Diszkrét és folytonos: a gráfelmélet, algebra, analízis és geometria találkozási pontjai = Discrete and Continuous: interfaces between graph theory, algebra, analysis and geometry

Sok eredmeny szuletett a grafok novekvő konvergens sorozataival es azok limesz-objektumaival, ill. az ezek vizsgalatara szolgalo graf-algebrakkal kapcsolatban. Kidolgozasra kerultek a nagyon nagy sűrű grafok (halozatok) matematikai elmeletenek alapjai, es ezek alkalmazasai az extremalis grafelmelet teruleten. Aktiv es eredmenyes kutatas folyt a diszkret matematika mas, klasszikus matematikai teruletekkel valo kapcsolataval kapcsolatban: topologia (a topologiai modszer alkalmazasa grafok magjara, ill a csomok elmelete), geometriai szerkezetek merevsege (a Molekularis Sejtes bizonyitasa 2 dimenzioban), diszkret geometriai (Bang sejtesenek bizonyitasa), veges geometriak (lefogasi problemak, extremalis problemak q-analogonjai), algebra (felcsoport varietasok, grafhatvanyok szinezese), szamelmelet (additiv szamelmelet, Heilbronn problema), tovabba grafalgoritmusok (stabilis parositasok, biologiai alkalmazasok)) teruleten. | Several results were obtained in connection with convergent growing sequences of graphs and their limit objects, and with graph algebras facilitating their study. Basic concepts for the study of very large dense graphs were worked out, along with their applications to extremal graph theory. Active and successful research was conducted concerning the interaction of discrete mathematics with other, classical areas of mathematics: topology (applications of topology in the study of kernels of graphs, and the theory of knots), rigidity of geometric structures (proof of the Molecular Conjecture in 2 dimensions), discrete geometry (proof of the conjecture of Bang), finite geometries (blocking problems, q-analogues of extremal problems), algebra (semigroup varieties, coloring of graph powers), number theory (additive number theory, heilbronn problem), and graph algorithms (stable matchings, applications in biology).