We develop new methods in computational mathematics and apply them to problems from versatile problem domains, including exploration of mathematical structures in discrete mathematics, geometry, combinatorics, formalisation and management of mathematical knowledge, and large network analysis. Our applications are grounded in state-of-the-art theoretical research in discrete and numerical mathematics and theoretical computer science.
- Full name: Computationally intensive methods in theoretical computer science, discrete mathematics, combinatorial optimization, and numerical analysis and algebra with applications in natural and social sciences
- Funding agency: Slovenian research agency (ARRS)
- Project code:
- Principal Investigator: Primož Potočnik
- Funding period: January 2020 — December 2025
- Participating organisations:
- Symmetries of discrete objects
- We are interested in all aspects of symmetry (and the lack-there off) in discrete mathematics. We are particularly interested in highly symmetrical discrete structures, such as vertex-transitive graphs, regular maps, abstract polytopes and manifolds etc.
Maruša Lekše (PhD student)
- Enumerative and algebraic combinatorics
- We use sophisticated techniques for enumeration (both exact and approximate) of objects arising in algebra and geometry.
- Mathematical chemistry
- We study properties of graph classes with relevance in chemistry (e.g. benzenoid and fullerene graphs). We are interested in their spectral properties (e.g. nullity), combinatorial properties (e.g. the number of perfect matchings) and their enumeration and characterisation. We also study constructions that produce larger graphs from smaller graphs and preserve a property of our interest. We also have experience in mathematical modelling behind self-assembly of polypeptides and DNA.
- Mathematical knowledge management
- We collaborate with the Research Group of the Professorship for Knowledge Representation and Processing at FAU Erlangen-Nürnberg on the mathematical data platform MathDataHub.
- Network and data analysis
- We are developing methods for network and data analysis. Current emphasis is on analysis of temporal networks based on temporal quantities (TQs), analysis of bibliographic networks and analysis of symbolic data.
Simona Korenjak Černe,
- Foundations of mathematics and theoretical computer science
- We explore mathematical foundations of computation and data processing. Our explorations in type theory and programming languages aid development of proof assistants, formalised mathematics and programming languages.
- Numerical methods
- We study systems of bivariate polynomials and applications, new interpolation and approximation schemes, the inverse eigenvalue problem and cubic splines in the context of computer aided geometric design.