Seminar for Combinatorics, Geometry, Algebra and Topology
PROGRAM
Seminar Kombinatorika, Geometrija, Topologija, Algebra (KGTA)
PLAN RADA ZA NOVEMBAR 2023:
Četvrtak, 09.11.2023. u 12:15, Kneza Mihaila 36, sala 301f
Gyula O.H. Katona, Alfréd Rényi Mathematical Institute, Budapest
TOWARDS A BARANYAI THEOREM WITH ADDITIONAL CONDITION
Baranyai's theorem states that if $k$ divides $n$ then there are ${n-1\choose k-1}$ partitions of the $n$-element set into $k$-element subsets in such a way that every $k$-element subset occurs in exactly one of these partitions. However nothing is known about the pairwise relation of the partitions.
We will show some results moving in this direction. The objects considered here will be families of $\ell$ pairwise disjoint $k$-element sets rather than partitions (one can call them partial partitions). We say that two partial partitions are far if there are no two pairs of classes in these partitions with pairwise intersection more than $k/2$. It is proved that if $n$ is large, one can find such partial partitions far from each other in such a way that every $k$-element subset, with a few (bounded number) exceptions, is in one of them exactly once.
Petak, 10.11.2023. u 14:15, Kneza Mihaila 36, sala 301f
Miklós Simonovits, Alfréd Rényi Mathematical Institute, Budapest
STABILITY METHODS IN EXTREMAL GRAPH THEORY
Extremal Graph Theory is one of the fastest developing areas in Discrete Mathematics. It started in the 1940's (by Turán theorem) and was in strong connection with two other important areas of Discrete Mathematics, namely, to Ramsey Theory and to to Combinatorial Number Theory. Soon, Extremal Graph Theory and Ramsey Theory became the sources of several further important research areas.
In Extremal Graph Theory we fix some kind of objects, some parameter of these objects, and try to maximize or minimize some other parameters.
Stability methods mean that the extremal structures are very similar to some simple structure, and that the almost extremal structures are similar to the extremal strucures. For that part of Extremal Graph Theory when we consider simple graphs (no loops, neither multiple edges) and the minimum chromatic number of excluded subgraphs is at least 3, the Erdős-Simonovits theorem asserts that the stability holds. To prove sharp results in Extremal Graph Theory we mostly use stability results. We shall explain this approach, on the other hand, we shall show cases where the stability does not hold.
Further, we shall sketch several approaches to prove the stability, several proofs of the Erdős-Simonovits theorem.
Zajednički sastanak sa Odeljenjem za matematiku.
Četvrtak, 23.11.2023. u 12:15, Kneza Mihaila 36, sala 301f
Rade Živaljević, Matematički institut SANU
KRATAK PREGLED TEHNIKA TOPOLOŠKE KOMBINATORIKE I
Ovde je reč je o topološkoj kombinatorici u kojoj se kombinacijom metoda algebarske (homotopske) topologije i kombinatornih tehnika dobijaju informacije o geometriji i topologiji (homotopski tipovi) raznih konfiguracionih prostora (npr. simplicijalnih i poliedralnih kompleksa). Akcent će biti na nekim tipičnim (elementarnim) primerima i konkretnim izračunavanjima, sa posebnim osvrtom na (kombinatornu) Morsovu teoriju i tehniku dijagrama prostora.
Predavanje je namenjeno najširem krugu slušalaca, uključujući studente i matematičare drugih specijalnosti.
Četvrtak, 30.11.2023. u 12:15, Kneza Mihaila 36, sala 301f
Rade Živaljević, Matematički institut SANU
KRATAK PREGLED TEHNIKA TOPOLOŠKE KOMBINATORIKE II
Ovde je reč o topološkoj kombinatorici u kojoj se kombinacijom metoda algebarske (homotopske) topologije i kombinatornih tehnika dobijaju informacije o geometriji i topologiji (homotopski tipovi) raznih konfiguracionih prostora (npr. simplicijalnih i poliedralnih kompleksa). Akcent će biti na nekim tipičnim (elementarnim) primerima i konkretnim izračunavanjima, sa posebnim osvrtom na (kombinatornu) Morsovu teoriju i tehniku dijagrama prostora.
Predavanje je nastavak prethodnog po temi, ali nezavisno po sadržaju i izloženim primerima.
Predavanja imaju pregledni karakter i namenjena su najširem krugu slušalaca
