The project Discrete Morse Theory and its Applications is jointly funded by the Ministry of Science of the Republic of Slovenia and the Ministry of Education, Science and Technological Development of the Republic of Serbia as part of the bilateral scientific collaboration of the two countries for period 2020-2021, which was extended also to 2022 due to the Covid-19 pandemics. This project is a continuation of the successful long-term scientific cooperation between Serbian and Slovenian topological research groups in the fields of computational algebraic topology, topological combinatorics and their applications, which has been renewed and intensified in the last decade.

The leading institutions of the project are the Institute for Mathematics, Physics and Mechanics of the University of Ljubljana and the Mathematical Institute SANU, with Prof Aleš Vavpetič (Slovenia) and Dr Đorđe Baralić (Serbia) as the project leaders. The other project members from the Slovenian team are: Prof Petar Pavešić, Prof Matija Cencelj and Boštjan Lemež from IMPM ULJ and Prof Žiga Virg and Dr Leon Lampret from the Faculty for Mathematics and Physics, the University of Ljubljana, and from the Serbian team: Dr Rade Živaljević, Dr Filip Jevtić, and Mladen Zekić from MI SANU, Dr Marija Jelić Milutinović (FM UB) and Prof Jelena Ivanović (FA UB).

The main goals of the project are research and applications of discrete and algebraic Morse theory in problems in combinatorics and algebraic topology, such as study of graph complexes and topological complexity. These methods offer possibility for substituting complex discrete structure appearing in topology by simpler topological spaces which are more convenient for studying and even open a way for applying computational technics for determination of certain topological invariants. Nowadays they are also successfully implemented in machine learning, data science and industry.

A special attention is paid to organisation of joint workshops, seminar and exchange of researchers in topology from Slovenia and Serbia, which develops continually and evolving from the previous bilateral project, successfully realised by the two teams in the period 2015-2016.