In January, seven members of the Hungarian Academy of Sciences elected on 7 May 2025 — full members, corresponding members, and external members belonging to the Section of Mathematical Sciences—delivered their inaugural lectures.
The series started with Gábor Tardos, research professor at Rényi Institute, on 7 January his lecture entitled Forbidden Substructures in Ordered Graphs and 0–1 Matrices. The central question of the talk was how many edges a simple graph with a given number of vertices must have in order to necessarily contain a triangle or some other “forbidden” subgraph. Similar extremal questions concerning forbidden substructures are studied in many other settings as well: instead of graphs, in hypergraphs, directed graphs, vertex- or edge-ordered graphs, geometric graphs, or 0–1 matrices. Results obtained in this area are widely applicable in other branches of combinatorics and in computer science. The lecture presented recent results concerning acyclic forbidden substructures.
The recording of Gábor Tardos’s inaugural lecture can be viewed HERE, and photos taken at the event are available HERE.
Also on 7 January, Balázs Szegedy, professor and head of Rényi Institute’s Artificial Intelligence Research Department, delivered his inaugural lecture. In his talk, Szegedy discussed the asymptotic behavior of large structures. Over the past 20 years, mathematics has seen a number of results that have significantly reshaped our thinking about large structures. These include limit theories of graphs, hypergraphs, additive structures, and other fundamental mathematical objects. Balázs Szegedy demonstrated how these new theories have found applications in graph theory and additive combinatorics, and through them in a new branch of mathematics, higher-order Fourier analysis. One of the main goals of the lecture was to convey the extraordinary richness of this field. In this context, he also touched upon dynamical systems, groups, ultraproducts, random graph models, and neural networks.
The recording of the inaugural lecture is available HERE, and photos from the event can be found HERE.
How does lattice homology appear in different branches of mathematics? This question formed the title of the inaugural lecture by András Némethi, research professor at Rényi Institute. In the introduction to his lecture, delivered on 14 January, he stated: “I would like to show how lattice homology is able to extract essential structural information in a unified way from very different mathematical objects.” Examples included numerical semigroups, Artin algebras, monomial ideals, closed 3-manifolds, embedded knots, and singular points of complex multivariable polynomials. András Némethi also highlighted a common phenomenon shared by algebra, topology, combinatorics, and algebraic geometry.
Photos from the inaugural lecture are available HERE, and the video recording can be viewed HERE.
Lajos Gábor Molnár, professor at the University of Szeged, who also participates in the work of Rényi Institute’s Optimal Transport research group, delivered his inaugural lecture entitled On the Symmetries of Operator Structures. As stated in the brief description of the event: “Linear operators, and their finite-dimensional counterparts, matrices, appear in many areas of mathematics and its applications, and depending on the field and the problems studied, they may form different kinds of structures. They may be equipped with certain numerical quantities, such as distances, as well as operations, orderings, etc.” Referring to symmetry as one of the most important general concepts in mathematics, the central question of the lecture was how the symmetries (isometries, automorphisms, etc.) of the operator and matrix structures under consideration can be described, and how different notions of symmetry relate to one another.
The recording of the inaugural lecture can be found HERE, and photos taken at the event can be viewed HERE.
In addition to colleagues of Rényi Institute, József Balogh, elected as an external member of the Hungarian Academy of Sciences and living and working in the United States since 1997, also delivered his inaugural lecture. The academician gave his talk entitled Counting Independent Sets Using the Container Method on 13 January. On 14 January, Károly Simon, head of the Department of Stochastics at the Budapest University of Technology and Economics, delivered his inaugural lecture entitled The Transversality Method in Fractal Geometry. On 28 January, an inaugural lecture was delivered by Tibor Gyimóthy, founder and former head of the Department of Software Engineering at the University of Szeged, entitled A Needle in a Haystack – Fault Localization for Large Programs.
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(source: mta.hu)