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, harmonic analysis, dynamical systems, control theory in its various manifestations, optimization, game theory, approximation and complexity of functions, numerical analysis, singularity theory, and robotics.

The probability theory with a special emphasis on random walks on graphs and groups, percolation, is prominently featured in the research between analysis and geometry. 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.

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

Z. Artstein 

Control and optimal control, singular perturbations, hybrid systems, stabilization, relaxation.

Decisions under uncertainty, information structures, games and uncertainty.

Dynamical systems, ordinary differential equations, singular perturbations, invariant measures, nonautonomous systems, relaxation.

I. Benjamini 

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

V. Berkovich 

Algebraic geometry.
V. Berkovich, S. Yakovenko

Number theory.
V. Berkovich, S. Gelbart

p-adic analytic geometry.

A. Dvoretzky

Banach spaces.
A. Dvoretzky, G. Schechtman

S. Gelbart 

Automorphic forms and L-functions.
S. Gelbart, F. Shahidi, E. Lapid, S. Miller

Group representations.

M. Gorelik 

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

D. Holcman 

Modeling biological systems
D. Holcman, Z. Schuss, J. Korenbrot

Analysis on manifolds
D. Holcman, I. Kupka, C. Pugh

A. Joseph 

Lie algebras and enveloping algebras, quantum groups.

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, Itai Benjamini, Gideon Amir, Omer Angle, Marek Biskup...

Harmonic Analysis
G. Kozma, Alexander Olevskii, Jean Bourgain

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 

Limit cycles of vector fields, analytic theory of ordinary differential equations.
S. Yakovenko, Y. Yomdin, D. Novikov

Singularity theory.

Y. Yomdin 

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

Zeroez distribution in Families of Analytic Functions
Y. Yomdin, M. Briskin, N. Roytvarf

Semialgebraic Complexity of functions, Signals Acquisition via non-linear model approximation
Y. Yomdin, G. Comte, N. Roytvarf

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