Institute of Mathematics (ELTE) – Between tradition of the past and challenges of the future

Institute of Mathematics (ELTE) –
Between tradition of the past and challenges of the future

Going back one hundred years in the history of mathematics at ELTE, there were several famous scholars, such as Frigyes Riesz (one of the founders of functional analysis), his younger brother Marcell Riesz (with essential work in analysis and number theory), and Lipót Fejér (seminal contributions to harmonic analysis and Fourier analysis). The younger generation involves, among others, János Neumann (mathematical foundations of quantum mechanics), Pál Turán (number theory, graph theory), and Pál Erdős (number theory, combinatorics). In the second half of the 20^th century, combinatorics and graph theory became a Hungarian specialty: it is perhaps enough to mention, for example, the names of László Lovász (winner of the 1999 Wolf Prize and the 2010 Kyoto Prize), Endre Szemerédi (winner of the 2012 Abel Prize), as well as the so-called Hungarian method – an algorithm in combinatorial optimisation, based on the results of Dénes Kőnig and Jenő Egerváry. In addition to combinatorics, one should also mention the rapid development of such areas as topology, algebraic geometry, real analysis, or, among more applied topics, numerical analysis and probability theory.

The current structure of the Institute of Mathematics at ELTE (with its eight departments) reflects the areas in which research is currently undertaken:

algebra (groups, rings, commutative algebra, general algebraic systems)
analysis (real, complex, functional)
combinatorics (graph theory, algorithms, computer science, cryptography)
differential equations (ordinary, partial, and dynamical systems)
geometry and topology (convex, differential, and discrete geometry, algebraic and differential topology)
number theory (additive, algebraic, analytic, combinatorial)
numerical analysis (ODE’s, PDE’s)
operations research (discrete and continuous optimisation)
probability theory and statistics (stochastic processes, applied statistical methods, financial mathematics)
set theory and mathematical logic

One could also list some projects in the field of applied mathematics:

bioinformatics (protein technology, investigation of the brain graph, data mining in 3D protein datasets)
large networks and graph limits (dynamics and the structure of networks, like the human brain, social networks, and the internet)
data security and cryptography
industrial optimization (logistic systems for customer serving warehouses, optimal utilisation for 3D printing technology)
spread of epidemics on networks

The academic achievements of ELTE members are highly recognised by many ongoing co-operations with universities from Germany, the United Kingdom, France, Slovenia, Netherlands, Italy, Switzerland, the USA, etc. Our academic staff regularly participates in projects supported by the Hungarian Research Fund, and also in other programmes, such as those of the Hungarian Academy of Sciences (Momentum groups) and the European Commission (Marie Curie Fellowship). The international appreciation of some scholars of the institute is also clearly shown by the following events:

András Némethi was invited as a speaker to the 2018 International Congress of Mathematicians held in Rio de Janeiro (among other invited speakers we can find four more former students and professors of ELTE).
In 2018, László Lovász won a Synergy Grant of the ERC (jointly with Albert-László Barabási from CEU and Jaroslav Nešetril from Charles University) with the project titled Dynamics and the Structure of Networks.
In 2018, one of the main events in combinatorics was the conference held in honour of László Lovász on his 70^th birthday (Building Bridges II).
In June 2018, the Institute of Mathematics co-hosted the 20^th European Conference on Mathematics for Industry, a major event of the European Consortium for Mathematics in Industry (ECMI).

The Institute of Mathematics aims at maintaining academic excellence of both research and teaching performed at ELTE. Besides employing distinguished members of a younger generation of researchers and strengthening the international research relations, it is also important to make the teaching programmes more accessible for international students. A new English-language MSc programme in applied mathematics is going to be introduced in 2019 (complementing the existing master’s programme in pure mathematics and a PhD programme in both fields). In addition to the traditional areas of mathematics, connections with high-tech industries and financial institutions should also be strengthened.