Projects By Department of Mathematics:
A Partial Differential Equation Approach to Robust Control Design of Smart Materials and Structures: Theoretical, Computational, and Experimental Aspects
Lasiecka, Irena. Sponsor: U.S. Dod - Army - Aro
The present Supplement Request originates in the research setting of the regular ARO Grant, DAA H04-96-1-0059, to generate a program of new directions of research and educational activities of the PI's. ... A Partnership Project: Building Innovative Distance Learning Mathematics Courses for High School Teachers
Pitt, Loren D. Sponsor: Virginia Department Of Education
This partnership between the University of Virginia's Department of Mathematics
and the public school divisions of Bristol City and Roanoke City will develop a set of three innovative distance learning ... Aerospace Graduate Research Fellowship - I.M. Daniels
Lasiecka, Irena. Sponsor: Virginia Space Grant Consortium
The goal of the research is to establish wellposedness and control results for a nonlinear system of partial differential equations arising in structural acoustic interactions. Such research aims to ... Aerospace Graduate Research Fellowship - K.A. Ott
Mitrea, Irina. Sponsor: Virginia Space Grant Consortium
My research is concerned with problems at the interface between Harmonic Analysis and Partial Differential Equations. The main theme is understanding the nature of the boundary integral operators associated ... Affine Algebras, Lie Superalgebras, Hecke Algebras, & Representations
Wang, Weiqiang. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Alfred P. Sloan Research Fellowship for Dr. Chongchun Zeng in Mathematics
Zeng, Chongchun. Sponsor: Sloan Foundation
• Past Research. First, I have being working with Prof. P. Bates and Prof. K. Lu at Michigan State University (previously at Brigham Young University) on general theory of invariant manifolds for semiflows ... AMC-SS: Measure Valued Processes & Stochastic Systems
Gromoll, Hans Christian (Christian). Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Applications of Krein Space Operator Theory
Rovnyak, James L. Sponsor: U.S. National Science Foundation
The proposal is concerned with operator theory and function theory involving the generalized Schur and Nevanlinna classes and two-isometries on Pontryagin spaces. A generalization of Nudelman's problem ... Calculus of Functors & Applications
Arone, Zvi Gregory (Greg). Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The main goal of this project is to apply calculus of functors, especially the "orthogonal calculus" version developed by M. Weiss, to the study of spaces of embeddings. In more detail, let M, N be smooth ... Calculus of Functors and Homotopy Theory
Arone, Zvi Gregory (Greg). Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Arone is interested in applying the theory of calculus of functors (developed by T. Goodwillie and M. Weiss) to study the unstable homotopy of such spaces as spheres and classifying spaces of compact ... Calculus of Functors, Operads, & Manifolds
Arone, Zvi Gregory (Greg). Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
In this proposal the PI would like to continue his investigation into the interplay between calculus of functors, operads and geometric topology. In recent work, and work in progress, the PI has investigated ... Calculus of the Embedding Functor
Volic, Ismar. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Knots are some of the most interesting objects of study in topology both because they are easy to define and visualize and because they are of interest to physicists, chemists, etc. Some fundamental ... CAREER: Spectral Theory for Singular Integrals, Validated Numerics
Mitrea, Irina. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Chaos & Stability In Quantum Mechanics
Howland, James S. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Howland will study (1.) stability and chaos in discrete quantum systems driven by time-dependent perturbations; (2.) the asymptotics of resonance widths in multiscale perturbation problems; and (3.) the ... Classification Theory of 4-Manifolds
Krushkal, Vyacheslav (Slava). Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
This research project concerns the geometric classification theory of topological 4-manifolds. The classification techniques are known to hold for a class of good fundamental groups, and are conjectured ... Coding Theory & Quantum Computing
Parshall, Brian J. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The Department of Mathematics and the Institute for Mathematical Sciences at the University of Virginia will sponsor an interdisciplinary conference on quantum computing and coding theory at the University ... Collaborative Project: A Comprehensive WeBWorK Problem Library
Holt, Jeffrey J. Sponsor: U.S. Nsf - Directorate For Ed. & Human Resources
WeBWorK is a free, online homework system that has been shown to be effective in helping students learn mathematics. At present, it is somewhat technical to use. The goal of this project is to make it ... Computations in Classical Chromatic Homotopy Theory, Algebraic K-Theory, and Motivic Homotopy
Hill, Michael Anthony (Mike). Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Conference on Infinite Dimensional Lie Theory
Parshall, Brian J. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
This award will partially support a conference to be held at the University of Virginia, May 21-25, 2000. The conference will focus on the interaction between infinite dimensional Lie theory in mathematics ... Conference on Infinite-Dimensional Aspects of Representation Theory & Applications
Wang, Weiqiang. Sponsor: U.S. National Science Foundation
The funds are being requested to organize a meeting on infinite-dimensional aspects of representation theory and applications. The conference will be held at University of Virginia in May 2004. The meeting ... Conference on Low-Dimensional Topology
Krushkal, Vyacheslav (Slava). Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The subject of the conference is one of the most active and important areas of modern mathematics. The conference will bring together leading researchers in several areas of low-dimensional geometry and ... Congruence Subgroups Problem & Groups & Finite Representations
Rapinchuk, Andrei S. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
This proposal continues investigations into groups of rational points of simple algebraic groups over number fields and of their S-arithmetic subgroups. One of the goals of the project is to prove the ... Control Problems for Strongly Coupled Non-Linear Partial Differential Equations
Lasiecka, Irena. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
1 Overview. The research work proposed here, for which supplemental funding is re-quested, fits into the main core of the present NSF project, which is focused on control of interactive structures, ... Control problems for systems of strongly coupled partial differential equations with variable coefficients
Lasiecka, Irena. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
In recent years, the emerging technology of smart materials and structures has brought to the fore of scientific investigation the pressing need to control, optimize, and stabilize dynamical 'interactive' ... Control Problems for Systems of Strongly Coupled Partial Differential Equations with Variable Coefficients
Lasiecka, Irena. Sponsor: U.S. National Science Foundation
In recent years, the emerging technology of smart materials and structures has brought to the fore of scientific investigation the pressing need to control, optimize, and stabilize dynamical 'interactive' ... Duality Between Representations of Lie Superalgebras & Lie Algebras Via Kazhdan-Lusztig Theory
Wang, Weiqiang. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Stimulated by connections and applications to supersymmetry and string theory, the representation theory of Lie superalgebras has been an important research direction. Having many similarities on one ... Eigenfunction Estimates on Manifolds with Boundary and Applications to Partial Differential Equations
Xu, Xiangjin. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Intellectual Merit: Harmonic Analysis on compact manifolds and applications of these methods and results to Partial Differential Equations. In this project, following established developments of Fourier ... GAAN Fellowship Program
Thomas, Lawrence E. Sponsor: U.S. Department Of Education - Post Secondary Ed.
Geometric Variational Problems & Rearrangement Inequalities
Burchard, Almut. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Two sets of problems are proposed, one related with elastic curves, and the other with rearrangement inequalities. The first set of problems concerns the dynamics of an elastic curve moving in three-dimensional ... Geometry Leadership Project
Pitt, Loren D. Sponsor: State Council Of Higher Education(Schev)
Geometry Of Random Curves
Burchard, Almut. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Random systems exhibiting curves or collections of curves are typically constructed on a fine lattice on some box of finite size. Examples include: Random spanning trees (where every pair of points is ... Graduate Assistance in Areas of National Need Fellowship Program
Thomas, Lawrence E. Sponsor: U.S. Department Of Education - Post Secondary Ed.
With the help of a GAANN single-discipline grant, the Department of Mathematics of the University of Virginia will enroll a diverse cohort of eight outstanding students who show exceptional promise ... Graduate Assistance in Mathematics
Thomas, Lawrence E. Sponsor: U.S. Department Of Education - Post Secondary Ed.
The purpose of this grant is to establish a new program of 12 traineeships in mathematics, providing 12-month stipends and tuition for graduate students, for the period June 1, 2001 to May 31, 2004. ... Hamiltonian Motions Under Strong Constrains
Zeng, Chongchun. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The project focuses on Hamiltonian ODEs and PDEs under strong constraining forces. For an given Hamiltonian composed of the kinetic energy and a potential energy, consider particles restricted to a submanifold ... Historia Mathematica
Parshall, Karen H. Sponsor: Academic Press, Inc.
Krein Space Operator Theory and Applications
Rovnyak, James L. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Topics in operator theory and function theory will be pursued in several directions that involve Krein spaces and indefinite inner products (as opposed to Hilbert spaces). The project will continue previous ... Lie Superalgebras, Supergroups and Correlation Functions
Wang, Weiqiang. Sponsor: NATIONAL SECURITY AGENCY
This research plan is focused on the representation theory of Lie superalgebras and algebraic supergroups over a field of prime characteristic, and on the Bloch-Okounkov correlation functions on modules ... Mathematics Specialist in K-5 Schools: Research & Policy Pilot Study
Pitt, Loren D. Sponsor: Virginia Commonwealth University
Teacher Professional Continuum (TPC) addresses critical issues and needs regarding the recruitment, preparation, enhancement, and retention of science, technology and mathematics (STM) teachers for grades ... Mathematics Teachers' Leadership Project
Pitt, Loren D. Sponsor: State Council Of Higher Education(Schev)
The eight participating school divisions in this proposal have formed a mathematics leadership partnership with the University of Virginia and members of the Virginia Mathematics and Science Coalition ... Mellin Transform & Global Optimization Techniques for Partial Differential Equations
Mitrea, Irina. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Summary of progress to date. The two main general themes of the research proposal that the PI made progress on are:
A. The Spectral Radius Conjecture for Elliptic Boundary Layer Potentials ... Modular Representation Theory of Finite & Algebraic Gro
Parshall, Brian J. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
This proposal, by Parshall and Scott, is being submitted in coordination with Ed Clive at the University of Oklahoma. Clive, Parshall and Scott have been collaborating for more than 24 years.
The long-term ... Modular Representations
Parshall, Brian J. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The modular representation theory of finite groups of Lie type is a major, active topic of mathematical research. The area has both inspired and been strongly influenced by developments in other areas, ... Modular Representations & Cohomology
Parshall, Brian J. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The modular representation theory and cohomology of finite groups G(q) of Lie type is a major, active topic of mathernatical research. The area has both inspired and been strongly influenced by developments ... Modular Representations & Cohomology
Parshall, Brian J. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
There are three great classes of representations of the finite groups of Lie type. First, in the defining characteristic theory, the underlying module is taken over a field with the same characteristic ... Modular Representations and Cohomology
Parshall, Brian J. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
New Problems in Homotopy, K-Theory, & Representation Theory
Kuhn, Nicholas J. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Homotopy theory, K-theory and representation theory are mathematical subjects in which one is trying to discover, and ultimately classify, fundamental "building blocks" of structure: homotopy dealing ... New Topological Structures in Condensed Matter Physics
Krushkal, Vyacheslav (Slava). Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The intellectual merit of the proposed activity.
The proposed research lies at the interface of Mathematics (quantum topology) and theoretical Condensed Matter Physics (integrable lattice ... Normal Subgroup Structure of the Groups of Rational Points of Algebraic Groups and of Their Special Subgroups
Rapinchuk, Andrei S. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
This award provides funding for an investigation of the normal subgroup structure of groups of rational points of algebraic groups over general as well as over special (primarily, global) fields. The ... Normal Subgroups of the Groups of Rational Points of Algebraic Groups
Rapinchuk, Andrei S. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Principal Investigator Andrei Rapinchuk will conduct systematic investigation of a wide range of well-known problems focused on understanding the structure of groups of rational points of algebraic ... Orthogonal Polynomials Of Several Variables
Dunkl, Charles F. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The classical orthogonal polynomials of one variable are significantly involved in several aspects of mathematics, for example: the Chebyshev, Legendre, and Hermite polynomials are used in approximation ... Orthogonal Polynomials of Several Variables
Dunkl, Charles F. Sponsor: U.S. National Science Foundation
The analysis of multi-variable functions or configurations is an important problem area with connections to topics like quantum systems of many bodies, multi-variate statistical distributions, special ... Perturbation Problems in PDE Dynamics
Zeng, Chongchun. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
This project is concerned with various perturbation problems in the dynamics of some Hamiltonian or near Hamiltonian PDEs, such as nonlinear wave equations and nonlinear Schroedinger equations, etc. The ... Preparing Virginia's Mathematics Specialists
Pitt, Loren D. Sponsor: Virginia Commonwealth University
During the five years of this award Masters degrees for K-5 Mathematics Specialists will be established at the three Virginia universities; Norfolk State University, the University of Virginia, and ... Problems in Homotopy Theory and Group Cohomology
Kuhn, Nicholas J. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
1. Intellectual Merit
Homotopy theory and group cohomology are mathematical subjects in which one is trying to discover, and ultimately classify, fundamental ‘building blocks' of structure: ... Problems in Homotopy, K-therory, & Representation Theory
Kuhn, Nicholas J. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Professor Kuhn has a long record of developing methods to solve interesting problems in homotopy theory, K-theory, and representation theory. The goal of the largest part of this project is to connect ... Quantum Mechanics & Random Fields
Brydges, David C. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
A major problem in equilibrium statistical mechanics is the calculation of critical exponents. The construction of Euclidean quantum field theory is a closely related problem. The standard tools in theoretical ... Representation Theory of Infinite-Dimensional Lie Algebras & related Topics
Wang, Weiqiang. Sponsor: NATIONAL SECURITY AGENCY
This research plan consists of several related projects on resentation theory of infinite-dimensional Lie algebras such as affine Lie alegebras, ĝl∞, and W1+∞ ... Representations of Infinite Dimensional Lie Algebras and the McKay Correspondence
Wang, Weiqiang. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The investigator studies the connections among representation theory of infinite dimensional Lie algebras, finite groups and geometry. Influenced by the works of Nakajima, Grojnowski, Segal and others, ... Robust Battlefield Acoustic Target Identification
Lake, Douglas E. Sponsor: U.S. Dod - Army - Aro
This project will continue research on robust target identification using the output of arrays of battlefield acoustic sensor performed by the PI as an ASEE Postdoctoral Fellow at the Acoustic Signal ... Robust Detection of Regular Minefield Point Patter
Lake, Douglas E. Sponsor: U.S. Dod - Navy - Office Of Naval Research (Onr)
Sloan Research Fellowship
Burchard, Almut. Sponsor: Sloan Foundation
Sonja Kovalevsky HS Day 07
Mitrea, Irina. Sponsor: Association for Women in Mathematics
Through grants from Elizabeth City State University and the National Security agency (NSA), The Association for Women in Mathematics expects to support Sonia Kovalevsky High School Mathematics Days ... Stability and Control in Nonlinear Elastic Dynamics--Applications to Aerospace Structures
Lasiecka, Irena. Sponsor: U.S. National Academy Of Sciences
The main focus of the project proposed is mathematical analysis of partial differential equations arising in nonlinear models of dynamic elasticity. Particular emphasis will be given to nonlinear oscillations ... Stabilization & Control of Structural Acoustic Systems
Lasiecka, Irena. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Statistical Mechanics & Field Theory
Imbrie, John Z. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
1. The purpose of this project is to enhance our understanding of fundamental problems in statistical mechanics and probability theory through the use of mathematical methods involving supersymmetry ... Studies In Classical & Quantum Mechanics
Thomas, Lawrence E. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
Three areas of mathematical physics will be investigated: the semi-classical and high-energy limits for Schroedinger operators, the polaron model for an electron interacting with a quantized field and ... Studies in Classical and Statistical Mechanics
Thomas, Lawrence E. Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The investigator will work primarily in two areas of mathematical physics. 1) Models in Non-Equilibrium Statistical Mechanics. A typical model consists of a chain of coupled anharmonic oscillators (or ... Surfaces & 4-Manifolds
Krushkal, Vyacheslav (Slava). Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
The Virginia Mathematics Specialist Project
Pitt, Loren D. Sponsor: Virginia Department Of Education
The Virginia Mathematics Specialist Project is a school/higher education partnership sponsored by the Virginia Mathematics and Science Coalition and dedicated to establishing K-8 mathematics specialist ... Topology of Four-Manifolds
Krushkal, Vyacheslav (Slava). Sponsor: U.S. Nsf - Directorate Math. & Physical Sciences
This project is centered around the classification theory of topological 4-dimensional manifolds. One goal is to find sufficient algebraic conditions for splitting of a 4-manifold as a connected sum, ... US-France Cooperative Research (INRIA): Control of Interactive Structures with Dynamic Shells
Lasiecka, Irena. Sponsor: U.S. Nsf - Directorate Soc., Behav. & Eco. Science
This three-year award for US-France collaboration in applied mathematics involves research teams at the University of Virginia and the Institut National pour la Recherche en Informatique et en Automatique ... Virginia Algebra Project
Pitt, Loren D. Sponsor: Virginia Department Of Education
On behalf of the Virginia Mathematics and Science Coalition (VMSC), the University of Virginia will partner with 7 other universities and 36 school divisions to create an innovative Algebra 1 endorsement ... Virginia Collaborative for Excellence in the Preparation of Teachers
Pitt, Loren D. Sponsor: Virginia Commonwealth University
We will pursue the following activities:
1. The development of an integrated set of mathematics and science courses that will be especially appropriate for K-8 teachers.
2. Continuing to work through ... Virginia Middle School Teacher Corps
Pitt, Loren D. Sponsor: Virginia Department Of Education
The University of Virginia has received a grant of $83,062.80 from the Virginia Department of Education to support teachers in the Virginia Middle School Teacher Corps to attend courses and professional ... VSGC Fellowship - V. Zimmern
Mitrea, Irina. Sponsor: Virginia Space Grant Consortium
WeBWorK in the Mathematics Curriculum
Holt, Jeffrey J. Sponsor: U.S. Nsf - Directorate For Ed. & Human Resources
The project focuses on improving student mathematical achievement at the University of Virginia by expanding a pilot implementation of the WeBWorK online homework system. We will develop comprehensive ...
Faculty:
Abdesselam, Abdelmalek – Assistant Professor
Abramenko, Monika C – Lecturer
Abramenko, Peter – Professor
Arone, Zvi Gregory – Professor
Cooper, Benjamin J. – Instructor
Dascaliuc, Radu – Instructor
Du, Jie – Visiting Scholar
Dunkl, Charles F – Professor Emeritus
Ershov, Mikhail V – Assistant Professor
Faulkner, John R – Professor Emeritus
Fraser, Virginia A. – Instructor in Mathematics
Gerber, Katherine M – Lecturer in Mathematics
Gromoll, Hans Christian – Assistant Professor
Grujic, Zoran – Associate Professor
Guadagni, Gianluca – Lecturer
Gul, Ugar – Visiting Scholar
Herbst, Ira W – Professor
Hill, Michael Anthony – Assistant Professor
Holt, Jeffrey J – Associate Professor & Chair, Statistics
Howland, James S – Professor Emeritus
Imbrie, John Z – Professor
Kankaanrinta, Marja K – Lecturer in Mathematics
Klintworth, Karen E – Lecturer in Mathematics
Kriete, Thomas L – Professor
Krushkal, Vyacheslav – Professor
Kuhn, Nicholas J – Professor
Lasiecka, Irena – Professor
MacCluer, Barbara D – Professor
Mark, Thomas E – Assistant Professor
Matucci, Francesco – Instructor
McCrimmon, Kevin M – Professor
Melcher, Tai Alexis – Assistant Professor
Mohajeri, Manouchehr – Lecturer
Parshall, Brian J – Professor
Parshall, Karen H – Associate Dean for Social Sciences & Professor
Pisano, Stacie – Lecturer
Pitt, Loren D – Professor Emeritus
Ramirez, Donald E – Professor & Chair
Rapinchuk, Andrei S – Professor
Rovnyak, James L – Professor Emeritus
Scott, Leonard L – Professor
Sherman, David Edward – Assistant Professor
Snider, Daria M – Lecturer
Thomas, Lawrence E – Professor
Triggiani, Roberto – Professor
Wang, Jianpan – Visiting Scholar
Wang, Weiqiang – Professor
Ward, Harold N – Professor Emeritus
Wells, Benjamin Baxter – Lecturer
Wood, Beverly L. – Lecturer in Mathematics
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