This project aims to investigate orbits of subspaces under classical group actions in Galois geometry, focusing on their interaction with algebraic varieties over finite fields. The study of non-standard group actions on Segre and Veronese varieties provides new insights into the structure of tensor decompositions, secant varieties, and geometric invariants relevant to combinatorics and algebraic geometry. A key objective is to examine the orbit structure of subspaces in the ambient space of these varieties, with particular emphasis on the ambient space of the Veronese varieties and their connection to linear systems of quadrics. Understanding these orbits has implications for tensor rank problems and secant varieties, contributing to the broader study of algebraic geometry over finite fields. By developing new and extending the known computational techniques (e.g. using the GAP-package FinInG), the project aims to establish proof-of-concept results that support a deeper theoretical understanding of high-dimensional group actions. The outcomes will advance the knowledge in finite geometry, algebraic varieties, and their structural properties.

Terms and Conditions

• The position is available for one year.
• Applicants must possess (or expect to obtain shortly) a PhD in Mathematics or a related area, and show evidence of excellence in algebra, finite geometry, or algebraic geometry. Candidates who completed their PhD recently or will do so by next September are encouraged to apply.
• Relevant expertise in projective geometry, group theory, algebraic geometry over finite fields, or computational algebra (e.g. GAP) is desirable.
• The postdoctoral researcher will have access to funding for travel, conferences, and visitors.
• The compensation is set according to the academic title by Slovenian law governing higher education and is expected to be about 1800 - 1900 EUR / month after tax.

Deadline and Application Process

Applications will be assessed on a rolling basis until the position is filled, beginning September 2025. The starting date is flexible, but preferably no later than October 2026.

To apply, please email the following documents to razpisi.famnitiam@upr.si with the subject line "University of Primorska Postdoc 2025 - Michel Lavrauw":

• Curriculum Vitae,
• Publication List,
• Research Statement,
• Copies of at most three recent papers or preprints,
• Names and e-mail addresses of two or three persons who can be contacted for reference (and who have agreed to be contacted).

Informal inquiries may be directed by email to Prof. Dr. Michel Lavrauw (michel.lavrauw@upr.si).