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.

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, singular perturbations, hybrid systems, variational analysis.

Decisions under uncertainty, information structures.

Ordinary differential equations, singular perturbations, nonautonomous systems.

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

Non-Archimedean analytic geometry.

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, V. Kac

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 Angel, Marek Biskup...

Harmonic Analysis
G. Kozma, Alexander Olevskii, Jean Bourgain

E. Mossel

Algorithms, Bioinformatics and Combinatorial Statistics
E. Mossel, M. Braverman, C. Daskalakis, A. Sly, M. Steel, S. Roch

Influence of Functions, Computational Complexity and Social Choice
E. Mossel, P. Austrin, G. Kalai, R. O'Donnell, K. Oleszkiewicz, O. Schramm

Discrete Probability
E. Mossel, Y. Peres, S. Roch, A. Sly

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, G. Binyamini, D. Novikov

Singularity theory.
S. Yakovenko, G. Binyamini

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

O. Zeitouni

Motion in random media

Random matrices

Applications in nonlinear filtering, Communication and Information theory