2020 research activities
The principal research interests of the department lie in the broadly understood areas of analysis, probability, algebra, and geometry.
Topics covered in Analysis include operator and matrix theory, spectral theory, linear and nonlinear ordinary and partial differential equations, functional and harmonic analysis, ergodic theory and dynamical systems, control theory in its various manifestations, optimization, game theory, approximation and complexity of functions, numerical analysis, singularity theory and robotics.
Research in Probability theory covers random walks and graphs, motion in random media, percolation, random matrices, Gaussian fields and other probabilistic models in mathematical physics.
Areas of Geometric research include the structure of finite and infinite dimensional spaces, analytic, real algebraic and semi-algebraic geometry, typology of foliations and complex vector fields.
The Algebraic direction includes some aspects of algebraic geometry, geometric group theory, Lie Theory, representation theory, quantum groups, number theory, automorphic forms, ring theory, statistics of Young diagrams, algebraic combinatorics and enveloping algebras, invariants and crystals.
For the research done at our sister department, the Department of Scomputer Science and Applied Mathematics, see here.
Algebraic geometry: Algebraic groups, Singularity theory Geometric invariant theoryRepresentation theory of real and p-adic groups: Harmonic analysis on Spherical varieties, Gelfand pairs, asymptotic representation theoryFunctional analysis: Distributions and generalized functions, Microlocal analysis, Topological vector spaces.
Invariant distributionsCollaboration with: Avraham Aizenbud, Eitan SayagRepresentation theory of reductive groups over local fieldsCollaboration with: Siddhartha Sahi, Avraham Aizenbud, Eitan Sayag,Representations of real reductive groupsRepresentations of p-adic reductive groupsNon-commutative harmonic analysis on homogeneous spaces, or Relative representation theoryDegenerate Whittaker models and Fourier coefficients of automorphic formsMultiplicities in induced representations, Gelfand pairsNon-commutative harmonic analysis on spherical varieties
High Order Data Representation, Nonlinear Model Approximation. Taylor Models, High-Order Numerical methodsSemialgebraic Complexity of functions, Signals Acquisition via non-linear model approximationAnalytic Theory of Differential Equations, Generalized Moments, CompositionsZeroez distribution in Families of Analytic FunctionsModel-based image analysis, representation, compression. Model-based search, capturing, and animation