75th Anniversary of the Mathematical Institute SANU

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The Centre for Dynamical Systems, Geometry and Combinatorics (DSGC-synergy), is a result of a long-term collaboration of the Dynamical Systems group led by Vladimir Dragović and the Discrete Geometry/Topology group, led by Rade Živaljević. The emphasis in this collaboration was a high-level, coordinated research in the area of Dynamical Systems, Geometry, Mechanics, Geometric-Algebraic-Topological Combinatorics, Applied and Computational Geometry and Topology, and related fields.

An equally important objective was to create, through an organised and coordinated effort, a proper environment (incubator) for development of young scientists and prepare them for an independent research in some of the central disciplines of contemporary mathematics and mechanics. The symbolic trinity Integrability-Symmetry-Extremality credo summarises some of the principal ideas and unifying research themes, which inspired the creation of the Centre.

Aim, scope and vision: From the very beginning, the Centre was established as a long-term project, which should create proper environment for collaboration and transcend the boundaries between research groups, seminars and research institutions. While most of initial founders of the Centre (Vladimir Dragović, Milena Radnović, Božidar Jovanović, Borislav Gajić, Rade Živaljević) were permanently employed at the SANU Mathematical Institute, other official (internal and external) or unofficial members and external partners (see link ) were from other institutions, projects and seminars.

Following the credo Integrability-Symmetry-Extremality, the Centre covers a broad range of themes from some of the central fields of mathematics and mechanics, involving and connecting dynamical systems, geometry (algebraic, differential, discrete and computational), topology (algebraic, toric, combinatorial, discrete and computational), combinatorics (geometric, algebraic and topological), etc. A multidisciplinary approach and the synergy of the members of the Centre, allowed them to combine sophisticated methods and tools from different areas (see link for links to some of the publications). The Centre has played an outstanding key role in Serbia in the unification of activities and the development of novel algebraic-geometric-topological methods addressing fundamental questions of mutual interests in several core mathematical fields. The themes covered by members of the Centre included integrable systems, billiards and pencils of quadrics, geometric combinatorics, analytic theory of differential equations, nonholonomic and Hamiltonian mechanics, geometry of Lie groups, convex analysis and control, toric topology, convex polytopes, geometric, topological and algebraic combinatorics.

The multidisciplinary character of the Centre and the focus on research problems beyond the state of the art, guarantee a strong impact and dissemination of new results in several core fields. By attracting young scientists and supporting two seminars and international conferences with established reputation and long tradition, the Centre Dynamical Systems, Geometry and Combinatorics has served as a focal point and a coordinator of activities in these areas of mathematics in Serbia. Although officially associated to one of the three departments of the SANU Mathematical Institute, the Department of Mechanics, the Centre, by the scope and breadth of its activities, provides a link to other departments and transcends the boundaries between departments, seminars, and research groups.

Research seminars of the Centre:

Two permanent research seminars with long tradition are formally associated with the Centre: Combinatorics in Geometry, Topology, Algebra (CGTA), formerly GTA (Geometry-Topology-Algebra), link , link , which celebrated its 30th anniversary in 2016 and Mathematical Methods of Mechanics (MMM), which marked its 20th anniversary in 2013, link .

GDIS conferences:

Conference Geometry, Dynamics, Integrable Systems – GDIS 2018, Moscow, June 5-9, 2018,
Conference Geometry, Dynamics, Integrable Systems 2016, Izhevsk, 2–5 June 2016
Conference and School Geometry, Dynamics, Integrable Systems 2014, Trieste, 16–17 June 2014
Conference Geometry, Dynamics, Integrable Systems 2013, Izhevsk, 10–14 June 2013
Conference Geometry, Dynamics, Integrable Systems 2011, Lisbon – Sintra, 10–16 September 2011
Conference Geometry, Dynamics, Integrable Systems 2010, Belgrade – Fruska Gora, 7–13 September 2010
Conference Geometry, Dynamics, Integrable Systems 2008, Belgrade, 2–7 September 2008
A remarkable sequence of GDIS conferences illustrates a major role played by Belgrade Dynamical Systems group (Vladimir Dragović, Milena Radnović, Božidar Jovanović, Borislav Gajić, et al.), in coordinating and organising high-level scientific events, integrating Serbia in the larger European research network. These events brought the SANU Mathematical Institute in Belgrade (as a host and co-organiser) and its Centre for Dynamical Systems, Geometry and Combinatorics, on a par with such world centres as Steklov Mathematical Institute RAS (Moscow), Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, the University of Lisbon, Group of Mathematical Physics (GFMUL), Moscow Institute of Physics and Teсhnology, etc.

Early history of the Centre:

The process of creating the Centre for Dynamical Systems, Geometry and Combinatorics had several phases, linked with important events serving as milestones in its development. One of the earliest such events was the organisation (1989) of the conference Geometric Combinatorics, which took place in Kotor, Montenegro, as a satellite conference of the International Congress of Mathematicians in Berlin, link . The conference, organised by R. Živaljević, S. Vrećica and V. Dragović, created the environment for interaction and gave new impetus to the already existing collaboration of the two research groups, and the associated seminars (CGTA and MMM) and scientific projects. The conference Geometric Combinatorics was (at the time) one of the most exciting mathematical events organised on the territory of former Yugoslavia. As a satellite conference of an international congress of mathematicians, it was able to provide the participation of some of the invited speakers and other distinguished, world-renowned mathematicians such as Louis Billera (Cornell), Anders Björner (KTH Stockholm), Boris Dubrovin (SISSA, Trieste), Herbert Edelsbrunner (Urbana – Champaign), Sergey Fomin (MIT), Mikhail Kapranov (Northwestern), Janos Pach (NYU), Stevo Todorčević (Belgrade), Victor Vassiliev (Steklov Institute, Moscow), Günter Ziegler (Berlin), and others. Additionally, this led to a prolonged collaboration with some of the leading experts and their research groups (Boris Dubrovin, SISSA-Trieste; Herbert Edelsbrunner, IST Austria, Günter M. Ziegler, FU-Berlin, Jiří Matoušek, Charles University, Prague, and others). This tradition was continued and brought to a new level by organising a highly successful sequence of GDIS conferences (GDIS = Geometry, Dynamics, Integrable Systems), link . These remarkable events illustrate a long-term cooperation of the Belgrade Dynamical Systems group (led by Vladimir Dragović) with some of the leading research teams in this area including the groups from Steklov Mathematical Institute RAS (Moscow), SISSA (Trieste), the University of Lisbon (GFMUL), ICTP (Trieste) etc. The Centre has co-organised numerous workshops, mini conferences, visits of leading experts, lecture series, and regional projects. One of the most recent (2016-2017), among the collaborative projects co-organised by the Centre, was the Serbia-Slovenia bilateral project “Applied and Computational Algebraic Topology" (led by Rade Živaljević, MISANU, and Petar Pavešić, University of Ljubljana). From the beginning, the Centre maintained a strong multidisciplinary character of its activities, providing a stimulating atmosphere for interaction and cooperation of research projects, seminars, research groups and individuals. The Centre hosted two parallel projects, associated with the seminars (MMM) and (CGTA) for decades. For example, there were two research projects in the period 2011-2016 supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, directly associated with the activities of the Centre: 1. Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems, led by Vladimir Dragović; 2. Manifolds and discrete structures in Topology, Geometry and Global Analysis, led by Siniša Vrećica.

The Centre has also served as the host for the project “Viva Math" (Živa Matematika), which started in 2011 as a project by the Ministry of Education, Science and Technological Development (proposed by R. Živaljević and V. Dragović) and focused on the popularisation of mathematics and on organisation of introductory research lectures and mini courses for talented university and high school students. The early success of the Viva Math project marked the beginning of the fruitful cooperation of the SANU Mathematical Institute and the Serbian Centre for Promotion of Science, which culminated in co-organisation of global national and regional events such as May, the Month of Mathematics (MMM).

More details about the early history of the Centre, its initial members, international cooperation, projects, strategic and regional partners, publications, etc., can be found at link , and link .