2024 research activities
Overview
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.
ScientistsShow details
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Prof. Avraham Rami Aizenbud
Algebraic geometryCollaboration with: Nir Avni, Raf Cluckers, Dmitry GourevitchAlgebraic groupsSingularity theoryGeometric invariant theoryMotivic integrationAlgebraic StacksRational pointsRepresentation theoryCollaboration with: Nir Avni, Dmitry Gourevitch, Shachar Carmeli, Eitan Sayag.Representation theory of real groupsRepresentation theory of p-adic groupsRepresentation theory of finite groups of Lie typeHarmonic analysis on Spherical varietiesGelfand pairsAsymptotic representation theoryFunctional analysis:Collaboration with: Dmitry Gourevitch, Shachar Carmeli, Raf CluckersDistributions and generalized functionsMicrolocal analysisTopological vector spaces
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Prof. Zvi Artstein
Decisions, the impact of evolution.Ordinary differential equations, singular perturbations, averaging.Control and optimal control, singularly perturbed systems, variational analysis.Teaching mathematics in view of evolution
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Prof. Harry Dym
Classical analysis.Operator theory.Collaboration with: Damir Z. Arov, Vladimir DerkachInverse problems.Collaboration with: Damir Z. Arov
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Dr. Ronen Eldan
High dimensional phenomena in probability and geometryAnalysis and functional inequalitiesApplications of high dimensional theory to learning theory and optimization
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Prof. Maria Gorelik
Representation theory and Lie superalgebrasCollaboration with: Dimitar Grantcharov, Victor Kac, Vera Serganova.
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Dr. Dmitry Gourevitch
Invariant distributionsCollaboration with: Avraham Aizenbud, Eitan Sayag, Siddhartha Sahi, Eyal KaplanRepresentation theory of reductive groups over local fieldsCollaboration with: Siddhartha Sahi, Avraham Aizenbud, Eitan Sayag, Eyal KaplanRepresentations 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 varietiesWave-front sets of distinguished representationsFourier coefficients of small automorphic representationsCollaboration with: Henrik P. A. Gustafssonb; Axel Kleinschmidt; Daniel Persson; Siddhartha Sahi
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Prof. Anthony Joseph
Lie algebras and enveloping algebras, quantum groups. Invariant theory.Collaboration with: Yasmine Fittouhi
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Prof. Victor Katsnelson
Operator theoryHarmonic analysis.Classical analysisAnalytic theory of differential equations.System representation theory of matrix functions.
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Prof. Boaz Klartag
AnalysisConvex GeometryHigh-dimensional effects (i.e., when the dimension tends to infinity).
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Prof. Amitai Regev
Non-commutative ring theory, Algebras satisfying polynomial identitiesCollaboration with: Allan Berele, Doron ZeilbergerCombinatorics: Symmetric functions, Permutation statistics
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Dr. Ran Tessler
Mathematical physicsCollaboration with: Dr. Chaim Even Zohar Mr. Tsviqa Lakrec Dr. Xavier Blot Dr. Sybille Rosset Dr. Yizhen Zhao Mr. Elad Tzalik. Prof. Tali Kaufman
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Prof. Sergei Yakovenko
Analytic theory of ordinary differential equations.Singularity theory. Singular foliations, limit cycles, holonomy.
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Prof. Yosef Yomdin
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
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Prof. Ofer Zeitouni
Motion in random mediaRandom matricesApplications in nonlinear filtering, Communication and Information theoryLogarithmically correlated random fields
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