**Selected Mathematical Works **

**Alfred G. Noël**

** **

__Refereed
Papers__

- Progress and
Process in Math Excel at Northeastern University. Co
authors Maurice P. Gilmore, Thomas P. Stephens,Jr. The Center
for Innovation in Urban Education Studies, Volume II, 1996 edited by J.
Frazer, Northeastern University.
__Classification of Nilpotent Orbits in Symmetric Spaces.__Proceedings of the American Mathematical Society DIMACS African Americans in Mathematical Sciences volume 34 (123-127) 1997.- Nilpotent
Orbits and Theta-stable Parabolic Subalgebras
American Mathematical Society Journal of Representation Theory, Volume 2 (1-32) 1998. Click here to get postscript version__.__ - Component
Groups of Centralizers of Nilpotents in
Symmetric Space
Co-author Donald R. King . Journal of Algebra Vol 232__.__ __Classification of Admissible Nilpotent Orbits in Simple Exceptional Lie Algebras of Inner Type__. American Mathematical Society Journal of Representation Theory, Volume 5 (455-493) 2001.__Classification of Admissible Nilpotent Orbits in Simple Exceptional Lie Algebras of Type E6(6) and E6(-26)__American Mathematical Society Journal of Representation Theory, Volume 5 (494-502) 2001.__Computing maximal tori using LiE and Mathematica__. Lectures Notes in Computer Science, Springer-Verlag. Vol 2657 (728-736) 2003.__Computing theta-stable parabolic subalgebras using LiE. Lectures Notes in Computer Science__, Springer-Verlag Volume 3039 (335-342) 2004.__A LiE subroutine for computing prehomogeneous spaces associated with nilpotent Complex Orbits__Co-author Steven Glenn Jackson Lecture Notes in Computer Science, Springer-Verlag Vol 3516, (611—618), 2005.__A LiE subroutine for computing prehomogeneous spaces associated to real nilpotent orbi__*ts*__Prehomogeneous spaces associated with complex nilpotent orbits____Prehomogeneous spaces associated to nilpotent orbits in simple real Lie algebras E6(6) and E6(-26)____Some remarks on Richardson orbits in complex symmetric spaces__Mathematical Society Mathematics of Computation. Volume 75 (395-417), 2006.__Prehomogeneous spaces associated with real nilpotent orbits__, with Steven Glenn Jackson. Journal of Algebra Volume 305, Issue 1, (194-269) 2006.__Polarizable theta-stable parabolic subalgebras and $K_C$-saturation in the non-compact real forms of $G_2$ and $F_4$,__with Steven Glenn Jackson. Lecture Notes in Computer Science, Springer-Verlag Vol 3992, (422—429), 2006.__A general computational scheme for testing admissibility of nilpotent orbits of real Lie groups of inner type__. Lecture Notes in Computer Science, Springer-Verlag Vol 4151, (1—11), 2006.__Maximal Tori of Reductive Centralizers of Nilpotents in Complex Symmetric Space__Mathematical Society Contemporary Mathematics, Volume 467 (103 – 139) 2008.__The Atlas of Lie groups and representations: scope and successes__American Mathematical Society Contemporary Mathematics, Volume 467 (85 – 101) 2008.__A new approach for computing generators for U(g)^K__with Steven Glenn Jackson__Mining Player Ranking Dynamics in Team Sports____Incidence Geometry in a Weyl Chamber I: GL_n,with__Mboyo Esole, Steven Glenn Jackson, and Ravi Jagadeesan http://arxiv.org/abs/1508.03038 Advances in Applied Mathematics 119 (2020) 102048__Incidence Geometry in a Weyl Chamber II: SL_n,with__Mboyo Esole, Steven Glenn Jackson, and Ravi Jagadeesan http://arxiv.org/abs/1601.05070 Advances in Applied Mathematics 119 (2020) 102049__Tau Signatures and Characters of Weyl Groups__with Steven Glenn Jackson**,**Todor Milev, and Thomas Folz-Donahue https://arxiv.org/pdf/1810.05556.pdf ( In revision)

__Memoirs
and Books__

- Ph.
D. Thesis
**,** __Council for African American Researchers in the Mathematical Sciences: Volume III. Fifth Conference for African American Researchers in the Mathematical Sciences, June 22-25, 1999, University of Michigan, Ann Arbor, Michigan.__Alfred G. Noël, Earl Barnes, Sonya A. F. Stephens Editors. American Mathematical Society Contemporary Mathematics, Volume 275. (2001)__Council for African American Researchers in the Mathematical Sciences: Volume V. Thirteenth Conference for African American Researchers in the Mathematical Sciences, June 19-22, 2007, Northeastern University and the University of Massachusetts Boston.__Alfred G. Noël, Donald R. King, Gaston M. N’Guérékata, Edray H. Goins Editors. American Mathematical Society Contemporary Mathematics, Volume 467. (2008)__Analiz____Matematik Tòm I.__Alfred G. Noël Presses Internationales GRAHN Monde Montreal Canada (2019). http://www.grahn-monde.org/index.php/17-articles/175-nouvelle-parution-des-presses-internationales-grahn-monde__Analiz____Matematik Tòm II.__Alfred G. Noël (Submitted)__Mathématiques____Terminale S__Alfred G. Noël et al. (In preparation)

__Problems
and Abstracts__

__A canonical basis for maximal tori of the reduc tive centralizer of a
nilpotent element__* *Proceedings
of the NATO Advanced Study Institute
Computational Noncommutative Algebra and Applications July 6--19, 2003 Il
Ciocco Resort Hotel, Italy. Edited by Jim Byrnes,** **Nato Science Series II. Mathematics, Physics and Chemistry
– Vol. 136.

__A Short Note on Nipotent
Orbits Associated to Coxeter Cells____ __(with
Steven Jackson) ACM Communications in Computer Algebra, Issue 168, Vol. 43, N0.
2, (52-53), June 2009.

** **

__Expository
Papers and Selected Talks__

- TITS SYSTEMS, PARABOLIC
SUBGROUPS, PARABOLIC SUBALGEBRAS, Northeastern University, June 1996.
This paper was written as part of the requirements for a course, Topics in
algebraic geometry, taught by Prof. V. Lakshmibai
in the Spring 1996 quarter. Click here to
download the postscript version
- NOTICED
NILPOTENT ORBITS OF REAL LIE ALGEBRAS.
- CENTRALIZERS
OF NILPOTENTS AND THE BALA-CARTER CLASSIFICATION.
- COMPONENT GROUPS OF CENTRALIZERS OF NILPOTENTS IN
SYMMETRIC SPACES
__.__This file contains a talk that was given at CAARMS5, University of Michigan, in June 99. The general theory is studied using the group SL(n,R) as an example. This is for an audience of non-specialists. There is no Lie structure theory. Everything is done in thecontext of Linear Algebra. Click here to download the postscript version. - ON THE
ADMISSIBILITY OF NILPOTENT ORBITS OF SIMPLE EXCEPTIONAL REAL LIE GROUPS OF
INNER TYPE. This is
the content of a talk given at an AMS Sectional Meeting held at University
of South Carolina Columbia on March 16-18, 2001, Special Session on
Algebraic Structures Associated with Lie Theory, III.
- Quantization in Physics and
Mathematics, Science Colloquium Hour The
University of Massachusetts Boston April 9, 2004
- Richardson
Orbits for Real Semisimple Lie Groups Conference
on Nilpotent Orbits and Representation Theory, 2004 Fuji-Zakura
So, Japan September 5-10 2004
- Prehomogeneous
Spaces Associated with Nilpotent Orbits of Complex Lie Group
*s*AMS Special Session on Representations of Lie Algebras AMS Joint Mathematical Meeting January 5- 8, 2005 Atlanta Georgia. - A LiE subroutine for computing prehomogeneous spaces
associated to real nilpotent orbits International Conference on Computational Science and its
Applications (ICCSA 2005) May 9 - 12, 2005 Suntec, Singapore, Singapore.
- The Atlas
of Lie groups and representations: scope and successes CAARMS 13 June
19-22, 2007 Boston MA
- The
Uncontroversial Mathematics Behind Garrett Lisi’s
Controversial ``Theory of Everything’’ (In Memory of My Grandmother Vilicia Auguste: 1914 – 2008). Société Scientifique Haïtienne
(HSS), University of Massachusetts Boston, July 26, 2008.
- The Orbit
Method: An insight from Physics, Mathematics Department Colloquium
Medgar Evers College Brooklyn New York, December 2, 2009

**Preprints,
Tables and Work in Progress**

__Associating elliptic Pseudo-Levi subalgebras to nilpotent conjuagcy classes in the classical simple real Lie algebras____.__(Unfinished manuscript)__Maximal Tori of Reductive Centralizers of Nilpotents__. (tables).__Tables of prehomogeneous spaces associated with exceptional Lie algebras__http://www.math.umb.edu/~anoel/publications/tables

**Funded
Proposals**

- AY 1998-99 Faculty Internal Grants Program. This
proposal was written in March 1999 for a UmassBoston
competition . My goal was to acquire internal
funds for equipment and travels.It
contains a research proposal which may give some insight on future work
and proposals
__.__ - Martin Luther King Professorship at MIT. This proposal
was at the basis of the MLK professorship which was awarded during the
2000-2001 academic year by the Mathematics department of the Massachusetts
Institute of Technology .
- National Science Foundation Research
Opportunity Award.
This
proposal was funded for a year (3/2002 - 3/2003) by the NSF for work to be
done at the Massachusetts Institute of Technology with David Vogan.