Department of Mathematics

Sergei Yakovenko, Head

The principal research interests of the department lie in the broadly understood areas of analysis, algebra, and geometry, very often on the cross-roads between these areas, and closely related to the research at the department of computer science and applied mathematics.

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.

Probability theory is prominently featured at the interface between analysis and geometry. Special emphasis is put on the study of random walks on graphs and groups, motion in random media, percolation theory, and random matrices. Other areas of geometric research include the structure of finite and infinite dimensional spaces, analytic, real algebraic and semialgebraic geometry and topology of foliations.

The algebraic direction includes some aspects of algebraic geometry, representation theory, quantum groups, number theory, automorphic forms, ring theory, statistics of Young diagrams, algebraic combinatorics and enveloping algebras, invariants and crystals.

Although the approach taken is primarily that of theoretical mathematics, some of the research leans towards possible applications.

Z. Artstein

Control and optimal control, singularly perturbed systems, variational analysis.

Decisions under uncertainty.

Ordinary differential equations, singular perturbations, averaging, nonautonomous systems.

I. Benjamini

Probability and geometry.
I. Benjamini, A. Dvoretzky, G. Schechtman, O. Schramm

V. Berkovich

Non-Archimedean analytic geometry.

Algebraic geometry.
V. Berkovich, S. Yakovenko

Number theory.
V. Berkovich, S. Gelbart

H. Dym

Inverse problems.

Operator theory.
H. Dym, V. Katsnelson, M. Solomyak

Classical analysis.
H. Dym, V. Katsnelson, Y. Yomdin

S. Gelbart

Complex and p-adic Automorphic forms and L-functions.
S. Gelbart, F. Shahidi, A. Panchishkin, S. Miller

M. Gorelik

Representation theory and Lie superalgebras
M. Gorelik, V. Serganova, V. Kac

D. Gourevitch

Representation theory of reductive groups over local fields
D. Gourevitch, A. Aizenbud, S. Sahi

1.  Representations of real reductive groups

2.  Representations of p-adic reductive groups

3.  Relative representation theory

4.  Gelfand pairs

Invariant distributions
D. Gourevitch, A. Aizenbud, E. Sayag

A. Joseph

Lie algebras and enveloping algebras, quantum groups. Invariant theory.

Y. Kannai

Mathematical economics, statistical analysis of occurrence of asthma in children.

Partial differential equations.
Y. Kannai, M. Solomyak

V. Katsnelson

System representation theory of matrix functions.
V. Katsnelson, Dym, H.

Analytic theory of differential equations.
V. Katsnelson, Volok, D.

Harmonic analysis.
V. Katsnelson, Gurarii, V.

Operator theory

Classical analysis

G. Kozma

Probability
G. Kozma, Gil Alon, Gideon Amir, Omer Angel, Itai Benjamini, Nick Crawford, HJugo Duminil-Copin, Asaf Nachmias, Ariel Yadin

Harmonic Analysis
G. Kozma, Jean Bourgain, Nir Lev, Shahaf Nitzan, Alexander Olevskii,

D. Novikov

Hilbert 16th problem

Ordinary differential equations

A. Regev

Non-commutative ring theory

Combinatorics
A. Regev, Yuval Roichman

1.  Symmetric functions

2.  Permutation statistics

G. Schechtman

Convex geometry

Functional analysis and geometry of Banach spaces

Probability

S. Yakovenko

Analytic theory of ordinary differential equations.
S. Yakovenko, G. Binyamini, D. Novikov

Singularity theory. Singular foliations, limit cycles, holonomy.
S. Yakovenko, G. Binyamini

Y. Yomdin

Analytic Theory of Differential Equations, Generalized Moments, Compositions
Y. Yomdin, M. Briskin, N. Roytvarf, F. Pakovich, D. Batenkov

Zeroez distribution in Families of Analytic Functions
Y. Yomdin, M. Briskin, N. Roytvarf, D. Batenkov, O. Friedland

Semialgebraic Complexity of functions, Signals Acquisition via non-linear model approximation
Y. Yomdin, D. Batenkov, N. Sarig

High Order Data Representation, Nonlinear Model Approximation. Taylor Models, High-Order Numerical methods
Y. Yomdin, N. Roytvarf

Model-based image analysis, representation, compression. Model-based search, capturing, and animation
Y. Yomdin, G. Dinkin, M. Briskin, D. Haviv, D. Batenkov

O. Zeitouni

Motion in random media

Random matrices

Applications in nonlinear filtering, Communication and Information theory