For the development of this subject field, the University will take into account current conditions. At present, the alignment of methods employed by both mathematics and physics is still underway. These efforts have produced the most significant results over the past decades and will continue to top the academic agenda until at least 2030. The presence of various applications contributes to the growth of research in “discrete” fields and shifts mainstreams research conducted in applied mathematics from analysis to combinatorics, while productive use of topological, “continuous” methods for studying discrete systems commences at the same time. The search for symmetries, including hidden ones, in complex algebraic and analysis systems prompts the creation of methods for solving specific problems.
Research focus areas which will be further intensified
Development model of a subject field will combine prompt selective incubation of world-class excellence centres, while also maintaining leadership and ensuring balanced development of the fields, in which the University has advancements recognized on a global scene. With this in mind, retaining its leadership in such areas of mathematics as representation theory, algebraic geometry, mathematical physics is an important objective. Furthermore, promising fields may include dynamical systems, topology, geometric analysis, logic, and probability theory.
On the one hand, the University already has internationally known research groups, and, on the other hand, it possesses the potential for further growth. Upon determining the priority fields from among those on the research agenda, the focus will shift from incentivizing multi-disciplinary approaches to highlighting validity of contemplated research.
As the first step for further development, provisions should be made to take the Nizhny Novgorod group of topological dynamics to the next level. To this end, lead scientists should be invited to Nizhny Novgorod, thereby forming an inter-campus laboratory for dynamical systems, which will bring together Moscow and Nizhny Novgorod researchers in this field. In the longer term, building an international research team in mathematics may be possible at the regional campus in Perm. Due to the fact that 90% of national publications of the global level are produced in three cities, i.e., Moscow, St. Petersburg, and Novosibirsk, development of research-focused activities in regions is of critical importance.
Interaction between basic and applied research requires improvement. The most effective method for this is to integrate respective research groups, including bringing the Faculty of Mathematics, Faculty of Computer Science and Faculty of Physics closer together, location-wise.
For the development of mathematics at the University, it is crucial to extend academic visits of outstanding foreign researchers over longer periods. This will allow to achieve a quality breakthrough and ensure the development of taught and research programmes. The creation of network laboratories with Kyoto University, the University of Bologna, and University of Reims is one of the most promising areas of work.
In the longer term, the University embraces a nation-wide mission to lay the groundwork for groundbreaking mathematical studies in regions. To this end, partnerships with research organizations, educational centre Sirius, and major Moscow-based and regional academic institutions will be bolstered.
Contributions to the Development of Education
Demand for mathematicians on the part of industry employers is on the rise. However, job positions offered for mathematicians, although they involve solving novel and complicated problems, fail to include mathematical pursuits properly. Therefore, programmes in basic and applied mathematics perform one and the same function. HSE University recognizes its mission to preserve Russia’s school preparing researchers in mathematics. For amplifying the academic course of the development of mathematics and safeguarding integration with applied tasks, the education model will be aimed at creating flexible tracks under degree programmes in mathematics. In particular, academic track will be enhanced; it will proffer academic careers in applied or basic mathematics, which will become a competitive alternative to the career in the industry.
Master’s studies in Mathematics and Mathematical Physics will be incorporated into the unified track “Master’s – doctoral school” as its part; students of these programmes will be offered attractive conditions modelled after academic doctoral programmes.
The University will take part in the project “Moscow Doctoral Programme in Mathematics”. The goal behind the creation of such Moscow-wide doctoral programme is to launch a significant research and education cluster in Moscow patterned after Berlin Mathematical School.
To increase the level of pre-university training among school students, a community of teachers of mathematics is planned to be built, who will be in contact with research mathematicians. This community will primarily draw on graduates of “HSE – Centre for Teaching Excellence Joint Bachelor’s Programme”. Also, world-class centres for the development of mathematics and mathematical education will be set up at HSE University, with their mission steering towards increasing the quality of mathematical training and research throughout the country.
The REU programme (Research Experiences for Undergraduates), which is implemented as part of HSE Summer University, is planned to be expanded. This programme will help to attract those international students who are seeking to engage in research activities. For the purposes of providing additional educational options for students from external universities, including regional ones, online courses, distance consultations, and short-term exchange programmes will be further scaled up.