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Classification: Algebraic Geometry The Departments of Mathematics of the Faculty of Mathematics, Natural Sciences and Information Technologies (FAMNIT) and Andrej Marušič Institute (IAM) of the University of Primorska are seeking a top early-career researcher for a postdoctoral position in the area of Galois geometry and group actions, in connection with the research grant of Prof. dr. Michel Lavrauw, "High-Dimensional Actions of Classical Groups in Galois Geometry" funded by the Slovenian Research and Innovation Agency. 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.