Department of Mathematics 

Sergei Yakovenko, Head

The principal research interests of the department lie in the two general areas of mathematical analysis and its applications, and of algebra, mainly representation theory, algebraic geometry, and number theory. Topics covered in analysis include structure of finite and infinite dimensional spaces, operator and matrix theory, function theory on the plane, graphs and Riemann surfaces, spectral theory, several aspects of probability and some applications of statistics, 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 algebraic direction includes some aspects of algebraic geometry, representation theory, quantum groups, number theory, automorphic forms, ring theory, 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

H. Dym 

Inverse problems.

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

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

S. Gelbart 

Automorphic forms and L-functions.

Group representations.
S. Gelbart, A. Joseph, A. Regev

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

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
Y. Yomdin, G. Comte

High Order Data Representation, Nonlinear Approximation, based on Normal Forms of Singularities. Numerical methods