Mathematics

I am the George Gund Professor of Economics and Business Administration in the Department of Economics at Harvard University, and in the Harvard Business School. My research interests are in game theory, in experimental economics, and in market design (for which game theory, experimentation, and computation are natural and complementary tools).

The Math Center consists of roughly four dozen members of technical staff, who conduct research primarily in the areas of statistics, mathematics of networks, performance analysis, mathematical foundations of computing, communication theory, and core mathematics. Some topics currently receiving research emphasis in the Center are broadband networking design tools and methods, ATM admission control, traffic characterization and modeling, simulation methods for networks and systems, statistics of large databases, fraud detection, statistical software, statistics of software development, experimental design, data mining and visualization, modeling/analysis/design principles for wireless communications systems, signal processing, coding, and information theory. A wide variety of mathematical areas of expertise are brought to bear on these topics, via an environment that encourages collaboration across organizational boundaries and disciplines. You can find out more about our current research under the individual department listings.

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.

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 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 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 Multiscale Plasma Dynamics (CMPD) is a Department of Energy Fusion Science Center, hosted jointly by the University of Maryland and UCLA. Our mission is to extend established first-principles, microscopic, kinetic simulation techniques to problems that intrinsically involve the slow evolution of macroscopic variables, and to validate the simulations against experimental observations.

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.

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.

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.

The primary goal of the Center is to foster research activity that highlights the interplay between novel computational algorithms and mathematical modeling, as complementary avenues to theory and experiment. To stimulate such research activity, CSCAMM fosters collaborative research which involves local scientists, graduate students and visiting post-docs together with world renowned scholars. CSCAMM sponsors an active visitors program through a series of seminars, lectures and workshops and it supports an educational program with a series of tutorials, courses and active involvement with the AMSC graduate program.

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.

Since the mid-1970s, the Chaos Group at Maryland has done extensive research in various areas of chaotic dynamics ranging from the theory of dimensions, fractal basin boundaries, chaotic scattering, controlling chaos, etc. It is hoped that the knowledge we have gained is of use to others, and it is the objective of this web site to disseminate those fruits of labor. It is found that the ideas of chaos have been very fruitful in such diverse disciplines as biology, economics, chemistry, engineering, fluid mechanics, physics, just to name a few. Chaos is a multidisciplinary science, and this is reflected in the fact that the members of the group are affiliated with diverse departments and institutes. The Maryland Chaos Group has been ranked #1 (tied with the University of Texas, Austin) in the country by U.S. News!

The Clay Mathematics Institute is a privately funded operating foundation dedicated to increasing and disseminating mathematics. CMI supports the work of leading researchers at various stages of their careers and organizes conferences, workshops, and an annual summer school. Contemporary breakthroughs are recognized by its annual Research Award. The Institute operates in programs that introduce high school students to mathematical research: the Clay Research Academy, the Ross and PROMYS programs. CMI organizes public lectures and publishes conference proceedings and monographs. The Institute is a principal funder of the Independent University of Moscow. A recent initiative was the preparation of a digital edition of the oldest extant manuscript of Euclid's Elements (Byzantium, 888 AD).

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.