp. 44-57.
18. Inner product on B*-algebras of
operators on a free Banach space over the Levi-Civita field, Jose Aguayo, Miguel Nova and Khodr Shamseddine, Indagationes Mathematicae, Volume 26 #
1, 2015, pp. 191-205.
19. A brief survey of the study
of power series and analytic functions on the Levi-Civita fields, Khodr Shamseddine, Proceedings of the 12th International Conference on p-Adic
Functional Analysis, Contemporary
Mathematics, American Mathematical Society, Volume 596 (Advances in Ultrametric Analysis), 2013, pp. 269-280.
20. One-variable and multi-variable calculus
on a non-Archimedean field extension of the real numbers, Khodr Shamseddine, p-Adic
Numbers, Ultrametric Analysis, and Applications,
Volume 5 # 2, 2013, pp. 160-175.
21. Characterization of compact and
self-adjoint operators on Free Banach spaces of countable type over the complex
Levi-Civita field, Jose Aguayo, Miguel Nova and Khodr Shamseddine, Journal of
Mathematical Physics, Volume 54 # 2, 2013.
22. New results on integration on the
Levi-Civita field, Khodr Shamseddine, Indagationes Mathematicae, Volume 24 #
1, 2013, pp. 199-211.
23. Preliminary notes on Fourier series
for functions on the Levi-Civita field, Khodr Shamseddine and William Grafton, International
Journal of Mathematical Analysis, Volume 6 # 19, 2012, pp.
941-950.
24. On locally uniformly
differentiable functions on a complete non-Archimedean ordered field extension
of the real numbers, Khodr Shamseddine and Todd Sierens, ISRN
Mathematical Analysis, Volume 2012, Article ID 387053, 20 pages.
25. Absolute and relative
extrema, the mean value theorem and the inverse
function theorem for analytic functions on a Levi-Civita field, Khodr Shamseddine, Contemporary Mathematics, American Mathematical Society, Volume 551
(Advances in Non-Archimedean Analysis), 2011, pp. 257-268.
26. Nontrivial order preserving
automorphisms of non-Archimedean fields, Khodr Shamseddine, Contemporary
Mathematics, American Mathematical Society, Volume 547 (Function Spaces in
Modern Analysis), 2011, pp. 217-225.
27. On the topological structure of
the Levi-Civita field, Khodr
Shamseddine, Journal of Mathematical Analysis and Applications, Volume 368,
2010, pp. 281-292.
28. Analysis on the Levi-Civita
field, a brief overview, Khodr
Shamseddine and Martin Berz, Contemporary
Mathematics, American Mathematical Society, Volume 508 (Advances in p-Adic
and Non-Archimedean Analysis), 2010, ISBN 978-0-8218-4740-4,
pp. 215-237.
29. The implicit function theorem in a
non-Archimedean setting, Khodr
Shamseddine, Trevor Rempel and Todd Sierens, Indagationes Mathematicae, Volume 20 # 4, 2009, pp. 603-617. [This
paper is the result of my work with two NSERC-USRA students at the University
of Manitoba in Summer 2009]
30. Intermediate value theorem for analytic
functions on a Levi-Civita field, Khodr
Shamseddine and Martin Berz, Bulletin
of the Belgian Mathematical Society-Simon Stevin, Volume 14, 2007, pp.
1001-1015.
31. Generalized power series on a
non-Archimedean field, Khodr
Shamseddine and Martin Berz, Indagationes
Mathematicae, Volume 17 # 3, 2006, pp. 457-477.
32. Analytical properties of power
series on Levi-Civita fields, Khodr
Shamseddine and Martin Berz, Annales Mathématiques Blaise Pascal, Volume 12 # 2, 2005, pp.
309-329.
33. Constrained
second order optimization on non-Archimedean fields, Khodr Shamseddine and Vera Zeidan, Indagationes Mathematicae, Volume 14 # 1, 2003, pp. 81-101.
34. Measure
theory and integration on the Levi-Civita field, Khodr Shamseddine and Martin Berz, Contemporary Mathematics, American Mathematical Society, Volume 319
(Ultrametric Functional Analysis), 2003, ISBN: 0-8218-3320-0, pp. 369-387.
35. Intermediate
values and inverse functions on non-Archimedean fields, Khodr Shamseddine and Martin Berz, International Journal of Mathematics and
Mathematical Sciences, Volume 30 # 3, 2002, pp. 165-176.
36. On the existence and uniqueness of
solutions of differential equations on the Levi-Civita field, Khodr Shamseddine, International Journal of Differential Equations and Applications,
Volume 4 # 4, 2002, pp. 375-386.
37. Infinite
dimensionality of the
solution space of y’=0 on non-Archimedean fields, Khodr Shamseddine, International Journal of Differential Equations and Applications,
Volume 4 # 1, 2002, pp. 25-30.
38. One-dimensional
optimization on non-Archimedean
fields, Khodr Shamseddine and
Vera Zeidan, Journal of Nonlinear and
Convex Analysis, Volume 2 # 3, 2001, pp. 351-361.
39. Convergence
on the Levi-Civita field and study of power series, Khodr Shamseddine and Martin Berz, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker,
Proceedings of the Sixth International Conference on P-adic
Analysis, July 2-9, 2000, ISBN 0-8247-0611-0, pp. 283-299.
40. The
differential algebraic structure of the Levi-Civita field and applications,
Khodr Shamseddine and Martin Berz, International Journal of Applied Mathematics,
Volume 3 # 4, 2000, pp. 449-464.
41. Power
series on the Levi-Civita field, Khodr
Shamseddine and Martin Berz, International
Journal of Applied Mathematics, Volume 2 # 8, 2000, pp. 931-952.
42. Exception
handling in derivative computation with non-Archimedean calculus, Khodr Shamseddine and Martin Berz, Computational
Differentiation: Techniques, Applications, and Tools, M. Berz, C. Bischof, G.
Corliss, A. Griewank, eds., SIAM, Philadelphia, Penn, 1996, pp. 37-51.
43. COSY
INFINITY and its applications to nonlinear dynamics, Martin Berz, Kyoko
Makino, Khodr Shamseddine, Georg
Hoffstatter and Weishi Wan, Computational
Differentiation: Techniques, Applications, and Tools, M. Berz, C. Bischof, G.
Corliss, A. Griewank , eds., SIAM,
Philadelphia, Penn, 1996, pp. 363-367.
1. On the complex Levi-Civita field: algebraic and topological structures, and foundations for analysis, 15^{th} International Conference on p-adic Analysis and Dynamical Systems, an online meeting, July 11 and 14, 2023.
2. Introduction to Non-Archimedean Analysis (mini-course: 3 hours), the Canadian Mathematical Society Summer Meeting, St. John’s, Newfoundland, June 3-6, 2022.
3. On non-Archimedean Valued Fields and Ultrametric Spaces: the Hahn Fields and Levi-Civita Fields, CIMPA-CIMAT Research School, p-Adic Numbers, Ultrametric Analysis, and Applications, Guanajuato, Mexico, May 23-31, 2022.
4. On non-Archimedean valued fields: a survey of algebraic, topological and metric structures, analysis and applications, Eighth International Conference on p-adic Mathematical Physics and its Applications, an online conference, May 17-28, 2021.
5. Calculus theorems for locally uniformly differentiable functions on a non-Archimedean ordered field extension of the real numbers, Seventh International Conference on p-adic Mathematical Physics and its Applications, Covilha, Portugal, September 30-October 4, 2019.
6. One-variable and Multi-variable Integral Calculus over the Levi-Civita Field and Applications, Sixth International Conference on p-adic Mathematical Physics and its Applications, Mexico City, Mexico, October 23-27, 2017.
7. On the Levi-Civita Fields: Introduction and Summary of Selected Recent Research, 11^{th} Congress of the International Society for Analysis, its Applications and Computations (ISAAC), Växjö, Sweden, August 14-18, 2017.
8. Calculus on a non-Archimedean field extension of the real numbers: The intermediate value theorem, mean value theorem, inverse function theorem and implicit function theorem, 14^{th} International Conference on p-Adic Functional Analysis, Aurillac, France, June 30-July 5, 2016.
9. On the Levi-Civita fields: introduction and survey of recent research, 14^{th} International Conference on p-Adic Functional Analysis, Aurillac, France, June 30-July 5, 2016.
10. One-variable and Multi-variable Integral Calculus over the Levi-Civita Field and Applications, NUMTA2016 (Numerical Computations: Theory and Applications), The 2^{nd} International Conference and Summer School, Calabria, Italy, June 19-25, 2016.
11. Characterization of compact and self-adjoint operators, and study of positive operators on a Banach space over a non-Archimedean field, International Conference on p-Adic Mathematical Physics and its Aplications, Belgrade, Serbia, September 7-12, 2015.
12. New results on the Lebesgue-like measure and integration theory on the Levi-Civita field and applications, 13^{th} International Conference on p-Adic Functional Analysis, Paderborn, Germany, August 12-16, 2014.
13. On positive operators on a Banach space over the complex Levi-Civita field, The Seventh Conference on Function Spaces, Southern Illinois University- Edwardsville, Illinois, USA, May 20-24, 2014.
14. Preliminaries in non-Archimedean Functional Analysis, The Seventh Conference on Function Spaces, Southern Illinois University- Edwardsville, Illinois, USA, May 20-24, 2014.
15. Analysis on non-Archimedean ordered field extensions of the real numbers and applications, NUMTA2013 (Numerical Computations: Theory and Applications) International Conference and Summer School, Falerna, Italy, June 16-23, 2013.
16.
B*-algebras of operators and study of positive
operators on a free Banach space of countable type over the complex Levi-Civita
field, 12th
International Conference on p-Adic Functional
Analysis, University of Manitoba, Winnipeg, Canada, July 2-6, 2012.
17.
(Co-author, talk given by Jose Aguayo)
Characterization of Compact and self-adjoint operators on free Banach spaces of
countable type over the complex Levi-Civita field, 12th
International Conference on p-Adic Functional
Analysis, University of Manitoba, Winnipeg, Canada, July 2-6, 2012.
18.
(Co-author, talk given by Todd Sierens) On
locally uniformly differentiable functions: the Inverse Function Theorem and
the Implicit Function Theorem in a non-Archimedean setting, 12th
International Conference on p-Adic Functional
Analysis, University of Manitoba, Winnipeg, Canada, July 2-6, 2012.
19.
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.
20.
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.
21.
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.
22.
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.
23.
Analytical
properties of power series on Levi-Civita fields, Eighth International
Conference on P-adic Functional Analysis,
Clermont-Ferrand, France, July 5-9, 2004.
24.
Measure
theory and integration on the Levi-Civita field, Seventh International
Conference on P-adic Functional Analysis, Nijmegen,
The Netherlands, June 17-21, 2002.
25.
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.
26.
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.
27.
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
Invited
Talks, Seminars and Colloquia at Universities
My research interests and
activities include various areas of non-Archimedean Analysis: one-variable and
multi-variable calculus, power series and analytic functions, measure theory
and integration, optimization, existence and
uniqueness of solutions of differential equations, complex analysis, and
functional analysis over non-Archimedean valued fields. 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) is of particular interest; it is shown to be the smallest
non-Archimedean ordered field extension of the real numbers that is complete in
the topology induced by the order and real closed. In fact, R 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 in my
research group two topologies on R: 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, that the valuation topology is not
a vector topology while the weak topology is, and that R 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.
We studied convergence of
sequences and series in both topologies mentioned above, 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
dropped that restriction and showed that power series on the 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 ordered
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. 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 generalized the results to two and three
dimensions. In particular, we defined a Lebesgue-like
measure on R^{2} (resp. R^{3}). Then we defined measurable functions on
measurable sets using analytic functions in two (resp. three) variables and
showed how to integrate those measurable functions using iterated integration.
The resulting double (resp. triple) integral satisfies similar properties to
those of the single integral as well as those properties satisfied by the
double and triple integrals of real calculus.
Together with my collaborators Jose Aguayo and Miguel
Nova from Concepcion (Chile), we developed an operator theory on the Banach
space c_{0} over C:=R+iR,
where c_{0} denotes the space
of all null sequences of elements of C.
The natural inner product on c_{0}
induces the sup-norm of c_{0}.
We showed that c_{0} is not
orthomodular; then we characterized those closed subspaces of c_{0} with an orthonormal
complement with respect to the inner product. Such a subspace, together with
its orthonormal complement, defines a special kind of projection, the so-called
normal projection. We presented a characterization of such normal projections
as well as a characterization of other kinds of operators, the self-adjoint and
compact operators on c_{0}.
Then we worked on some B*-algebras of operators, including those mentioned
above; we studied normal and Hilbert-Schmidt operators; and finally, we studied
the properties of positive operators, which we then used to introduce a partial
order on the B*-algebra of compact and self-adjoint operators on c_{0} and studied the properties
of that partial order.
While the Levi-Civita field R is interesting to study in detail for the
reasons stated above, I have also expanded my research focus to include any
non-Archimedean field extension of the real numbers that is real
closed and complete in the topology induced by the order and whose Hahn group
is Archimedean; such a field is denoted by F.
For example, we studied the properties of weakly locally uniformly
differentiable functions at a point or on an open subset of F or F^{n} and we proved local
versions of the intermediate value theorem, the mean value theorem and Taylor's
theorem for weakly locally uniformly differentiable functions on F. We also proved the inverse function
theorem and implicit function theorem for weakly locally uniformly
differentiable functions from F^{n} to F^{n} and from F^{n} to F^{m}^{ }(m < n), respectively. Moreover, the
work on the topological structure as well as on the integration theory and its
applications on the Levi-Civita field R
has recently been extended to
the field F.
Training of Highly Qualified Personnel (at
U of M)
I.
Postdoctoral Fellows:
1. Angel Barria Comicheo (March
1-August 31, 2020); Department of Mathematics and Department of Physics and
Astronomy (joint appointment).
2. Angel Barria Comicheo (March
1-August 31, 2019); Department of Mathematics.
II.
Graduate Students
1. Arij Alameh (September 2021- );
candidate for M.Sc. in Physics.
2. Darren Flynn (September 2014- August
2019); PhD in Physics.
3. Angel Barria Comicheo (January 2013-
October 2018); PhD in Mathematics.
4. Andrew Senchuk (January 2011- May
2018; I was co-advisor, with advisor: Prof. Gerald Gwinner); PhD in Physics.
5. William Grafton (September 2013-
August 2016); M.Sc. in Mathematics.
6. Darren Flynn (July 2012- August
2014); M.Sc. in Physics.
III.
Undergraduate Students
o
Summer
Students
2.
Aaron
Shalev (2023); undergraduate summer student in the joint Math-Physics Honours program.
3.
Mateo
Restrepo Borrero (2022); MITACS Globalink intern
(from Colombia).
4.
Vatsal
Srivastava (2022); MITACS Globalink
intern (from India).
5.
Aaron
Shalev (2022); NSERC-USRA student in the joint Math-Physics Honours
program.
6.
Jeremy
Croitor (2021); NSERC indigenous -USRA student in the joint Math-Physics Honours program.
7.
Jeremy
Croitor (2020); NSERC indigenous -USRA student in the joint Math-Physics Honours program.
8. Yudong Chen (2019); MITACS Globalink intern (from China).
9. Zhenghang Du (2019); MITACS Globalink intern (from China).
10. Changying Ding (2017); MITACS Globalink intern (from China).
11. Jeremy Friesen (2017); NSERC-USRA
student in the joint Math-Physics Honours program.
12. Gidon Bookatz
(2016); undergraduate summer student in the joint Math-Physics Honours program.
13. Ryan Sherbo (2015); NSERC-USRA student
in the joint Math-Physics Honours program.
14. Gidon Bookatz
(2015); NSERC-USRA student in the joint Math-Physics Honours
program.
15. Gidon Bookatz
(2014); NSERC-USRA student in the joint Math-Physics Honours
program.
16. Gidon Bookatz
(2013); NSERC-USRA student in the joint Math-Physics Honours
program.
17. William Grafton (2012);
undergraduate summer student in the joint Math-Physics Honours
program.
18. James Roberts (2011); undergraduate
summer Honours student, Department of Physics at the
University of Winnipeg.
19. William Grafton (2011).
20. Todd Sierens (2010); undergraduate
summer student in the joint Math-Physics Honours
program; currently a PhD student at the University of Waterloo and the
Perimeter Institute.
21. Todd Sierens (2009); NSERC-USRA
student in the joint Math-Physics Honours program.
22. Trevor Rempel (2009); NSERC-USRA
student in the joint Math-Physics Honours program;
currently a PhD student at the University of Waterloo and the Perimeter
Institute.
o
Undergraduate
Honour Thesis:
21. Cheng Tang (2012-2013).
I.
At the University of Manitoba (May
2008- present)
o
Winter 2023: PHYS 7590, Electromagnetic Theory
o
Fall 2023:
Ø
PHYS
3496, Mathematical Physics II
Ø
PHYS 1020, General Physics I
o Winter 2023:
Ø PHYS 7590, Electromagnetic Theory
Ø PHYS 3496, Mathematical Physics II
o
Fall
2022: No teaching
o Winter 2022: on research leave
o
Fall 2021:
Ø
PHYS 3496, Mathematical Physics II
Ø
PHYS 7440, Foundations of Non-Archimedean
Analysis and Applications in Physics (a reading course)
o
Fall 2020: PHYS 3496, Mathematical Physics II
o Fall 2019: PHYS 3496, Mathematical
Physics II
o Winter 2019: PHYS 2496, Mathematical
Physics I
o Fall 2018: PHYS 3496, Mathematical
Physics II
o Winter 2018: on research leave
o Fall 2017: Teaching credit as an Ian
C. P. Smith Integrated Science (SIS) Faculty Scholar.
o Winter 2017: PHYS 2490, Theoretical
Physics II
o Fall 2016:
Ø PHYS 2390, Theoretical Physics I
Ø PHYS 3650, Classical Mechanics II
o Winter 2016: PHYS 2490, Theoretical
Physics II
o Fall 2015:
Ø PHYS 1020, General Physics I
Ø PHYS 2390, Theoretical Physics I
o Winter 2015: PHYS 2490, Theoretical
Physics II
o Fall 2014:
Ø PHYS 1020, General Physics I
Ø PHYS 2390, Theoretical Physics I
o Winter 2014: PHYS 2490, Theoretical
Physics II
o Fall 2013:
Ø PHYS 1020, General Physics I
Ø PHYS 2390, Theoretical Physics I
o
Summer
2013: MATH 8430, Non-Archimedean Operator Theory (a reading course)
o
Winter
2013:
Ø MATH 8430, Non-Archimedean Analysis
(a reading course)
Ø PHYS 2490, Theoretical Physics II
Ø PHYS 3640, Electro- and Magnetodynamics and Special Relativity
o
Fall
2012: PHYS 2390, Theoretical Physics I
o
Winter
2012:
Ø PHYS 2490, Theoretical Physics II
Ø PHYS 3640, Electro- and Magnetodynamics and Special Relativity
o
Fall
2011: on sabbatical leave
o
Winter
2011:
Ø PHYS 2490, Theoretical Physics II
Ø PHYS 3640, Electro- and Magnetodynamics and Special Relativity
o
Fall
2010: PHYS 7590, Electromagnetic Theory
o
Winter
2010:
Ø PHYS 2490, Theoretical Physics II
Ø PHYS 3640, Electro- and Magnetodynamics and Special Relativity
o
Fall
2009: PHYS 7590, Electromagnetic Theory
o
Winter
2009:
Ø PHYS 2490, Theoretical Physics II
Ø PHYS 3640, Electro- and Magnetodynamics and Special Relativity
o
Spring
2008
Ø MATH 133, Calculus and Analytic
Geometry
Ø MATH 391, Writing in the
Mathematical Sciences
o
Fall
2007
Ø MATH 137, Applied Calculus I
Ø MATH 651, Elements of Modern
Analysis
o
Spring
2007
Ø MATH 133, Calculus and Analytic
Geometry
Ø MATH 391, Writing in the Mathematical
Sciences
o
Fall
2006
Ø MATH 137, Applied Calculus I
Ø MATH 551, Methods of Classical
Analysis
o
Spring
2006
Ø MATH 133, Calculus and Analytic
Geometry
Ø MATH 391, Writing in the
Mathematical Sciences
o
Fall
2005
Ø MATH 137, Applied Calculus I
Ø MATH 599, Special Topics: Methods of
Classical Analysis
o
Spring
2005
Ø MATH 137, Applied Calculus I
o
Fall
2004
Ø MATH 137, Applied Calculus I
Ø MATH 430, Multivariable Calculus
o
Spring
2004
Ø MATH 137, Applied Calculus I
Ø MATH 435, Introduction to Real
Variables
o
Fall
2003
Ø MATH 137, Applied Calculus I
Ø MATH 311, Linear Algebra
o
2002-2003:
MATH 234, Multivariable Calculus
o
2001-2002:
MATH 234, Multivariable Calculus
o
Spring
2000, Fall 2000 and Spring 2001: MATH 235, Differential Equations.
I.
At the University of Manitoba (May
2008- present)
a.
PhD Students Advisory Committees
1. Iris Halilovic, PhD in Physics: May
2023- present
2. Brock Klippenstein, PhD in Physics:
April 2023- present
3. Naz Roshanshah, PhD in Physics: May
2021- present
4. Brett Meggison, PhD in Physics:
April 2021- present
5. Erica Franzmann, PhD in
Astrophysics: August 2015- September 2022 (successfully
defended her thesis)
6. Brad Cownden,
PhD in Physics: November 2015- July 2020 (successfully defended his thesis)
7. L.J. Zhou, PhD in Physics: May 2016-
December 2018 (successfully defended his thesis)
8. Ievgen Bilokopytov, PhD in Mathematics: November 2014-
December 2018 (successfully defended his thesis)
9. Mark McCrea, PhD in Physics: May
2011- January 2017 (successfully defended his thesis)
10. Chandra Podder; PhD in Mathematics:
Successfully defended his thesis in 2010
11. Mohammad Safi; PhD in Mathematics:
Successfully defended his thesis in 2010.
b.
M.Sc. Students Examining Committees
1. Brett Meggison, M.Sc. in Physics:
2020
2. Mitul Patel, M.Sc. in Physics: 2019
3. Mahnaz Alavinejad,
M.Sc. in Mathematics: 2016
4. Jesse Bellec, M.Sc. in Physics: 2015
5. Lindsay Simpson, M.Sc. in
Mathematics: 2015
6. Mahdi Kamaee,
M.Sc. in Chemistry: 2014
7. Fereshteh Nazari, M.Sc. in
Mathematics: 2014
8. Bryan Penfound,
M.Sc. in Mathematics: 2010.
c.
Departmental Committees
1. Outreach and Recruitment Committee
(Member): Fall 2022-
2. Undergraduate Studies Committee
(member): Fall 2021-
3. Undergraduate Studies Committee
(Chair): Fall 2019- June 2021
4. Curriculum Committee: 2008-2011
(Member); 2011-2019 (Chair)
5. Management Committee (member): Fall
2019- June 2021
6. Budget Committee (Member): 2018-2019
7. Nominating Committee: 2014-2015 and
2018-2019
8. Term Work Appeals (Chair): 2012-2019
9. Honours/Majors
Committee: 2009-2015 (Chair); 2017- 2019 (Member)
As the Associate head for Undergraduate
Studies, I assisted the Department Head with all undergraduate matters; for
example, I chaired the Undergraduate Studies Committee (see below), I decided
on undergraduate students awards and I reviewed applications for course credit
transfers.
As the chair of the Undergraduate Studies Committee, formerly the
Curriculum Committee, (2011- 2021), I worked with other members of the
Committee on making necessary curriculum and course changes. Then I presented
those changes to COCAP for approval before being forwarded to the University
Senate. Our undergraduate programs underwent an external review in 2015, which
led to an overhaul of all honours and major programs:
· I
actively participated in preparing the report that was distributed to the
undergraduate program review committee prior to their visit as well as in
meetings with the review committee during the visit (March 2-4, 2015) and in
drafting the Department’s response to the review committee.
· Following the recommendations in the
report from the undergraduate review committee, I led the efforts in 2015-2017
of the Curriculum Committee and the Department on making major changes to our
undergraduate programs as well as the joint honours
programs with Chemistry, Computer Science and Mathematics. Then I presented the
package of changes for approval by COCAP (Faculty of Science Committee on
Courses and Programs), then by the Faculty Council and finally by SCCCC (the
Senate Committee on Curriculum and Course Changes). The changes were approved
by all of the aforementioned committees and they
became effective as of the fall 2018 term.
Moreover,
as the chair of the Curriculum Committee, I coordinated the preparation at U of
M of the 2015 CAP University Prize exam (which was written throughout Canada on
Feb 3, 2015); and then I coordinated the grading of all written exams.
As the chair of the Honours/Majors Committee
(2009-2015), I assigned a mentor for each of the students in our undergraduate
programs and I served as a mentor myself for all the students in the Physics
& Math Joint Honours program. Moreover, I
assisted the Department Head in selecting the qualified
students for the undergraduate awards.
d.
Faculty of Science Committees
1. The Faculty-based
Promotion Committee: 2020-2023
2. The Local Discipline Committee:
2008- 2021
3. Committee on Students, Programs and
Undergraduate Degrees (SPUD): July 2018- June 2021
4. Committee on Courses and
Programs (COCAP): 2011- June
2021
5. Hiring Committee (Spousal Assistant
Professor Position, Dept. of Mathematics): December 2018
6. Past Director of the Winnipeg
Institute for Theoretical Physics: January 2017- December 2018
7. Faculty of Science Executive
Council, July 2016- June 2018
8. Hiring Committee (Spousal Assistant
Professor Position, Dept. of Mathematics): March 2017
9. Hiring Committee (Assistant
Professor Position, Dept. of Statistics): August 2015- March 2016
10. Director of the Winnipeg Institute
for Theoretical Physics: January 2015- December 2016
11. Hiring Committee (Assistant
Professor Position, Dept. of Mathematics): October 2014- April 2015
12. Director Elect of the Winnipeg
Institute for Theoretical Physics: January 2013- December 2014
As the Director of the Winnipeg Institute for Theoretical
Physics (WITP) in 2015 and 2016, I was in charge
of all administrative aspects of the institute, e.g.
· organizing
all WITP seminars at the University of Manitoba (8 to 10 per year);
· approving
all WITP expenses and balancing the budget;
· organizing
a WITP summer research symposium at the end of August at which undergraduate
and graduate students from the U of
Manitoba and U of Winnipeg
presented their work to other students and professors;
· preparing
the WITP annual report in December, which included all the research activities
of the WITP and its members (publications, talks, etc.);
· maintaining
the website of the WITP.
As the
Past Director of WITP, I was one of three judges selecting the best PhD thesis
in theoretical Physics for the DTP-WITP PhD Thesis Award; in 2017 there were 6
excellent submissions, totaling more than 1000 pages. Moreover, I was a
co-organizer of a two-day WITP summer research symposium on July 31 and August
1 (2017) at the University of Manitoba to which we invited three
well-established theoretical physicists and a mathematician (my collaborator
from the University of Concepcion in Chile) as guest speakers to give one or
two lectures each at the symposium.
As the
Director Elect of WITP (2013 and 2014), I worked with the Director (A. Frey-
University of Winnipeg) on preparing the 5-year review of WITP and on securing
a significant increase in funding for the institute from the three universities
in Manitoba (University of Manitoba, University of Winnipeg and Brandon
University).
e.
Conference Organization and
International Committees
2. Member
of the Scientific Committee for the 15^{th} International Conference on
p-Adic
Analysis and Dynamical Systems to be held in Poznan, Poland (July 3-8, 2023)
3. Member of the International
Organizing Committee, Eighth International Conference on p-adic Mathematical Physics and its Applications, Online
Conference (May 17-28, 2021)
4. Member of the Scientific Committee
for the 15^{th} International Conference on p-Adic Functional Analysis (Poznan, Poland, July 6-10, 2020)-
This was postponed to a later date due to COVID-19
5. Member of the International Advisory
Committee for the Seventh International Conference on p-Adic Mathematical Physics and its
Applications (Covilha, Portugal, September 30-
October 4, 2019)
6. Member of the Scientific Committee
for NUMTA2019: Numerical Computations: Theory and Algorithms (Crotone, Italy, June 15-21, 2019)
7. Member of the Scientific Committee
for the 15^{th} International Conference on p-Adic Functional Analysis (Poznan, Poland, July 2-6, 2018)-
This was postponed to July 6-10, 2020.
8. Member of the Scientific Committee
for the 14^{th} International Conference on p-Adic Functional Analysis (Aurillac, France, July 4-9, 2016)
9. Member of the Scientific Committee
for NUMTA2016: Numerical Computations: Theory and Algorithms (Pizzo Calabro, Italy, June
20-24, 2016)
10. Member of the Scientific Committee
for the 13^{th} International Conference on p-Adic Functional Analysis (University of Paderborn, Germany,
August 12-16, 2014).
11. Organizer of a special session on non-Archimedean
Functional Analysis at the Seventh Conference on Function Spaces, Southern
Illinois University at Edwardsville, May 20-24, 2014.
12. Member of the Scientific Committee
for NUMTA2013: Numerical Computations: Theory and Algorithms (Falerna, Italy, June 17-23, 2013)
13. Organizer and chair of the
Scientific Committee for the 12^{th} International Conference on p-Adic Functional Analysis (University of Manitoba, July 2-6,
2012)
14. Member of the Scientific Committee
for the 11^{th} International Conference on p-Adic Functional Analysis (Universite
Blaise Pascal, France, July 5-9, 2010)
15. Co-organizer and member of the
Scientific Committee for the 10^{th} International Conference on p-Adic and Non-Archimedean Analysis (Michigan State
University, USA, June 30-July 3, 2008)
f.
Refereeing and Review services
1. External reviewer of a PhD thesis in
Mathematics, Universidad de la Frontera, Chile (2021)
2. External reviewer for candidates for
a tenure-track assistant professor position, Department of
Mathematics, Linnaeus University, Sweden (2020)
3. Reviewer for Zantrablatt
Math and Mathematical Reviews (more than 25 papers since 2009)
4. Referee of several papers for Math
journals (more than 20 papers since 2008.)
5. Referee
of 6 research proposals (2 for Qatar Foundation, 2 for the Austrian Science
Fund, 1 for BIRS, and 1 for CONICYT- Chile.)
g.
Community Service: Member of the Board of Directors for
Campus Daycare May 2011- August 2014.
h.
Outreach: Volunteered at info days every year
(2009-2014).
II.
At Western Illinois University
(August 2003- May 2008)
a.
Graduate Students Advisory
Committees
1. 2003-2004: Javid Siddique; M.Sc. in
Mathematics.
2. 2003-2004: Duygu Inceoz; M.Sc.
in Mathematics.
b.
Thesis External Examiner
1. 2008: Dodzi Attimu;
PhD in Mathematics; Howard University (US).
c.
Departmental Committees
1. 2007-2008
2. 2006-2007
3. 2005-2006
4. 2004-2005
5. 2003-2004
As the Chair of the Graduate Committee (Fall 2004-Spring 2008), I led the efforts of that committee in recruiting and advising graduate students as well as assisting the Department Chair with various matters pertaining to the graduate program. I have led the efforts of the Graduate Committee in preparing the proposals for revisions in the graduate program including new structure, courses and tracks to better serve the needs of the incoming graduate students. I gathered ideas, thoughts and suggestions from the various groups in the Department about the structure and the contents of the courses in the revised program and designed a web page for that purpose to facilitate the discussions and the exchange of ideas in the Department. As a result, proposals for a revised program were submitted and approved by the Dean and the Graduate Council; and the revised program started in Fall 2006.
d.
College (Arts and Science) and
University Committees
1. 2007-2008
2. 2006-2007
3. 2005-2006
1. College
of Arts & Sciences Graduate Studies Committee
III.
At Michigan State University: Coordinator of the Math Learning Center (2002-2003), supervising
all the tutors and teaching assistants who worked at the center.
o The University of Manitoba and the University
of Manitoba Faculty Association’s 2018 Merit Award in Teaching, Service and Research,
May 29, 2019.
o Ian C. P. Smith Integrated Science
Faculty Scholar at the University of Manitoba for two consecutive terms: July
1, 2017- June 30, 2020 and July 1, 2020- June 30, 2022.
o Nominated for the J. S. Frame Teaching Excellence Award for Faculty, Spring
2003, Department of Mathematics, Michigan State University.
o Nominated for the J. S. Frame Teaching Excellence Award for Faculty, Spring
2002, Department of Mathematics, Michigan State University.
o Hariri Foundation Fellowship
to study in the USA (M.Sc.: 1988-1990 and PhD: 1993-1997); see this
article, p.4.
o Member of The Honor Society of Phi Kappa Phi.
o Member of Phi Beta Delta, the Honor
Society for International Scholars.
o BS in Physics with High Distinction,
American University of Beirut, June 1988.
o Philip Hitti Award, American
University of Beirut, June 1988, for graduating with the highest average in the
Faculty of Arts and Sciences.
o Dean's Honor List, faculty of Arts
and Sciences, American University of Beirut, 1986-1988.
o
Malcolm
Kerr Award, American University of Beirut, 1986-1988.
o
American Mathematical Society
o
Canadian Association of Physicists
o
Canadian Mathematical Society
o Arabic: fluent (reading, speaking and writing).
o English: fluent (reading, speaking and writing).
o
French:
good (reading, speaking and writing).