Current
and on-going research activities
Professor Jonathan Arazy Dr. Arazy does research in several areas of analysis on symmetric domains
using Jordan theoretic tools. Some of the problems in this field have origin
in Mathematical Physics (quantization).
The Center for Computational
Mathematics and Scientific Computation (CCMSC)
at the University of Haifa hosts the following Current and
on-going research
activities by members of the CCMSC:
1.
Department of Mathematics
Faculty of Sciences and Science Education
University of Haifa
Here is a partial list of his research themes:
Explicit (Besov Type) description of invariant inner products in spaces of holomorphic
functions of symmetric domains;
Covariant functional calculi and eigenvalues of invariant operators on symmetric
domains;
Asymptotic expansions of invariant operators on symmetric domains in the Planck
constant (strong correspondence principle);
Boundary behavior and limits of iterates of Berezin transforms on Cartan domains;
Pointwise multipliers in spaces of holomorphic functions on Cartan domains;
Maximal and minimal invariant spaces of holomorphic functions on Cartan and
Siegel domains.
2.
Professor Dan Butnariu
Department of Mathematics
Faculty of Sciences and Science Education
University of Haifa
Dr. Butnariu uses tools of nonlinear and convex analysis, fixed point theory
and Banach space geometry in order to design, study and improve computational
procedures for finding solutions of decision making problems represented in
mathematical form.
He is also interested in mathematical aspects of the theory of fuzzy sets as
an instrument of modeling logical uncertainty often occurring in decision-making.
Dan Butnariu is the co-author of two monographs: Triangular norm Based Measures
and Games with Fuzzy Coalitions (1993) written jointly with E.P. Klement and
Totally Convex Functions for Fixed Point Computation and Infinite Dimensional
Optimization (2001) written jointly with A.N. Iusem.
He authored and co-authored more than 70 mathematical articles.
3.
Professor
Yair Censor
Department of Mathematics
Faculty of Sciences and Science Education
University of Haifa
Dr. Censor
works in Computational Mathematics where his main fields of interest include:
Optimization Theory (mathematical theory and development of algorithms), Linear
Algebra and Convex Analysis (large and sparse systems of linear and nonlinear
equations or inequalities), Numerical Analysis, Inverse Problems, Optimization
Theory Techniques in Image Reconstruction from Projections, Algorithms for Parallel
Computing and Iterative methods in matrix balancing, game theory, transportation
problems and binary tomography.
He has published over 80 research articles in refereed scientific journals,
conference proceedings and as book chapters.
He co-authored with S.A. Zenios the book: Parallel Optimization: Theory, Algorithms,
and Applications, Oxford University Press, New York, NY, USA, 1997.
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4.
Dr. Joshua
Feinberg
Department of Mathematics and Physics
Faculty of Sciences and Science Education
University of Haifa at Oranim
Dr. Feinberg
researches non-perturbative methods in quantum field theory (QFT) and in statistical
mechanics. QFT is the synthesis of special relativity and quantum mechanics.
Observed phenomena of elementary particle physics, down to a distance scale
of a ten-thousandth the size of a proton are described by a QFT: the Standard
Model of elementary particle physics.
QFT methods are applicable in other physical disciplines (e.g., statistical
mechanics, condensed matter physics), and in mathematics (to stochastic processes,
the theory of knot invariants and the Jones polynomial, in DonaldsonŐs theory).
Dr. Feinberg studies non-perturbative QFT issues such as vacuum (ground state)
structure and the related issues of dynamical symmetry breaking the effects
of external conditions, color confinement in quantum chromodynamics (QCD - the
theory of strong interactions), extended objects (solitons, instantons, QCD
strings, random surfaces and their random geometries), and fluctuations around
them.
His work in condensed matter physics and statistical mechanics focuses on the
study of disordered systems.
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5.
Professor
Alex Gordon
Department of Mathematics and Physics
Faculty of Sciences and Science Education
University of Haifa at Oranim
Professor
Alex GordonŐs areas of scientific interest are:
1. Magnetism of a non-spin nature in non-magnetic metals in high quantizing
magnetic fields.
2. Equilibrium and non-equilibrium phase transitions and proton superconductors
and the applications to crystal growth and construction of fuel cells.
3. Advanced, ŇsmartÓ, multifunctional materials and applied physics with applications
to sensors, actuators, control capabilities and memory cells.
4. First-principle calculations of oxide fuel cell cathodes.
6.
Dr. Gilad
Lifschytz
Department
of Mathematics and Physics
Faculty of Sciences and Science Education
University of Haifa at Oranim.
String theory is a theoretical framework for a unified description of all forces
in nature including gravity.
Currently it is the only viable candidate for a theory of quantum gravity.
String theory describes all the particles in nature as different vibrations
of strings (closed loops) moving in ten-dimensions, and all interactions between
the particles as joining and splitting of the strings.
String theory relies heavily on advanced mathematics and the problems one needs
to solve are formidable.
As such both analytical and numerical methods are used. Dr. Lifschytz research
concerns the way space and time emerges in string theory, in order to uncover
the true nature of space-time.
A useful guide to this, and a goal by itself is the understanding of the physics
of black holes.
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7.
Dr. Reuven
Granot
Department of Mathematics
Faculty of Sciences and Science Education
University of Haifa
Robotics
is a multidisciplinary area and as being such, an introductory course enables
students with mathematic background to receive first hand basic knowledge from
scientific and engineering disciplines like physics, control engineering, system
design and integration as well as more mathematically oriented applied areas
from computer science like machine vision and artificial intelligence.
The research in robotics and telerobotics at University of Haifa is in its preliminary
stages of organizing a laboratory oriented toward teaching and graduate level
research.
The research will be focused in the area of development of software control
agents to represent a human operator interfacing with a complex telerobotic
system environment.
This activity should be based in addition to the software development environment
also on experimental robotics, resulting in the need to be equipped with mobile
robots and advanced robotic toys.
8.
Professor Efrat Shimshoni
Department
of Mathematics and Physics
Faculty of Sciences and Science Education
University of Haifa at Oranim.
Electronic systems cooled down to very low (sub Kelvin) temperatures
exhibit a variety of fascinating phenomena, that are primarily manifested
in terms of peculiar and anomalous conduction properties. These become
particularly pronounced in systems of reduced dimensions (i.e., thin films
or wires), and originate from the interplay of two ingredients: quantum
mechanical effects, and strong correlations among the many particles,
associated with their mutual interactions. These effects can lead to the
emergence of a `correlated state', which can not be simply described as a
collection of the original particles. Instead, one should define collective
objects (`quasi-particles') which act as the `natural' building blocks of the
system. My research focuses on the theoretical understanding of several
examples of this scenario. These include transport phenomena in the fractional
quantum Hall regime, which is characterized by the emergence of elementary
quasi-particles whose charge is a fraction of the electron charge; the phase
transition from a superconductor to insulator observed in thin metal films
and or wires; and the anomalous electric and heat transport of strongly
interacting electrons restricted to a one-dimensional channel, in which the
charge and spin of the electrons effectively separate into two independent
carriers, of charge only (`holons') and spin only (`spinons').
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9.
Professor Raphael Yuster
Department of Mathematics
Faculty of Sciences and Science Education
University of Haifa
Part of Prof. Yuster's research is in the area of combinatorial packing and covering problems. This area of research has interesting applications in theoretical computer science and in statistics. In these problems we are given a small fixed combinatorial object (e.g., a fixed small graph) and we wish to pack (or cover) a larger combinatorial object (e.g. a larger graph) with copies of the small object (a copy is a sub object of the large object which is isomorphic to the small object) .
The goal is twofold: Find necessary and sufficient conditions for the existence of a packing or covering of a certain size,
and find efficient algorithms that construct an optimal (or almost optimal) packing (covering). In packing problems we require
that no element (e.g. edge) of the large object appears in two distinct copies of the small object, while in covering problems
we require that each element (e.g. edge) of the large object appears in at least one copy of the small object.
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10.
Dr. Toufik Mansour
Department of Mathematics
Faculty of Sciences and Science Education
University of Haifa
Dr. Mansour works in several areas of Combinatorics where his main
fields of interest include: Enumerative of Combinatorics and
algebraic Combinatorics. In particular, permutation patterns and
word patterns. This field proved to be a useful language in a
variety of seemingly unrelated problems, from stack sorting to the
theory of Kazhdan-Lusztig polynomials, singularities of Schubert
varieties, Chebyshev polynomials, and rook polynomials. Here is a
partial list of his research themes: Explicit enumeration for
number of permutations (words, compositions, matrices) with
different kinds of restrictions; Giving analogies of enumerative
results on certain classes of permutations characterized by
pattern-avoidance in the symmetric group; Counting elements of a
given discrete structure (as the symmetric group, hyperoctahedral
group, matrices with 0,1 entries, compositions, and matching
words) with different restrictions; Combinatorial identities;
Ordered patterns in words generated by morphisms; and Independent
sets and graphs.
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11.
Prof. Shay Gueron
Department of Mathematics
Faculty of Sciences and Science Education
University of Haifa
Prof. Gueron works in Applied Mathematics where his main fields of interest
include: Mathematical Biology, Applied Cryptography, Efficient Computational
Algorithms.
Dr. Kobi Peterzil
Department of Mathematics
Faculty of Sciences and Science Education
University of Haifa
Dr. Kobi Peterzil's areas of scientific interest are:
Model Theory of analytic structures and groups,
O-minimal structures, connections between complex
analytic geometry and model theory.
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