This volume contains selected papers based upon the presentations at the Thir-
teenth Conference for African American Researchers in the Mathematical Sciences
(CAARMS 13), held at Northeastern University and University of Massachusetts
Boston, on June 19-22, 2007. The Council for African American Researchers in
the Mathematical Sciences is the group that organizes this annual conference that
showcases the current research primarily, but not exclusively, of African Ameri-
cans in the mathematical sciences. CAARMS conferences have been held annually
since 1995. At these conferences, significant numbers of researchers have delivered
hour-long technical presentations and many graduate students have presented their
work in organized poster sessions. The participants in past CAARMS conferences
are discussed in greater detail in an article in this volume by William A. Massey,
Derrick Raphael and Erica N. Walker.
Research topics featured at past CAARMS conferences have come from pure
mathematics (e.g., number theory, analysis, topology, abstract algebra, and prob-
ability), mathematical physics, mathematical biology, operations research, applied
statistics, and computer science. In addition to the invited talks and tutorials, group
discussions are organized to stimulate, nurture, and encourage increased participa-
tion by African Americans and other under-represented groups in the mathematical
sciences. These events create an ideal forum for mentoring and networking in which
attendees can meet African American researchers and graduate students who are
interested in the same fields.
The representation theory of Lie groups and its applications were a major focus
of the talks at CAARMS 13. An article by Alfred G. Noel provides an overview
of the recent achievements of the Atlas of Lie groups Project, one of the most
important efforts currently underway in pure mathematics. An article by Alessan-
dra Pantano, Annegret Paul and Susana Salamanca-Riba illustrates the work that
remains to be done by the Atlas Project to understand fully the unitary represen-
tations of reductive groups. A second article by Noel highlights the significance of
scientific computing in Lie theory. A paper by Floyd L. Williams applies the repre-
sentation theory of Lie groups to the physics of black holes. The volume contains
two research papers not directly related to Lie theory: one by Aissa Wade on the
geometry of co-isotropic submanifolds of Poisson manifolds and one by .Arthur D.
Grainger on recent results on the structure of the set of ultrafilters on the collection
of finite subsets of an infinite set.
We would like to thank the following individuals from our gracious host institu-
tions for making the conference a success: Professor Robert C. McOwen (Northeast-
ern University), Joanne Durham (Northeastern University), Dean emeritus Michael
Greeley (University of Massachusetts, Boston), Dean William Hagar (University
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