Research

Research Areas

Read about the four main research areas, faculty, and research centers at NYU Abu Dhabi.

• Analysis, PDEs, and Applications

  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 17^th 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.

  Principal Investigators

  

  Diogo Arsénio

  Research Areas:
  Partial Differential Equations, Collisional Kinetic Theory

  

  Elena Beretta

  Research Areas:
  Inverse Problems for Partial Differential Equations

  

  Nader Masmoudi

  Research Areas: 
  Fluid Mechanics

  

  Tej-eddine Ghoul

  Research Areas:
  Partial Differential Equations

  

  Francesco Paparella

  Research Areas:
  Geophysical Fluids, Earth-systems Processes

  

  Ilya Spitkovsky

  Research Areas: 
  Analysis, Operator and Matrix Theory

  

  Pierre Youssef

  Research Areas: 
  Probability, Convex Geometry, Random Matrices, Random Graphs

  Research Institute Centers

  

  Center for Stability, Instability, and Turbulence

  

  Center for Prototype Climate Modeling
• Geometry, Topology, and Algebra

  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.

  Principal Investigators

  

  Sofiane Bouarroudj

  Research Areas:
  Representation Theory, Mathematical Physics

  

  Qingtao Chen

  Research Areas:
  Mathematical Physics, Quantum Topology and Global Differential Geometry

  

  Arman Mimar

  Research Areas: 
  Arithmetical Dynamics, Arithmetic Geometry, Number Theory

  

  Hisham Sati

  Mathematical Physics, Quantum Field Theory, Differential Geometry, Algebraic Topology, Geometric and Topological Aspects of Physics
• Probability Theory and Statistical Mechanics

  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.

  Principal Investigators

  

  Diogo Arsénio

  Research Areas:
  Partial Differential Equations, Collisional Kinetic Theory

  

  Marwa Banna

  Research Areas: Random Matrix Theory, Free Probability Theory, Matrix Concentration Inequalities, Mathematical Aspects of Deep Learning, Weak Dependence

  

  Elena Beretta

  Research Areas:
  Inverse Problems for Partial Differential Equations

  

  Sofiane Bouarroudj

  Research Areas:
  Representation Theory, Mathematical Physics

  

  Federico Camia

  Research Areas:
  Statistical Physics, Probability Theory

  

  Qingtao Chen

  Research Areas:
  Mathematical Physics, Quantum Topology and Global Differential Geometry

  

  Alberto Gandolfi

  Research Areas:
  Statistical Mechanics, Models for Epidemics, Bioinformatics, Statistics of Unobserved Species

  

  Nader Masmoudi

  Research Areas: 
  Fluid Mechanics

  

  Tej-eddine Ghoul

  Research Areas:
  Partial Differential Equations

  

  Hisham Sati

  Research Areas:
  Geometric Aspects of Physical Theories, Theory of Everything

  

  Ilya Spitkovsky

  Research Areas: 
  Analysis, Operator and Matrix Theory

  Research Institute Centers

  

  Center for Stability, Instability, and Turbulence

  

  Center for Prototype Climate Modeling
• Mathematical Physics

  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.

  Principal Investigators

  

  Federico Camia

  Research Areas:
  Statistical Physics, Probability Theory

  

  Alberto Gandolfi

  Research Areas:
  Statistical Mechanics, Models for Epidemics, Bioinformatics, Statistics of Unobserved Species

  

  Pierre Youssef

  Research Areas: 
  Probability, Convex Geometry, Random Matrices, Random Graphs