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 stateoftheart 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:
P10294
 Principal Investigator: Primož Potočnik
 Funding period: January 2020 — December 2025
 Participating organisations:
Research topics
 Symmetries of discrete objects
 We are interested in all aspects of symmetry (and the lackthere off) in discrete mathematics. We are particularly interested in highly symmetrical discrete structures, such as vertextransitive graphs, regular maps, abstract polytopes and manifolds etc.

Researchers:
Primož Potočnik,
Nino Bašić,
Tomaž Pisanski,
Arjana Žitnik,
Alejandra Ramos,
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.

Researchers:
Matjaž Konvalinka
 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 selfassembly of polypeptides and DNA.

Researchers:
Nino Bašić,
Tomaž Pisanski
 Mathematical knowledge management
 We collaborate with the Research Group of the Professorship for Knowledge Representation and Processing at FAU ErlangenNürnberg on the mathematical data platform MathDataHub.

Researchers:
Katja Berčič,
Filip Koprivec,
Primož Potočnik
 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.

Researchers:
Vladimir Batagelj,
Simona Korenjak Černe,
Tomaž Pisanski
 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.

Researchers:
Andrej Bauer,
Katja Berčič,
Filip Koprivec,
Matija Pretnar,
Egbert Rijke,
Alex Simpson
 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.

Researchers:
Jan Grošelj,
Gašper Jaklič,
Bor Plestenjak