Одељење за математику - гостовање колега са Универзитета Приморска, 2. јун 2023.

• 31. Мај, 2023
• Коментари (0)

У петак, 2. јуна 2023, биће одржано специјално издање семинара Одељења за математику. Предавања ће одржати четворо гостију са института са Универзитета Приморске у Копру, Словенија. Предавања бити одржана у згради САНУ, Кнеза Михаила 35, сала 2 на 1. спрату, са следећим програмом:

11:00-11:45 Томаж Писански, Univerza na Primorskem, Словенија

FROM THE HISTORY OF THE JOURNAL ARS MATHEMATICA CONTEMPORANEA

Fifteen years ago, in 2008, the first issue of mathematical research journal Ars Mathematica Contemporanea was published. A brief history of the first Slovenian mathematical journal, as well as the strategy that was used for its launching and later development, will be presented.

11:45-12:30 Драган Марушич, Univerza na Primorskem, Словенија

ON HAMILTONICITY OF VERTEX TRANSITIVE GRAPHS

The following question asked by Lovász in 1970 tying together traversability and symmetry, two seemingly unrelated graph-theoretic concepts, remains unresolved after all these years: Does every finite connected vertex-transitive graph have a Hamilton path?In my talk I will discuss certain partial results obtained thus far together with a connection to another long standing problem regarding vertex-transitive graphs, the so called "polycirculant conjecture": is it true that every vertex-transitive graph admit a nontrivial automorphism with all orbits of the same size?

13:00-13:45 Клавдија Кутнар, Univerza na Primorskem, Словенија

ON INTERSECTION DENSITIES OF TRANSITIVE GROUPS AND VERTEX-TRANSITIVE GRAPHS

The Erdös-Ko-Rado theorem, one of the central results in extremal combinatorics, which gives a bound on the size of a family of intersecting k-subsets of a set and classifies the families satisfying the bound, has been extended in various ways. In this talk I will discuss an extension of this theorem to the ambient of transitive permutation groups and vertex-transitive graphs.

Let V be a finite set and G a group acting on V. Two elements g,h ∈ G are said to be intersecting if g(v) = h(v) for some v ∈ V. More generally, a subset F of G is an intersecting set provided every pair of elements of F is intersecting. The intersection density ρ(G) of a transitive permutation group G is the maximum value of the quotient |F|/|G_v|, where F runs over all intersecting sets in G and G_v is a stabilizer of v ∈ V.

The intersection density array [ρ_0,ρ_1, ...,ρ_(k-1)] of a vertex-transitive graph X is defined as a "collection" of increasing intersection densities of transitive subgroups of Aut(X), that is, for  any transitive subgroup G of Aut(X), we have ρ(G) = ρ_i for some и ∈ Z_k, with ρ_i<ρ_(i+1).

In this talk I will present some recent results about intersection densities of certain transitive permutation groups and vertex-transitive graphs of small valencies. This is a joint work with Ademir Hujdurović, Ištván Kovác, Bojan Kuzma, Dragan Marušić, Štefko Miklavič, Marko Orel and Cyril Pujol.


13:45-14:30 Александер Малнич, Univerza v Ljubljani i Univerza na Primorskem, Словенија

ON REFLEXIBLE POLYNOMIALS

Let p be an odd prime. A polynomial f(x) = a_0 + a_1 x + ... + a_n x^n over the field Z_p is reflexible if there exists λ ∈ Z^*_p such that either λ a_(n-i) = a_i (for all i = 0, 1, ..., n) or else λ a_(n-i) = (-1)^i a_i (for all i = 0, 1, ..., n).

Such polynomials were instrumental in the classification of 4-valent arc-transitive graphs arising as minimal elementary abelian covers of  doubled cycles [JCTB 131 (2018), 109–137, joint work with Boštjan Kuzman and Primož Potočnik]. In the talk I will present some properties of reflexible polynomials.

Напомене:
Предавања се могу пратити на даљину преко линка:
https://miteam.mi.sanu.ac.rs/call/T9XDGChhq8aDcNqmz/qw7wIwci2jv2rdg9I9CrXkm7OJhF_LB8DfjXZp4jTFV
 
Регистрациона форма је доступна на:
https://miteam.mi.sanu.ac.rs/asset/tz97w4Hu4c3unsJ7N