Pursuant to the mission of the Mathematical Institute of the Serbian Academy of Sciences and Arts, the principal activity of the Department of Mathematics is to support and provide the necessary infrastructure for the advancement of fundamental research in the field of mathematics. The pursuit of acquiring, processing and disseminating the broad spectrum of mathematical knowledge is threefold, going from the highest level of scientific research for leading experts, via doctoral studies and trainings for young scientists, to the popularisation of mathematics to non-scientific community. Put comprehensively, the activities of the Department take place on both national and international levels.

Extending the several-decade long tradition of successful research in all fundamental areas of mathematics, the Department fosters research in fundamental mathematical areas and into problems as well as into new challenges triggered by societal and technological developments. The research of the Department focuses on mathematical logic (set theory, proof theory, modal and probabilistic logics, model theory, recursion theory, type theory), mathematical analysis (differential and integral calculus, differential and integral equations, functional analysis, geometric function theory, generalised functions, distributivity equations), algebraic topology (homology theory, stable homotopy theory, knot invariants, configuration spaces, topological combinatorics, manifolds), algebra (theory of Lie groups, theory of group actions, automorphisms of free groups, algebraic structures, representation theory, combinatorial games), discrete mathematics (graph theory, spectral graph theory), category theory, differential geometry, combinatorics and combinatorial geometry (additive combinatorics), operations research, mathematical physics, complex systems (generalised entropies), history and philosophy of mathematics, mathematical aspects of music theory, and didactics of mathematics. As a fundamental discipline, mathematics finds its applications in other branches of science, and in view of these interconnections, the Department endeavours to collaborate with other departments of the Institute, universities, as well as with industrial companies.

Currently, there are thirty researchers in the Department of Mathematics in Belgrade with branches in Novi Sad and Niš. It is run by Silvia Ghilezan as Head of the Department, Zoran Petrić as Deputy Head of the Department, and Luka Milićević as Secretary.

The Department gathers researchers and builds upon the results, activities, collaborations and dissemination of research carried out within fundamental and interdisciplinary projects in the period 2011-2019, which were funded by the Ministry of Education, Science and Technological Development of the Republic of Serbia. The projects mobilised a wide range of existing experts, early-career researchers and PhD students into expert teams, which contributed with great success towards delivering high-quality research, promotion of results and internationalisation. The results of each project have been published in highly competent and competitive journals, books and monographs, and communicated at prestigious international conferences. The realisation of the projects also resulted in a good number of successfully defended PhD theses.

Among the numerous results, the published monographs deserve a special mention: Probabilistic Extensions of Various Logical Systems, published by Springer 2020; Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics, published by Springer 2019; Probability Logics: Probability-Based Formalisation of Uncertain Reasoning, published by Springer 2016. The most prolific authors of the Mathematical Institute are experts from the Department of Mathematics.

Currently, the cutting-edge research on the cross-border of mathematics and computer science with applications to artificial intelligence is gathered within the ongoing prestigious project AI4TrustBC Artificial Intelligence for Trustworthy Block-Chain of the Science Fund of the Republic of Serbia (2020-2022). The 2020 call within the IDEAS Program of the Science Fund has mobilised the researchers and several research teams have applied. The results of this call are eagerly awaited.

Researchers of the Department have a long-standing practice in participating in internationally funded projects such as H2020, FP7, FP6, COST, TEMPUS, ERASMUS and bilateral projects, thus ensuring that the boosted research should stay closely related to the state-of-the-art international research.

International projects, either ongoing or expected in the near future, involve: Horizon 2020: LeTSGEPs – Leading Towards Sustainable Gender Equality Plans in research institutions; COST Actions: EUGAIN – European Network For Gender Balance in Informatics (CA19122), SEADDA – Saving European Archaeology from the Digital Dark Age (CA 18128), G2NET – A network for Gravitational Waves, Geophysics and Machine Learning, (CA17137); Bilateral projects: Discrete Morse theory and its applications, (with Slovenia), Modern trends in chemical graph theory (with Slovenia), Multidimensional Persistence and Toric Topology (with Turkey).

The Department strongly endorses collaboration with other departments of the Mathematical Institute. Moreover, new teams will be formed around new calls for projects of the Science Fund of the Republic of Serbia and the Ministry of Education, Science and Technological Development, as well as within international frameworks and partnership with industry.

The Department members have held distinguished professorship and research positions abroad, at the University of Toronto, the University of Paris, the Free University of Berlin, Mathematical Sciences Research Institute Berkeley, the Technical University of Lisbon, Ecole Normale Supérieure de Lyon and the University of Oregon, among others.

Early career researchers comprise the majority of the Department staff, 20 out of 30 members. These early career researchers, though, already experienced researchers, along with PhD students are the driving force of the Department. Moreover, the Department envisages strengthening their participation. Researchers who have graduated abroad are endorsed to join the Department, following the footsteps of those early career researchers who recently joined the Department after graduating at Cambridge University, the University of Gent, the Free University of Brussels and Université Paris Diderot.

The Department of Mathematics fosters professional activities of its members: acting worldwide as keynote, invited and guest speakers, journal editors, book editors, program chairs, program committee members, reviewers for journals, conferences and doctoral thesis, project evaluators, among others, which, in turn, contribute to the internationalisation, dissemination and promotion of the results and research conducted at the Department.

The researchers of The Department of Mathematics are actively participating in more than ten seminars, some of which were founded as the core activity of the Mathematical Institute more than 60 years ago. The seminars are held on a regular basis at the Mathematical Institute, or at other state university centres (Belgrade, Novi Sad, Niš and Kragujevac). The seminars chaired by the Department members are the Mathematical Colloquium, which accommodates talks in all areas of mathematics, whereas seminars oriented towards topics that are more specific are the Mathematical Logic Seminar, the Probability Logic Seminar, the Mathematics and Music Seminar and the Students’ Seminar. Occasionally there are short courses and reading groups, which, through a series of lectures, systematically present contemporary research in related areas. The exchange of ideas is particularly intense in the Mathematics Colloquium, with a general mathematics audience, and at the Students’ Seminar, which, in an informal and friendly atmosphere, gathers young researchers whose early career interests revolve around mathematics, mechanics, computer science and related fields.

Three annual conferences have been held regularly since 2012: VLP – Probabilistic Logics and Applications, TINKOS – Information Theory and Complex Systems and LAP – Logic and Applications. Renowned international conferences ECSQARU 2019, TYPES 2016, USA-Serbia and West Balkan Data Science Workshop 2018 and other events bringing together top experts in different areas have been organised.

The results of the Department members are publicly available in the recently established Research Repository of the Mathematical Institute (http://researchrepository.mi.sanu.ac.rs).

The Department of Mathematics will continue pursuing the excellence in fundamental research in the fields of mathematics and its applications, while cultivating communities engaged in interdisciplinary mathematics at the intersection of academia and industry.

The expert teams of the Department will continue their investigations, which will be verified by publication in refereed scientific journals, proceedings and monographs. Positive trends in publishing monographs by international scientific publishers, organising international conferences, giving invited lectures at international conferences, research visits abroad and other activities, are expected to continue and thus confirm the international prestige of the researchers from the Department of Mathematics.

Through the activities of the seminars and internships, the Department of Mathematics will continue to support students and young researchers in the earliest stages of their career to help them promote and exchange their ideas, form scientific interests and master the skills required for carrying out research in mathematics, mechanics, computer science and related fields. The Department supports and will continue to contribute to the Open Science and Citizen Science initiatives. The Department will continue to be actively engaged in the popularisation of mathematical sciences, such as Mathematical Seminar at Petnica Science Center and M3: May Month of Mathematics.

The Department of Mathematics will strive to increase diversity and involvement of scientists from traditionally underrepresented groups.