Mathematics

The Banff International Research Station (BIRS) in Alberta, Canada addresses the imperatives of collaborative and cross-disciplinary research with a focus on the mathematical sciences and their vast array of applications in the sciences and in industry. Its modus operandi facilitates intense and prolonged interactions between scientists in a secluded environment, complete with accommodation and board, and the necessary facilities, for uninterrupted research activities in a variety of formats, all in a magnificent mountain setting. BIRS embraces all aspects of the mathematical, computational and statistical sciences from the most fundamental challenges of pure and applied mathematics, theoretical and applied computer science, statistics, and mathematical physics, to financial and industrial mathematics, as well as the mathematics of information technology, and the life sciences.

The mission of the MBI is: (1) to develop mathematical theories, statistical methods, and computational algorithms for the solution of fundamental problems in the biosciences; (2) to involve mathematical scientists and bioscientists in the solutions of these problems; and (3) to nurture a community of scholars through education and support of students and researchers in mathematical biosciences. MBI is based at Ohio State University.

The Max-Planck-Institut fr Mathematik is one about 80 institutes and constitutions of the Max-Planck-Gesellschaft zur F�derung der Wissenschaften e.V. The institute does research in following work areas: Algebraic geometry and number theory, Arithmetic algebraic geometry, Automorphic forms, Algebraic groups and arithmetic subgroups, Representation theory, Singularities, Complex analysis, Algebraic topology, Differential topology, Differential geometry, Mathematical physics.

A concern with physical quantities – energy, temperature, and the like – has inspired the development of modern mathematics. Scientific and engineering questions have provided a source of vitality to, among other fields, algebra, geometry and analysis.

A concern with logical and statistical quantities – information – is central to present-day science and engineering. The pertinent mathematics is being actively developed, as disciplines such as algorithms, complexity, communications and control motivate questions in adjoining fields such as probability, combinatorics, algebra and harmonic analysis. A common framework supporting the study of information and computation across disciplines is as yet a distant goal. The Caltech CMI is a home in which unfettered development of the mathematical foundations of information and computation can be influenced by, and influence in turn, progress in engineering and science.

SAMSI is a national institute whose vision is to forge a new synthesis of the statistical sciences and the applied mathematical sciences with disciplinary science to confront the very hardest and most important data- and model-driven scientific challenges. SAMSI achieves profound impact on both research and people by bringing together researchers who would not otherwise interact, and focusing the people, intellectual power and resources necessary for simultaneous advances in the statistical sciences and applied mathematical sciences that lead to ultimate resolution of the scientific challenges.

The primary mission of the IMA is to increase the impact of mathematics by fostering research of a truly interdisciplinary nature, linking mathematics of the highest caliber and important scientific and technological problems from other disciplines and industry. Allied with this mission, the IMA also aims to expand and strengthen the talent base engaged in mathematical research applied to or relevant to such problems. The Institute for Mathematics and its Applications was established in 1982 by the National Science Foundation, as a result of a national competition.

The Navy Center for Applied Research in Artificial Intelligence (NCARAI) has been involved in both basic and applied research in artificial intelligence since its inception in 1982. NCARAI, part of the Information Technology Division within the Naval Research Laboratory , is engaged in research and development efforts designed to address the application of artificial intelligence technology and techniques to critical Navy and national problems. The research program of the Center is directed toward understanding the design and operation of computer systems capable of improved performance based on experience; efficient and effective interaction with other systems and with humans; sensor-based control of autonomous activity; and the integration of varieties of reasoning as necessary to support complex decision-making. The emphasis at NCARAI is the linkage of theory and application in demonstration projects that use a full spectrum of artificial intelligence techniques. The NCARAI includes the Immersive Simulations section, the Intelligent Multimodal/Multimedia Systems section, the Intelligent Systems section, and the Interface Design and Evaluation section.

The Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) is a collaborative effort of Rutgers and Princeton Universities, AT&T Labs - Research, Bell Labs, Telcordia Technologies and NEC Laboratories America and their scientific personnel, as well as their colleagues nationwide, working together to play a national leadership role in the development, application and dissemination of discrete mathematics (dm) and theoretical computer science (tcs).

The Center for Computational Finance and Economic Systems is dedicated to the quantitative study of financial markets and their ultimate impact on society. By integrating the talents of economists, finance experts, computational scientists, engineers and other disciplines, CoFES will advance the boundaries of modeling and computational science in this important arena. Using a systems approach CoFES seeks to enhance academic disciplines, business operations and economic policy. The creation of CoFES represents Rice Universitys commitment to this important area of intellectual inquiry. A key component of the research center is the integration of probabilistic and mathematical modeling for complex, multidisciplinary investigations. Rice University is well suited for this endeavor because of its exceptionally bright student body; its distinguished faculty in engineering, business and economics; its world-class resources in high-performance computing; and an unusually flexible and collegial environment in which to pursue interdisciplinary research and education.

The Bristol Centre for Applied Nonlinear Mathematics is a 1M EPSRC funded research programme to address both the mathematical themes of the Bristol Laboratory for Advanced Dynamic Engineering (BLADE), and the grand engineering challenge of real-time dynamic substructuring. In addition, the permanent academic members of the centre have a wide range of research interests, including analysis and control of piecewise smooth systems; analysis of local and global bifurcations; numerical continuation of global bifurcations and solitary waves; computation of invariant manifolds; control and synchronisation of chaotic systems; nonlinear dynamics of laser systems; liquid crystal dynamics; electrical control of porous media flows; non-integrable nonlinear optics; localised elastic buckling in long structures; nonlinear dynamics of power electronics systems; fractal analysis of medical images.

The Center for Nonlinear Studies (CNLS) is part of the Laboratory's Theoretical Division, and it organizes research related to nonlinear and complex systems phenomena. CNLS was formed in October of 1980.

Financial Mathematics is a flourishing area of modern science. Since the pioneering days of Black, Scholes and Merton, the subject has developed rapidly into a substantial body of knowledge. Its numerous applications have become vital to the day to day functioning of the world's financial institutions. As a consequence, a solid command of the principles and techniques of quantitative finance is essential for a responsible approach to the trading, asset management, and risk control of complicated financial positions.

The Center for Applied Mathematics (CAM) administers the graduate Field of Applied Mathematics. Graduate education is a vital function at Cornell University. From the student's point of view, the Applied Mathematics graduate program offers not only the opportunity to work at a major university, but flexibility and accommodation to individual needs and interests. Applied Mathematics is one of the most diverse graduate fields; the range of possibilities of graduate research encompasses the areas of specialization of all the faculty members in the field, who currently number more than eighty. As a Cornell graduate student in applied mathematics, you will find a culture of respect and trust and a collegial atmosphere in which to study and that encourages you to excel. To apply to our program, see details here. Our faculty research interests include information theory, algebraic combinatorics, linear programming, parallel numerical methods, statistical genetics/genomics, Bayesian statistics, numerical optimization, dynamical systems, random processes, probability theory, theoretical population biology and evolutionary biology, mathematical biology, logic, data mining, fluid dynamics, and more.

The overall goal of this project is to develop flexible topological methods which will allow the analysis of data which is difficult to analyze using classical linear methods. Data obtained by sampling from highly curved manifolds or singular algebraic varieties in Euclidean space are typical examples where our methods will be useful. We intend to develop and refine two pieces of software which have been written by members of our research group, ISOMAP (Tenenbaum) and PLEX (de Silva-Carlsson). ISOMAP is a tool for dimension reduction and parameterization of high dimensional data sets, and PLEX is a homology computing tool which we will use in locating and analyzing singular points in data sets, as well as estimating dimension in situations where standard methods do not work well. We plan to extend the range of applicability of both tools, in the case of ISOMAP by studying embeddings into spaces with non-Euclidean metrics, and in the case of PLEX by building in the Mayer-Vietoris spectral sequence as a tool. Both ISOMAP and PLEX will be adapted for parallel computing. We will also begin the theoretical study of statistical questions relating to topology. For instance, we will initiate the study of higher dimensional homology of subsets sampled from Euclidean space under various sampling hypotheses. The key object of study will be the family of Cech complexes constructed using the distance function in Euclidean space together with a randomly chosen finite set of points in Euclidean space.

Welcome to the Department of Mathematics and Statistics. Our web pages contain information on our undergraduate and graduate programs, a list of our faculty and graduate students with their research interests, and information on department seminars. Our department has particularly strong groups in dynamical systems and its applications, geometry/topology, number theory, probability and statistics, as well as having specialized centers, the Center for BioDynamics and the Statistics and Consulting Unit. We were recognized as having the most improved research department in the 1995 National Research Council survey of mathematics programs, and we are in the top Group I ranking of graduate programs by the American Mathematical Society. We are also an academic sponsor of the Mathematical Sciences Research Institute. We are happy to answer any questions you have about the Department, and you are welcome to visit our Department and meet with the faculty.

Over a century ago, Maurice Couette created a simple device to measure the viscosity of a fluid. He placed the fluid between two concentric cylinders and measured the amount of torque required to turn the inner cylinder. As one increases the rotation rate of the inner cylinder, more torque is required. However, at a certain rotation rate, the variation of torque with cylinder speed changes abruptly. This occurs at the onset of an instability, the sudden change of the pattern of fluid flow as a parameter is varied. In this case, a series of circulating cells known as Couette-Taylor vortices emerge in the fluid flow . The presence of this instability places limits on the utility of Couette's viscometer. Many fluid instabilities have such practical consequences; for instance, the presence of fingering instabilities during oil extraction can mean that half of the oil in a reservoir is left in the ground. At the Center for Nonlinear Dynamics, we study fluid instabilities and pattern formation in many fluid systems.

Research in the Center for Nonlinear Dynamics concerns complex dynamics, instabilities, chaos, and pattern formation in systems driven far from thermodynamic equilibrium. Diverse systems exhibit remarkably similar, sometimes even universal behavior. Studies in the Center of solid, fluid, granular, low-temperature gas, chemical, and biological systems involve laboratory experiments, numerical simulations, and theoretical analyses. Problems currently being examined include instabilities at fluid interfaces, dynamics of fluidized beds, spatial patterns and shock waves in granular flows, pattern formation in chemical reaction-diffusion systems, crack propagation in crystalline and amorphous materials, quantum chaos with ultra-cold atoms, nonlinear dynamics of bose condensates, general methods of laser cooling, viscoelasticity of actin networks, elastic properties of normal and pathological biological cells, and enhancement of neuronal growth.

Center for Numerical Analysis (CNA) is an organized research unit of The University of Texas at Austin. It is a subcenter within the Institute for Computational Engineering and Sciences (ICES). The faculty, staff, and students in the CNA are actively involved in carrying out research in numerical anlaysis, writing technical papers, and coding mathematical software. Our scientific research contributes to knowledge in numerical analysis, scientific computation, and mathematical software development. This is useful not only to faculty and students computer users at the local level but also to a larger group of mathematical software users worldwide.

Research in quantum field theory in the Mathematics Department covers the canonical quantization, the renormalization of Yang-Mills theory, quantum gravity, and string theory with an emphasis on the role of supersymmetry. Recent work involves the AdS/CFT correspondence (from which results on the strong coupling limit of certain 4-dimensional gauge theories can be obtained from calculations in classical 5-dimensional supergravity) and the renormalizability and high-precision experimental verification of the standard model.

Two subprograms in the Applied Mathematics groups are Physical Applied Mathematics and Combinatorics and Computer Science. Research in `physical' applied mathematics covers a broad range of fields of application including physics, chemistry, materials science, biology, and related fields of engineering, as reflected in the Physical Mathematics Seminar. Our general goal is to develop mathematical models and simulation techniques with direct relevance for real-world problems in science and engineering. We view applied mathematics as an an interdisciplinary science, which actively participates in new discoveries in the more traditional fields. We also see theory, experiment and computation as equally important components of scientific research, so we maintain two experimental laboratories, the traditional Fluid Dynamics Laboratory as well as a Dry Fluids Laboratory, and the Applied Mathematics Computational Laboratory.