Partial Differential Equations, Collisional Kinetic Theory
Research projects in the Program in Mathematics at NYUAD are both interdisciplinary and multidisciplinary, overlapping with — and having applications in —chemistry, computer science, physics, engineering, and economics.
The Mathematics faculty fall into four broad areas of research:
Read about the four main research areas, faculty, and research centers at NYU Abu Dhabi.
Analysis — along with algebra, geometry, and probability — is a major area of mathematics. It is therefore an extremely vast subject, stretching across a wide spectrum of topics, from very pure to fully applied. Even though its early developments can be traced back to antiquity and placed on several continents, the modern conception of mathematical analysis coincides with the scientific revolution of the 17th century and the advent of infinitesimal calculus.
Today, mathematical analysis is part of every mathematician’s toolbox and is essential in the description of other fields of science (natural and social). It takes shape in the form of numerous subareas of mathematics such as real, complex, functional, harmonic, or numerical analysis, and in the analysis of dynamical systems and partial differential equations (PDEs).
NYUAD harbors a strong research team in the field of mathematical analysis, with a particular focus on the analysis of PDEs, fluid dynamics, operator theory, and a natural inclination for interdisciplinary collaborations.
Geometry, Topology, and Algebra are major areas of mathematical research, providing many powerful techniques and applications to other branches of mathematics, to the natural and social sciences, as well as to arts and design. Algebra and geometry are two of the oldest branches of mathematics which originate from solving practical problems whose roots go back to ancient times. Topology, while more modern, has also been conceived in reaction to immediate practical problems facing communities: it originates with Euler studying the layout of bridges in the city of Konigsberg, a problem that has its modern incarnation in the design of subway routes. Modern versions of geometry are also conceived similarly: measuring the area of hilly lands in Hanover led Gauss to introduce the foundations for differential geometry.
The Geometry, Topology and Algebra Group at NYUAD covers a broad spectrum of topics ranging from the classification of symmetries via the theory of Lie algebras and Lie superalgebras, to arithmetic geometry, to the study and classification of spaces and manifolds. One main theme is applications to the sciences, most notably physics, through the study of geometric and topological aspects of physical theories, such as quantum field theory, gauge theory, string theory, and M-theory.
Mathematical Physics, Quantum Field Theory, Differential Geometry, Algebraic Topology, Geometric and Topological Aspects of Physics
Probability theory is one of the most active areas of research within modern mathematics. Because of its wide applicability and its eclectic nature — in both questions and methods — research in probability occurs naturally across borders, between different fields and communities. Probability theory started with the analysis of games of chance, and its development has since been largely driven by problems coming from economics, the applied sciences and physics, as much as from pure mathematics.
The Probability and Statistical Mechanics Group at NYUAD is active in the following areas: percolation, continuous phase transitions, scaling limits, and Euclidean field theory, including conformal field theory, random graphs, and random matrices. Most of the work conducted within the group concerns large systems whose behavior cannot be analyzed deterministically. One of the main goals of this work is to increase our understanding of the mathematical structures underlying the universal behavior of such systems. This research has connections with the study of stochastic differential equations (which are of interest to the PDE group at NYUAD), with quantum field theory and its applications (through the study of critical phenomena and scaling limits), and with biology, economics and other fields that can profit from the use of stochastic methods.
Research Areas: Random Matrix Theory, Free Probability Theory, Matrix Concentration Inequalities, Mathematical Aspects of Deep Learning, Weak Dependence
Geometric Aspects of Physical Theories, Theory of Everything
Mathematical physics is a very broad field of research that encompasses many subareas. Mathematicians at NYUAD are interested in various aspects of mathematical physics, from statistical mechanics to conformal and quantum field theory, from string theory to fluid dynamics.