In this project the principal investigator will analyze models             of nematic liquid crystals with variable degrees of orientation as              a means of studying highly nonlinear material behavior such as the              formation of structured domains and patterns.  The approach will                consist of an analytical part and an experimental part.  On the                 analytical side the principal investigator will employ mathematical             methods to describe the formation and evolution of banding                      structures, singularity lines and disclinations in the solutions of             the system of parabolic partial differential equations that governs             the behavior of the materials.  On the experimental side the                    principal investigator and a graduate student will conduct actual               experiments in the Fluid Dynamics Laboratory in the Mathematics                 Department at Penn State in order to discover some qualitative                  features of the coarsening processes of domain structures and the               nature of the interaction between singularity lines.                                 The project to be carried out by the principal investigator                and a graduate student is an exciting interplay between analytical              applied mathematics and experimental fluid dynamics.  For the past              few years the principal investigator has studied the systems of                 differential equations that govern the behavior of liquid crystals              using mathematical tools.  She plans now to combine this analytical             work with experimental studies of the phenomena modelled by the                 equations.  The research will have relevance to improving the                   industrial processing of anisotropic polymeric materials.
String theory is one of the most challenging and interesting fields inboth mathematics and physics.  Widely considered the most promisingapproach to formulating a complete unified model of physics at themost fundamental level, it has also spawned many ideas in puremathematics.  The original idea of string theory was that all fundamental constituents of the universe were open or closed loops of string.  It has become increasingly clear that this formulation of the theory is incomplete in essential ways.  One of the missing pieces is the phenomenon known as "D-branes", which naively appear to be geometric objects of variousdimensions: points, strings, membranes, and so on, which coexist with the fundamental strings of the theory.A satisfactory mathematical framework for studying these D-branes, and an understanding of their physical nature, are lacking.  In this project,mathematical techniques from algebra and geometry will be used to uncoverthe concepts required for a precise definition of these D-branes.  Theresearchers will develop new mathematical tools, as needed, as well asapply existing mathematical tools to attack this problem.  The physical nature of D-branes in non-trivial backgrounds will also be investigated in detail, using   methods from quantum field theory and insights from supergravity.  The insights gained from the study of D-branes will be applied back to the physics of gauge theory and string theory, as well.
Algebraic Geometry Summer Institute A large scale summer institute in algebraic geometry, three weeks induration, will be held during July-August 2005 at the University ofWashington, Seattle. Organizational support will be provided by theAmerican Mathematical Society and the Clay Mathematics Institute. Eachweek will have a general topic as a focus and at the same time willinclude a component of core "classical" algebraic geometry. The foci will be: Mathematical Physics in Algebraic Geometry; Combinatorics, Commutative Algebra and Classical Algebraic Geometry; and Arithmetic AlgebraicGeometry. Three plenary morning lecture series will be held in each week, lecturers having been selected as leading researchers who are at the same time exemplary expositors. In addition, leading specialists will beinvited to serve as seminar leaders, and will select high impact lectures given by the best lecturers for afternoon seminars.  Additional activities will include the CMI distinguished lectures and an evening graduateprogram.Algebraic geometry, the study of geometric shapes defined by polynomialequations, is a vast generalization of the high-school topic "analyticgeometry". It has enjoyed much cross-fertilization in past decades withareas in pure mathematics, applied mathematics, computing and theoretical physics. One way American algebraic geometers have maintained the vibrancy of the field is by holding a large scale, NSF-funded summer instituteabout every decade, an institute which aims to bring participants up tothe forefront of research in the salient direction the field has taken in the previous years, and to project directions which the field is expected to take in the following years. These institutes have had a crucialformative role on the subject, with enormous impact especially on theemerging careers of young researchers. This summer institute project aims to follow in their footsteps.
FouqueDMS-1409434     Challenging nonlinear problems arising naturally in the context of risk management under uncertain or randomly fluctuating volatility and under liquidity constraints are addressed in the first part of the project.  This work has direct applications to problems faced by practitioners in the financial industry, including pension funds managers.  The second part of the project is a study of systemic risk and mathematical analysis of the stability (or instability) of our banking system.  The recent financial crisis has revealed a lack of understanding of the risk of cascade of defaults in banking networks.  To help assess measures of such systemic risks, the investigator develops and analyzes new stochastic games models of borrowing and lending among banks.  A graduate student and a postdoctoral researcher are engaged in the project each year.  This project, including its training component, contributes to the effort started by the regulators in the recent creation of the Office of Financial Research.      In the first part of the project, the investigator establishes new results in the theory of asymptotic analysis and homogenization of nonlinear partial partial differential equations, with direct applications to several important and practical problems in financial mathematics.  These problems include risk management under uncertain volatility, portfolio optimization under stochastic volatility, and investment with co-integrated assets.  In the second part of the project, he studies stochastic games models of inter-bank borrowing and lending with applications to measures of systemic risk.  New mathematical problems arise naturally; they include backward-forward stochastic partial differential equations and stochastic games with delay.  A graduate student and a postdoctoral researcher are engaged in the project each year.
Led by principal investigators the Mathematics Department at Texas A&M will host a group of 12 talented undergraduates for research training during 8 weeks each summer. The REU faculty will specifically seek strong students who have been isolated from research opportunities at their home institution, be it from prior hardships or lack of resources. Students will have the opportunity to learn cutting-edge mathematical ideas from scratch, and contribute to solving hard problems underlying many real-world problems from biochemistry, engineering, cryptology, and quantum computing. Students will receive free housing, reimbursement for travel, and a stipend. Thematically, the REU program will have three research streams per summer. These are chosen on a rotating basis from four choices: (1) Algebraic Methods in Mathematical Biology, (2) Algorithmic Algebraic Geometry, (3) Number Theory, and (4) Quantum Computing. The first stream involves neural codes and biochemical reaction networks. The second stream focuses on A-discriminants, tropical approximation of algebraic sets, and applications to optimization. The third stream investigates questions on zeros of modular forms, L-functions, and class number bounds. The fourth stream focuses on topological approaches to quantum computing.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
The proposed workshop, 'Probabilistic Models of Cognition: The Mathematics of Mind,' will bring together leaders from cognitive science, computer science, mathematics, and statistics who are interested in developing  a common mathematical framework for all aspects of cognition, and review how it explains empirical phenomena such as vision, memory, reasoning, learning, planning, and language. This program is motivated by recent advances which offer the promise of modeling human cognition mathematically. The workshop will entail presentations by leading faculty-level lecturers and an audience of graduate students, postdoctoral researchers, and more senior researchers interested in focusing their efforts on probabilistic models of cognition and their applications. Attendees will represent a number of disciplines, including cognitive science, neuroscience, computer science, mathematics, physics, statistics, engineering, and education. Researchers interested in education should be equipped with a wide range of new computational, mathematical and statistical tools that can be used to improve educational technology, curriculum design and assessment, through the development of qualitatively more powerful models of human learning. Researchers in all of these fields, as well as basic cognitive-science researchers, should benefit immensely from interacting with each other and learning about this new generation of cognitive modeling approaches in an unprecedented interdisciplinary environment, with both basic and applied research themes represented among the lectures and discussions.
This project on inverse problems will develop mathematical                 recovery methods for unknown coefficients from second order                     partial differential equations in multi-dimensions.  The                        stability of these methods and their computational costs will                   also be analyzed.  Applications to age-structured populations                   will be investigated and information such as birth and death                    rates will be extracted from certain functionals of the                         population.                                                                          Inverse problems arise in mathematical models describing                   physical  systems containing uncertainties in coefficients or                   boundary  conditions.  Using additional information, in the form                of boundary data or interior measurements, a more accurate model                is sought -- one in which the output of the model conforms to the               measured data as closely as possible.  Important examples of                    inverse problems are medical imaging using CAT scans, acoustic                  sonograms, and non-destructive testing of aircraft wings in                     searching for damaged or failed sections.
The Mathematical Sciences Postdoctoral Research Fellowships                are awards to recent recipients of doctoral degrees.  The                       fellowship is designed to provide 24 months of support divided                  into 18 academic months and 3 periods of two summer months.  The                recipient has the option of a Research Instructorship which                     allows the 18 months of academic support to be taken as 9 months                of full-time support and 18 months of half-time support.                        Mathematical Sciences Postdoctoral Research Fellowship awards                   allow fellows to choose research environments that will have                    maximal impact on their future scientific development.                               Dr. Jonathan Weitsman received his doctoral degree from                    Harvard University, and will pursue research in the area of                     mathematical physics under the guidance of Dr. I. M. Singer at                  the Massachusetts Institute of Technology.
The proposed research will investigate the connection between the singularity theory of Harish-Chandra modules and the matrix coefficient asymptotics of Harish-Chandra modules. The first step is to link the existence of global Whittaker models, the structure of cell representations of the Weyl group, the theory of nilpotent orbits and the structure of Jacquet modules.  Next one uses recursive algorithm to compute the weight filtration of any degenerate series. Finally, relating the PI's earlier work on smooth embeddings with the embeddings of Matsuki-Oshima, one obtains better understanding of the embeddings of irreducible representations into principal series representations.      The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics.  As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.
The PI will investigate a number of problems, using homotopy aspects of arithmetic geometry, that may be thought of as generalizations of the period-index problem for the Brauer group, the u-invariant problem for quadratic forms, and the Hasse principle for a quadratic form over a number field. The project will focus on the interaction of field arithmetic and the complexity of algebraic structures, such as quadratic forms, Brauer groups, linear algebraic groups and homogeneous varieties. The project represents a set of techniques and experiments designed to capitalize on the new topological perspective in the study of algebraic structures. It will aim to support and further the interactions of these areas with arithmetic algebraic geometry, algebraic topology and the algebraic geometry of stacks and moduli.The relevance of these topics, rooted in algebra within pure mathematics, is exhibited by their connections to a wide range of other subjects in recent years. Besides their many ties to other branches of mathematics, the algebraic structures at the core of this proposal have also found applications within diverse areas from theoretical physics to wireless communications.  The research component of this project will seek to capitalize on and enrich our understanding of the many connections to other areas of study in order to gain more leverage in understanding these fundamental and important algebraic structures.  The project's outreach components include funding conferences aimed at establishing a community inclusive of graduate students and young researchers, undergraduate colloquium aimed at increasing interest in mathematics, and facilitating a mentoring program for high school students in northeast Georgia interested in mathematics. It will also pursue strategies towards improving the mentoring and retention of graduate students in mathematics.
The Geospace environment comprises a complex system of interlaced domains that interacts with the incoming solar wind plasma flow and transfers its energy and momentum from the Earth's magnetosphere outer layers down to the ionosphere and upper atmosphere. These physical processes take place mainly on the Earth's dayside, diverting most of the energy along geomagnetic field lines toward both the northern and southern polar regions. Understanding this complex interaction process that couples both polar ionospheres is important for developing physical models that can describe and predict space weather disturbances and help mitigate their impacts on humans' technological systems - from near-Earth space assets down to electrical grids and long pipelines. There is a strong need to collect sufficient geophysical data to investigate the above-mentioned processes, particularly from the southern hemisphere. With this award, the grantees will build and deploy additional ground-based observations platforms in the East Antarctic Plateau, enhancing capabilities of the existing meridional array of already deployed autonomous, low-powered magnetometers. This will make the southern array of magnetometers two-dimensional and geomagnetically conjugate to similar instruments deployed in Greenland and Svalbard, thus making possible a global view of the magnetospheric regions where natural, ultra-low frequency electromagnetic waves are generated. The research involves young scientists who will operate remote Antarctic magnetometers and analyze collected data to investigate space weather events and validate models. This project expands the Virginia Tech's partnership with the University of New Hampshire, New Jersey Institute of Technology, Polar Research Institute of China, and Technical University of Denmark.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
The PI proposes to use functionalized, fluorinated allenes to develop new fluorinated ring construction methodologies. They will first prepare a number of mono and difluoroallenes. The metallation, alkylation and substitution reactions of these compounds will be investigated followed by a study of their use in cyclization reactions to prepare both fluorinated heterocycles and carbocycles. With this award, the Organic and Macromolecular Chemistry Program is supporting the research of Dr. Gerald B. Hammond of the University of Massachusetts at Dartmouth. Dr. Hammond and his student co-workers will study the preparation and reaction chemistry of a number of organofluorine molecules known as fluorinated allenes. Many pharmaceuticals and agrochemicals are organofluorine containing molecules and this group will be devloping new synthetic groutes to these types of molecules. Students trained during the course of this work will gain experience in synthetic organofluorine chemistry and be acquiring skills needed by the pharmaceutical and agrochemical industries.
Research will be continued on the basic properties of chemistry-transport models (CTMs), focusing on: (1) correction of the numerical error in CTMs due to grid resolution, and (2) chemical mode studies that include the derivation of a stratosphere-troposphere coupled chemistry mode and the formulation of a simplified (parametric) model having the same modes as the CTM. A new approach for calculating the numerical errors associated with grid resolution will be developed and tested. The results will be broadly applicable to all CTMs, and will not only characterize the resolution errors but may also be used to help correct them. The existence of global chemical modes in CTMs will be used as a fundamental diagnostic of the models. The tropospheric chemical mode that describes decadal perturbations to methane will be coupled, for the first time in a CTM, with the century-long stratospheric mode involving nitrous oxide and ozone. Global chemical modes will be used to develop reduced-dimension parametric models using sensitivity calculations with a CTM. A reduced-dimension Jacobian will be calculated that completely defines the parametric model and can be compared with the modes of the full CTM.Broader impacts range from improving the atmospheric chemistry/composition elements in Earth system models to providing more accurate scientific input on global change. The quantification of even one component of uncertainty in projecting atmospheric composition should benefit Earth system models and their policy applications. This project will also help prepare undergraduate students, doctoral students, and post-docs working in atmospheric chemistry with the mathematical skills needed to diagnose and analyze complex Earth system models.
Nuclear Magnetic Resonance (NMR) spectroscopy is a                              non-degradative technique used to determine the positions and                   mutual interactions of atoms in molecules.  Chemistry                           departments depend on NMR instrumentation for the enhancement                   of front-line research in a number of areas of chemistry and                    for utilization in undergraduate instruction.                                                                                                                   This award from the Chemical Shared Instrumentation Program                     will help the Department of Chemistry of the College of William                 and Mary to acquire a 200 MHz NMR spectrometer. The instrument                  will be used to enhance the teaching of undergraduate chemistry                 in this RUI institution and to strengthen research efforts in                   the following areas of chemistry:                                                                                                                                  1) Photochemistry in organized media                                            2) Synthetic methods                                                            3) Natural products synthesis                                                   4) Transition metal peroxo compound synthesis                                   5) Cure cycle polymer processing studies                                        6) Mechanistic studies of nucleophilic vinylic substitution
Fried Research-based discovery science generates enormous enthusiasm among undergraduates. The organic chemistry laboratory sequence is being remodeled to take this fact into account. This course is populated primarily by biology majors and chemistry majors. Students are working individually, but sharing their results within a group of eight students. The research projects for this lab sequence include the isolation and identification of secondary plant metabolites, a study of the Claisen-Schmitt formation of chalcones, and an investigation of substitution reactions. These experiments were chosen in consultation with the biology department in order to emphasize the important of chemistry to the study of biology. The students working on these projects are using instrumentation presently available in the department as well as a GC-MS and an HPLC. Both of these instruments are greatly enhancing the students' laboratory experience. In order to provide further connections between biology and chemistry, both instruments are also being used in the plant biology courses.
This project is developing and evaluating the Connected Chemistry Curriculum (CCC), which incorporates software that employs visual representations embedded in a modeling environment as the core component of undergraduate learning activities in general chemistry. Students participating in the curriculum visualize and manipulate individual molecules in a chemical system and visualize the result of their experimental manipulations. The software makes the information embedded in two-dimensional representations explicit, and provides visual displays of molecular interactions for students to observe, as well as multiple representations to foster conceptual understanding and emphasize connections between symbolic representations. The goals of the project are to 1) design ten self-contained learning modules and supporting materials that include CCC simulations as a core component to address student difficulties in learning general chemistry concepts, 2) optimize the modules using embedded assessments and field observations of classroom practice, and 3) evaluate the efficacy the modules for improving chemistry achievement via a quasi-experimental study that compares the achievement of students learning with CCC modules to students learning from traditional lecture and laboratory methods alone. The project is expected to strengthen the knowledge base regarding student interpretation and manipulation of scientific representations and the affordances of visualization tools for teaching chemistry, as well as inform the design of new visualization-based science curricula.
Vitaly Rassolov of the University of South Carolina is supported by the Theoretical and Computational Chemistry Program to develop a new quantum chemistry paradigm based on strongly orthogonal electron geminals, and to test its suitability for chemistry-oriented applications. The geminal concept consists of a correlated two-electron function, in contrast to the one-electron function that is central to most modern quantum chemistry methods. If proven accurate, the geminal model will have a broad impact on theoretical studies of bond-breaking, reactive species, and transition metals due to favorable computational scaling with respect to system size.This Small Grant for Exploratory Research (SGER) supports high risk/high impact research in the theoretical modeling of chemical compounds and reactions. The goal is to develop a novel, computationally advantageous method that will accurately predict chemical properties important in understanding reactivity and bonding.
A computer-based gas chromatograph with a mass selector detector (GC/MS) is being used by the Chemistry Department at Evergreen State College for undergraduate instruction in organic chemistry, physical chemistry, environmental chemistry and faculty/student research. By coupling this instrumental unit with an existing laboratory computer network system, the advantages of computer interfaced analytical instrumentation in the sciences are also being demonstrated.
This project will carry out a novel approach for educating engineering students in the essentials of analytical chemistry. The course, which has been adopted as a core offering for one of the largest chemical engineering programs in the nation, treats analytical chemistry from a global viewpoint and emphasizes the general aspects of analysis: sampling, separations, data acquisition and data interpretation. The laboratory portion of the course will use hands-on experience with chromatographic, spectroscopic, mass spectrometric and flow injection analysis equipment to illustrate the concepts described in the lecture. This Instrumentation and Laboratory Improvement (ILI) award from the Chemical Instrumentation Program will help the Department of Chemistry at the Georgia Institute of Technology to acquire gas and liquid chromatography equipment, spectrophotometers, an ion-trap detector, and flow injection analysis equipment that will enhance undergraduate laboratory instruction.
This project supports the analysis of marine benthic samples collected in the vicinity of Arthur Harbor, Antarctica, following an oil spill that resulted from the grounding of the Argentine supply ship Bahia Paraiso. The vessel grounded on January 28, 1989, and spilled an estimated 170,000 gallons of diesel and aviation fuel, which contaminated shorelines located up to 15 miles from the site of the accident. Although small in size, this spill is of significance because the affected areas include sites that are used extensively for fundamental scientific research and are composed of highly rich and productive assemblages of marine flora and fauna, which might include components that are very sensitive to unusual anthropogenic disturbances. The experimental design includes tests for possible oil-spill effects on these various components of the intertidal and subtidal communities. In addition, a great deal of importance is placed on basic research approaches to provide detailed descriptions of the structure and composition of these communities and to determine the role of natural environmental factors (e.g., depth, sediment type, organic input, environmental stability) in controlling patterns of spatial distribution and long-term variability (for those components having an historical data base). These studies will provide an empirical assessment of possible effects of the Bahia Paraiso oil spill on benthic components of the Arthur Harbor region. In addition, data from these studies will be extremely important in providing a basis for a more comprehensive understanding of the natural structure and dynamics of the Arthur Harbor benthic ecosystem, as well as a basis for comparison of the benthos with other marine ecosystems of the world. Finally, these analyses will provide baseline data to support continued studies of long-term, natural and man-induced variation in important living components of this diverse and productive region.
Previous studies have suggested that tropical storms may introduce marine organic matter onto land via precipitation.  In the context of the Deepwater Horizon oil spill that occurred in the northern Gulf of Mexico in April, 2010, it is natural to focus attention on the potential for storms in this region to transport and deposit some portion of the pollutant oil inland.  As of June 10, 2010, a conservative estimate of the surface slick in the Gulf is 45,000 square kilometers.  While attention is currently focused overwhelmingly on impacts in the open marine and coastal environments, little -- if any -- attention has been given to examining the potential for tropical storms and hurricanes to move oil spill contaminants far inland.With funding through this Grant for Rapid Response Research (RAPID) researchers at East Carolina University will take a first look at the conveyance of components of the Deepwater Horizon to short-range and longer-range inland sites via the sea storm - rainfall route.  Post-storm rainfall samples will be collected at one coastal site (Lake Pontchartrain) and at one or more inland sites for analysis for aliphatic hydrocarbon (finger-printed to the material from the oil spill) and carbon isotopic composition.  This will be the first study of its kind.Broader Impacts:  Besides the obvious relevance to advancing our understanding of the near- and far-field environmental and human health impacts of the Deepwater Horizon spill, this simple study will also inform scientists, environmental managers, and policy makers working dealing with similar environmental catastrophes in the future and at other places.  A first-year female graduate student will also participate in this project.
Minorities are not well represented in careers in science, particularly the marine sciences. Considerable effort is being made to increase the participation of underrepresented minorities in marine science. This renewal is a two-year training program in marine sciences at the Duke University Marine Laboratory. It includes a semester-in-residence program for undergraduates in their junior or senior year of college, which provides a comprehensive educational and research experience for the students. This is combined with a mentor-in-residence and instructional assistant, who will function as tutors and role models. It also includes a visiting-scholar program in which each year four minority scientists will spend several days on campus interacting with the students.
This project is preparing Pacific Islanders to serve their home islands as informed leaders in natural resource management, protection, and restoration.  The primary focus is curriculum development and professional development of community college faculty.  Project objectives are to (a) provide community colleges with the tools needed to meet research needs, (b) provide students with skills to obtain employment in positions usually filled by non-islanders, (c) encourage students to transfer to four-year university programs, and (d) promote articulation between marine and environmental science programs at the following institutions:  University of Hawaii, University of Guam, Palau Community College, Northern Marianas College, College of the Marshall Islands, College of Micronesia, and American Samoa Community College. Anticipated outcomes include the development of courses in marine and environmental  science that are responsive to needs of local agencies, articulated with 4-year colleges, and incorporate training in modern technologies. Foot Locker workshops are being provided that address a range of topics including ocean currents, water quality studies, coral reef management,  molecular tools for pollution studies, and the taxonomy of coral reef organisms.  The project is also developing articulation agreements between participating universities and community colleges; professional development for community college faculty to enhance technical knowledge and research expertise; student research programs with supporting professional opportunities; and outreach to local high schools and community members. The project takes advantage of existing programs and laboratory resources including the NSF-Undergraduate Mentoring in Environmental Biology (UMEB), NSF Field Stations and and Marine Laboratories, Department of the Interior, Marine  Resources Pacific Consortium (MAREPAC), and National Oceanic and Atmospheric Administration (NOAA) -Coral Reef Initiative.
The dissolved organic carbon (DOC) in the world ocean is part of the global carbon cycle that interacts with the planetary climatic system through its connection with atmospheric carbon dioxide.  Keeping track of this DOC requires the cooperative effort of many marine laboratories worldwide.  Making sure that all of these laboratories are making accurate DOC measurements requires that each one have access to a standardized sample of seawater for which the DOC concentration is set by international consensus. This award will fund the University of Miami to continue a consensus reference material (CRM) program that was first developed in 1998 in support of consistent, high quality measurements of dissolved organic carbon by the international ocean chemistry community.  With continuation of this work, the US and international communities will create with confidence consistent measurements of a major marine carbon reservoir, thereby advancing society?s ability to assess changes in the marine carbon cycle and the role of the ocean in climate change.With continued strong international efforts to investigate the marine carbon cycle, the existing CRM program provides the necessary benchmark for globally comparable marine DOC measurements.  Water from the deep Florida Strait (~42 mol/kg DOC) will be collected, ampoulated, and distributed to the US and international community. Since program launch, 126,000 ampoules of deep seawater and 90,000 ampoules of low carbon water have been distributed to 240 US and international laboratories in 42 nations at the rate of 13,000/year. With renewal of the reference material program for a sixth 3-year period of support, distribution of deep ocean water containing biologically refractory dissolved organic carbon and low carbon reference water will continue to aid the analytical work of the DOM community.  A website is maintained that provides direct and convenient links to a growing number of DOM data collected from the global ocean.