Position for postdoctoral fellowship at the Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics of Vilnius University

Outline

Topics: topological invariants of Algebraic Structures: groups; lattices; non-permutability graph and commutativity degrees.

About the project.

The postdoc fellowship Project will focus on topological tameness conditions of groups and on invariants of combinatorial nature for lattices and topological groups. The research will be carried out under the supervision of Dr. Daniele Ettore OTERA.

The main aspect of the Project’s topics is to follow V. Poenaru’s and F. Russo’s ideas in terms of invariants of topological-combinatorial nature, which are related to the lattice of algebraic structures and also in the context of topological and discrete groups, focusing also on locally-compact groups. The underlying point will be the bridge between the research fields of (geometric) group theory, topology and graph theory. In particular, the two main topics will be the general concept of exhaustibility for discrete groups and some new notions related to the (subgroup) commutativity degree.

The main research lines are:

- to adapt the QSF property for new classes of topological (e.g. profinite) groups;

-  to enlarge the class of QSF groups;

- to further develop the theory of the subgroup commutativity degree focusing on connections with Graph Theory;

- to study the subgroup commutativity degree for large classes of topological groups;

- to possibly develop a theory of commutativity degree for other algebraic structures.

Prerequisite for a researcher: a doctoral degree awarded by a foreign or other (non-University) Lithuanian institution of science and studies, with no more than 5 years having elapsed since the awarding of the doctoral degree (the period of time during which the person has been granted maternity, paternity or parental leave is not included in the period of 5 years).

What is funded

Workload: full-time.

Monthly salary: 3100 EUR (before tax).

Duration

Duration of fellowship: 24 months starting at 1st of October, 2024.

Eligibility

Requirements:

- PhD in Mathematics, with a specialization in Algebra;

- Experience and knowledge in Topological Groups, Lattice Theory, Spectral Graph Theory, Commutativity degrees.

- Knowledge of advanced software in Graph Theory.

- Knowledge of advanced software in Group Theory.

- English language (C1, advanced).

Documents required:

• Completed application;
• Free-form description of life and scientific activities (CV);
• PhD diploma;
• Recommendations from two researchers.

Please submit your completed Application form with Application attachments via email to Dr. Daniele Otera by email: daniele.otera@mif.vu.lt in the subject line indicating ‘postdoctoral fellowship‘.