University of Primorska has three open PhD positions in Mathematics.
The PhD positions are fully funded for four years.
The Starting date is October 1st, 2022.
The Deadline for the applications is August 1st 2022.
The candidates for PhD positions should have a Master's degree in
Mathematics (obtained by September 11th 2022 at the latest), a very good
knowledge of the English language, and should be of age up to 28 years
(extension of this limit is possible in the case of using parental leave in
the past).
Short description of the three open PhD positions:
PhD position under the supervision of Prof. Dragan Marušič:
The work of the selected PhD candidate will be primarily focused on
studying symmetries of graphs.
There are many open problems that relate symmetry and combinatorial
properties of graphs.
One of such problems is the question if every connected vertex-transitive
graph admits a Hamilton path.
Although this is known to be true in some special cases, the general
question remains open.
The PhD candidate will work on several different open problems in this
area, the exact problems would be agreed with the candidate.
The candidate is expected to have a solid background in group theory.
Questions related to this PhD position should be sent to
dragan.marusic@upr.si
PhD position under the supervision of Prof. Bojan Kuzma:
The work will be primarily focused on research in the fields of functional
analysis, linear algebra, and graph theory.
The PhD student will be particularly involved in solving preserver problems
that come from functional analysis and linear algebra with the help of the
tools from graph theory. Typically, the preserver problems will be posed on
subsets of operators acting on Banach spaces and on subsets of matrices
over general fields. They will require characterizing all, possibly
nonlinear, maps which preserve a given property. Since linearity of the
preservers will not be assumed, an important approach which PhD student
will investigate will be to build (an infinite) graph with an edge between
two vertices if a given property holds for the two vertices. PhD candidate
will try to infer algebraic relations between operators through the basic
graph invariants (clique number, number of connected components,…) of the
corresponding vertices and, based on the obtained results, reduce the
problem to already known preservers.
Questions related to this PhD position should be sent to bojan.kuzma@upr.si
PhD position under the supervision of Prof. Enes Pasalic:
The work will be primarily focused on cryptography and different topics of
discrete mathematics.
APN (almost perfect nonlinear) functions are interesting discrete
combinatorial objects that are defined over Galois fields (with the binary
prime field) and have several different characterizations. These objects
can be specified using certain combinatorial properties, coding theoretic
concepts among others, but their most known characterization is given
through their differential properties. Since F: GF(2)^n to GF(2)^n can be
represented as a collection of n Bollean functions their structure may be
also analyzed in terms of its coordinates. These Boolean functions are
usually of some special form (bent or plateaued) which ensures that the APN
property is satisfied. The proposed research topic aims to further
investigate the structure of APN functions through its coordinate functions
and to suggest a generic framework for their construction. Minimum
requirements imposed on applicants include a good knowledge about finite
fields, number theory and some elementary coding theory. It is of benefit
if the applicant possesses a solid knowledge of group theory and algebraic
geometry.
Questions related to this PhD position should be sent to enes.pasalic@upr.si
More information about the open call for PhD positions can be found under
https://www.upr.si/en/about-university/669-news/news-and-announcements/razpis-za-mlade-raziskovalce-v-letu-2022-
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