Mathematics
Effective Biological Science
through Mathematics
The Effective Biological Science
Through Mathematics (EBSM) project is an interdisciplinary effort involving
faculty from the departments of Mathematics and Microbiology and Molecular
Genetics. The goal is to contribute directly to student success in selected
coursework areas in the biological sciences and to student retention in the
biological sciences. The primary development activities include the development
of an instructor- and student-friendly supplement on enzyme kinetics including
simple enzyme kinetics, various forms of inhibition, and the effect of gating
on Michaelis enzyme kinetics.
Sponsor: Howard Hughes Medical Institute
PIs: Douglas Aichele, Alan Noell
Microbiology and Molecular
Genetics: James Blankemeyer
Cohomology of Exponential
Sums
Exponential sums originally arose in basic problems in
number theory, such as trying to estimate the number of integer solutions to an
equation. This project will attempt to extend some of the classical results in
the subject to new classes of exponential sums.
Sponsor: National Science Foundation
PI: Alan Adolphson
Power: Complex Analysis and
Representation Theory
This study addresses questions
on analytic and geometric aspects of Representation Theory and its application.
The classification and geometric description of representations
“attached” to nilpotent orbits are important problems in
Representation Theory. So such classification is available and even for the
“known” examples there is no unified geometrical description of
such representations. This study uses techniques introduced by Goro Shimura in
a different setting in order to obtain analytic-geometric descriptions of a
certain family of small representations. The goal is to obtain Hilbert spaces and
natural descriptions of the group actions on them. The understanding of the
unitary structure is of particular interest.
Sponsor: National Science Foundation
PI: Letticia Barchini
Algebra for All
The “Algebra for
All” project is a five-year program to develop Internet-based
professional development training for middle-math teachers in algebra content
and pedagogy. The training will be delivered through exemplar inquiry-based
algebra-for-all lessons with an embedded instructional design that will serve to
train teachers in content and in effective ways to engage all students in
learning algebra.
Sponsor: United States Department of Education
Pi: James R. Choike
Oklahoma State University AP
Calculus Institute
This project conducts a week-long Summer Institute for
Oklahoma Mathematics teachers on the content, pedagogy, and assessment of
Advanced placement Calculus AB and BC.
Sponsor: Oklahoma
State Department of Education, Office of AP Initiative
PI: James R. Choike
Analytic Properties of
Automorphic L-functions and the
Converse Theorem
This research will continue investigation of the local and
global properties of L-functions of automorphic representations and the
application of these L-functions to the problem of lifting of automorphic
representations from classical groups to general linear groups via the Converse
Theorem.
Sponsor: National Science Administration
PI: James Cogdell
This project investigated L-functions of automorphic
representations and their applications in the following three contexts: 1) The
Converse Theorem for GL(n) and Functoriality; 2) Number Theoretic Applications
of L-functions for GL(3); 3) A exposition of the theory of L-functions for
GL(n).
Sponsor: National
Security Agency
PI: James Cogdell
This project involves the development and use of efficient
triangulations and normal surfaces in the study and understanding of
3-manifolds. The guiding principle of efficient triangulations is reducing
unnecessary normal surfaces and improving the efficiency of computations for
trangulation based algorithms. The project proposes further investigation of
efficient trangulations and their relationship to one-vertex and ideal
trangulations of 3-manifolds. Connections between efficient triangulations and
the topology of 3-manifolds and “blow-ups” of ideal points suggest
new approaches to Dehn fillings, the Homeomorphism Problem, the Word Problem
for 3-manifolds, and many new and more efficient algorithms from normal surface
theory.
Sponsor: National
Science Foundation
PI: William Jaco
Essential Surfaces in 3-manifolds: The Lopez Conjecture
This
project provides for a special semester at Stanford University to bring
together specialists in the area for an intense collaborative study of
essential surfaces in knot complements.
Sponsor: National
Science Foundation, AIM
PI: William Jaco
Topics in Number Theory and
Representation Theory
This project has two components.
The first concerns the arithmetical theory of prehomogenous vector spaces and
the second concerns L-functions and the representation theory of p-adic groups.
Sponsor: National Science Foundation
PI: Anthony Kable
Essential Laminations and
Essential Surfaces in 3-Manifolds
The goal of this project is to explore the topology of
3-manifolds using essential laminations and essential surfaces. The techniques
used in this project could have great impact on some fundamental problems in
knot theory, e.g. Property P for knots and the cabling conjecture.
Sponsor: National Science Foundation
PI: Tao Li
3-Manifolds and Floer
Homologies
The problems addressed in the
research are in the area of the instanton/monopole Floer theory of 3-manifold
and infinite-dimentional symplectic manifolds. The main theme in this study is
the fundamental and important properties of the guage-theoretic/symplecitic
Floer homology, and to study the interactive relation between the Floer
cohomology and the semi-infinite cohomology, and the Seilberg-Witten-Floer
theory intertwining the instanton and monopole results.
Sponsor: National Science Foundation
PI: Weiping Li
Representations of Finite
Groups and Applications
This project concerns the developments of an undergraduate,
upper division course and an accompanying textbook that would teach the theory
of the representations of finite groups, with specific and detailed
applications, to mathematics majors, mathematics education majors and to
students majoring in science and engineering.
Sponsor: National Science Foundation
PI: Lisa Mantini
Topology of 3-Manifolds
This project concerns the structure of 3-manifolds. In
particular in studies the question of when non-compact covering spaces of
3-manifolds. It also studies the questions of when hyperbolic 3-manifolds are
covered by surface bundles, when 3-manifolds with cubings of negative curvature
are hyperbolic, and whether non-Haken 30manifolds contain small knots.
Sponsor: National Science Foundation
PI: Robert Myers
Polynomials in Analysis and
Analytic Number Theory
The major direction of this research is the study of several
polynomial problems in Classical Analysis and Analytic Number Theory by using
the methods of Complex Function Theory, Potential Theory and Approximation
Theory as a unifying approach. The problems include sharp inequalities for
products and factors of polynomials, Faber polynomials, Beiberbach polynomials
and Bergman kernal methods in approximation of conformal mappings.
Sponsor: National Science Foundation
PI: Igor Pritsker
This project is devoted to the study of several central
topics in polynomials with integer coefficients, which is based on a unifying
approach via Potential Theory and Approximation Theory.
Sponsor: National
Security Agency
PI: Igor Pritsker
This research studies the relationships between the
following objects related to an embedded smooth projective variety X ⊂Pn: 1) Smooth curves embedded by line bundles of large,
by explicit, degree; 2) canonical embedding of smooth curves; 3) and smooth
varieties of dimension greater than or equal to two.
Sponsor: National
Security Agency
PI: Peter Vermeire
One
focus of this project in the study of tessellations of homogeneous spaces.
Namely, if G-H is a non-compact, simply connected homogeneous space of a
connected Lie group G, the question is whether there is a propery discontinuous
subgroup D of G, such that the orbit space D\G/H is compact. This project also
studies crystals in mathematical spaces other then the three-dimensional
universe that we live in. A crystal is a material whose atomic structure is
very symmetric. The most fundamental problem in this subject is to decide which
spaces contain crystals, and which do not. For this question, the most
interesting spaces are homogeneous, which means that every point of the space
looks exactly like all of the other points.
Sponsor: National
Science Foundation
PI: Dave Witte
The GeoSET project will support the full development and
dissemination of the curriculum and pedagogy for a discovery-based course in
geometry intended for prospective elementary teachers. A wide range of
curricular and pedagogical activities are supported by the prototype
workbook-style text currently used successfully at Oklahoma State University
including: group activities, extensive writing, math-literature connections,
project, constructions with manipulatives and proofs.
PIs: John Wolf,
Douglas Aichele
This fellowship provides financial support for visits to the
University of Chicago and the University of Texas at Austin. A project on applications
of the MHD equations to magnetic reconnection was initiated and two joint
papers on modeling nonlinear water waves were completed.
Sponsor: American Mathematical Society
PI: Jiahong Wu
The award is for the research project investigating
asymptotic limits for mathematical models of fluid flow. These kind of limits
under consideration arise in multidisciplinary areas when partial differential
equations are used as models.
Sponsor: Oak Ridge Associated Universities (ORAU)
PI: Jiahong Wu