You're searching for faculty members in:
Mathematics, Department of
28 matches found.
 | Dan Abramovich
Mathematics, Department of
The area Abramovich studies lies within algebraic geometry, the
branch of mathematics devoted to geometric shapes called algebraic
varieties, defined by polynomial equations. While algebraic geometry
has contributed applications in coding, industrial control, and
computation, Abramovich's research is more closely related to
applications in theoretical physics, where physicists consider
algebraic varieties as components of the fine structure of our
universe. |  | Thomas Banchoff
Mathematics, Department of
Thomas F. Banchoff is a geometer and has been a professor at Brown University since 1967.
His research areas include the geometry and topology of smooth and polyhedral surfaces in three- and four-dimensional space, as well as development and dissemination of Internet-based courseware for communication and visualization in undergraduate mathematics. He has a long-standing project on the history of the fourth dimension, including a biography of Edwin Abbott Abbott , "The Man Who Wrote 'Flatland'". | | | Alexander Braverman
Mathematics, Department of
Most of my recent research is a part of the so called geometric Langlands program. This is a relatively new field which grew out of an attempt to understand some phenomena of number theory predicted by Langlands; this subject lies on the border of such field of mathematics as number theory, representation theory and algebraic geometry. Recently it has also been realized that this subject is deeply connected with various phenomena from mathematical physics (such as S-duality in gauge theory). |  | Jeffrey Brock
Mathematics, Department of
A recent trend in geometry and topology is to develop models for geometric spaces. Such models sacrifice a certain degree of precision in the interest of capturing more large-scale structure. In a recent result of Brock with his collaborators, such models were used to classify all 'hyperbolic' three-dimensional spaces of infinite volume. This result solved the long-standing conjecture of W. Thurston that a certain piece of 'mathematical DNA' for a space determines its structure. | | | Brian Cole
Mathematics, Department of
Functional analysis and complex analysis | | | Georgios Daskalopoulos
Mathematics, Department of
My interest is in nonlinear geometric analysis and applications to topology, geometry, and mathematical physics. In the last years, I have been working on harmonic maps between singular spaces and applications to Teichmueller theory and three-dimensional topology.
In addition, I have been working on some nonlinear parabolic equations related to the Yang-Mills flow on Kaehler manifolds. | | | William Gillam
Mathematics, Department of
| | | Alexander Goncharov
Mathematics, Department of
Arithmetic algebraic geometry, geometry and integral geometry, representation theory.
Arithmetic algebraic geometry: mixed motives, motivic Galois groups, motivic cohomology, special values of L-functions of algebraic varieties, regulators, polylogarithms and their generalizations, motivic fundamental groups, geometry of modular varieties, Feynman integrals.
Geometry: higher Teichmuller theory and its quantization, quantum dilogarithm, quantum groups.
D-module approach to integral geometry. | | | Thomas Goodwillie
Mathematics, Department of
Topology of manifolds, abstract homotopy theory, algebraic K-theory | | | Bruno Harris
Mathematics, Department of
Bruno Harris, professor of mathematics, works on algebraic topology and algebraic geometry – areas with many applications to physics, including String Theory. Topology studies qualitative features, as distinguished from quantitative ones, of problems – thus topology decides whether an equation has solutions, and how many solutions, but does not calculate these solutions exactly. Algebraic geometry deals with equations in many variables involving relatively simple functions-polynomials. | | | Jeffrey Hoffstein
Mathematics, Department of
I use a combination of analytic and algebraic techniques to study L-series associated to number fields and automorphic forms on GL(n). For the past 25 years or so, one of my main themes has been the development of the theory of multiple Dirichlet series as a technique to tie together and study families of L-series. I also study lattice based public key cryptography, in particular NTRU. | | | Justin Holmer
Mathematics, Department of
| | | Nicolaos Kapouleas
Mathematics, Department of
Differential geometry and partial differential equations | | | Richard Kent
Mathematics, Department of
| | | Richard Kenyon
Mathematics, Department of
| | | Yueh Ko
Mathematics, Department of
Nonlinear partial differential equations, analysis |  | Alex Kontorovich
Mathematics, Department of
| | | Alan Landman
Mathematics, Department of
Algebraic geometry | | | Stephen Lichtenbaum
Mathematics, Department of
Algebraic geometry, algebraic number theory, and algebraic K-Theory | | | Hee Oh
Mathematics, Department of
| | | Benoit Pausader
Mathematics, Department of
| | | Jill Pipher
Mathematics, Department of
My primary area of research is harmonic analysis and its applications to elliptic partial differential equations with non-smooth coefficients.
I also have a research interest in cryptography, in particular lattice based cryptography. |  | Michael Rosen
Mathematics, Department of
Michael Rosen performs research in algebraic number theory, the arithmetic of algebraic function fields, and arithmetic algebraic geometry. | | | Richard Schwartz
Mathematics, Department of
I am interested in simple problems in geometry, topology, and dynamical systems. Much of my research deals with the consequences of allowing a simple pattern or phenomenon to repeat forever. The kinds of patterns and constructions I study are idealized versions of what you would see in everyday life, such as a billiard ball bouncing around on a table, or the pattern of shapes on a turtle shell, or a beam of light reflecting in a series of curved mirrors. |  | Joseph Silverman
Mathematics, Department of
Professor Silverman studies number theory, elliptic curves, arithmetic and Diophantine geometry, number theoretic aspects of dynamical systems, and cryptography. |  | Walter Strauss
Mathematics, Department of
Nonlinear waves are ubiquitous throughout the natural world. Some examples are ocean waves, solar wind, vibrational waves in materials, and laser beams. These disparate kinds of phenomena can be described by mathematical models that are based on hyperbolic, elliptic and dispersive partial differential equations and that are surprisingly similar to each other. My research is devoted to understanding the fundamental underlying features of these models and their relationships to physical phenomena. | | | Serguei Treil
Mathematics, Department of
General research areas: harmonic analysis, complex analysis and operator theory. | | | John Wermer
Mathematics, Department of
Complex Analysis |
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