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title: Computationally intensive mathematical methods
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# Computationally intensive mathematical methods

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)](https://www.arrs.si/en/index.asp)
* **Project code:** [`P1-0294`](https://cris.cobiss.net/ecris/si/en/project/18055)
* **Principal Investigator:** [Primož Potočnik](https://www.fmf.uni-lj.si/~potocnik/)
* **Funding period:** January 2020 — December 2025
* **Participating organisations:**
* [Institute of Mathematics, Physics and Mechanics](http://www.imfm.si/view?set_language=en)
* [Faculty of Mathematics and Physics](https://www.fmf.uni-lj.si/en/), [University of Ljubljana](https://www.uni-lj.si)
* [Andrej Marušič Institute](https://www.iam.upr.si/en), [University of Primorska](https://www.upr.si/en)
* [Abelium R & D d.o.o.](https://abelium.com/en/)

## Research topics

**Discrete geometry and symmetries of discrete objects**
: `YOUR DESCRIPTION HERE`

: **Researchers:**
Tomaž Pisanski,
Nino Bašić,
Primož Potočnik,
Arjana Žitnik

**Enumerative and algebraic combinatorics**
: We use sophisticated techniques for enumeration (both exact and approximate) of objects arising in algebra and geometry.

In [slope game](https://slope-game2.github.io/), every roll of the ball is an opportunity for you to improve your control skills and enjoy the fun of spectacular sharp turns.

: **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 self-assembly 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 Erlangen-Nürnberg](https://kwarc.info/) on the mathematical data platform [MathDataHub](https://data.mathhub.info/).

: **Researchers:**
Katja Berčič,
Filip Koprivec,
Primož Potočnik

**Network and data analysis**
: `YOUR DESCRIPTION HERE`

: **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