PhD Degree

The applicant for doctoral studies must contact a supervisor prior to being admitted to the
program. A research proposal must be submitted during the first semester, and no later than
the end of the first year.
Throughout their studies, the student is required to take an average of one course per
semester, in consultation with and with the approval of his supervisor. The student must
complete a total of eight courses, including at least four courses with numeric grades,
amounting to 12 credits.
Doctoral students are also required to participate regularly in one of the department's
research seminars.
Research Areas in the Department:
1. Algebra: Algebraic groups, semigroups, rings and algebras, Lie groups and
algebras, quantum groups, representation theory, homological algebra,
computational algebra, and cryptography.
2. Analysis: Complex analysis (in one and several variables), harmonic analysis,
functional analysis, operator theory, integral geometry, and mathematical
tomography.
3. Geometry and Topology: Algebraic geometry, differential geometry, computational
geometry, general and set-theoretic topology, dynamical systems, low-dimensional
topology, systolic geometry and topology, knot theory.
4. Number Theory: Algebraic number theory, arithmetic algebraic geometry,
automorphic functions and L-functions, Diophantine approximations, probabilistic
number theory.
5. Combinatorics: Finite and infinite combinatorics, Ramsey theory, automata,
algebraic combinatorics, combinatorics of the symmetric group, reflection groups,
graph theory.
6. Probability: Measure theory, stochastic processes, queueing theory, stochastic
geometry, applications in genetics and biology.
7. Applied Mathematics: Mathematical physics, mathematical biology, numerical
analysis, tomography, random networks and graphs, neural computation, modern
cryptography.