MISANU

PROGRAM

ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU

Registracija za učešće na seminaru je dostupna na sledećem linku:
https://miteam.mi.sanu.ac.rs/asset/tz97w4Hu4c3unsJ7N.
Ukoliko ste vec registrovani predavanje možete pratiti na sledećem linku (nakon sto se ulogujete):
https://miteam.mi.sanu.ac.rs/asset/J6zEMJyMSoAbTMMX7.
Neulogovani korisnici mogu pratiti prenos predavanja na ovom linku (ali ne mogu postavljati pitanja osim putem chata i ne ulaze u evidenciju prisustva):
https://miteam.mi.sanu.ac.rs/call/T9XDGChhq8aDcNqmz/qw7wIwci2jv2rdg9I9CrXkm7OJhF_LB8DfjXZp4jTFV.

PROGRAM ZA JUN 2023.

PETAK, 02.06.2023. u 11:00-11:45, SANU, Kneza Mihaila 35, 1. sprat, sala 2 i On-line
Tomaž Pisanski, Univerza na Primorskem, Slovenija
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.

PETAK, 02.06.2023. u 11:45-12:30, SANU, Kneza Mihaila 35, 1. sprat, sala 2 i On-line
Dragan Marušič, Univerza na Primorskem, Slovenija
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?

PETAK, 02.06.2023. u 13:00-13:45, SANU, Kneza Mihaila 35, 1. sprat, sala 2 i On-line
Klavdija Kutnar, Univerza na Primorskem, Slovenija
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 i ∈ 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.

PETAK, 02.06.2023. u 13:45-14:30, SANU, Kneza Mihaila 35, 1. sprat, sala 2 i On-line
Aleksander Malnič, Univerza v Ljubljani; Univerza na Primorskem, Slovenija
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.

SREDA, 07.06.2023. u 13:00, Kneza Mihaila 36, sala 301f i On-line
Alexey Semenov, Department of Mathematical Logic and Theory of Algorithms of Lomonosov Moscow State University; Axel Berg Institute of Cybernetics and Educational Computing of Russian Academy of Sciences; Russian Academy of Sciences; Russian Academy of Education
THE THEORY OF DEFINABILITY
Definability theory can be considered as an important part of all mathematics along with proof theory, model theory, and computation theory. This was constantly emphasized by Alfred Tarski, who owns remarkable results in this theory, the main question of which is: is it possible to define some concept or relation, through other concepts, relations.
The report will give a general overview of the results in definability theory since the XIX century, including the Svenonius Theorem (completeness theorem for definability), the latest results of the author, his students and colleagues are presented, and a wide spectrum of open problems and possible solutions are proposed. The presence of this spectrum is a characteristic feature of the current state of definability theory.
The report can also provide a general overview of the research on mathematical logic, theory of algorithms and Computer Science going on at Moscow University, Moscow, and Russia.
Zajednički sastanak sa Logičkim seminarom.

PETAK, 09.06.2023. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Aleksandra Marinković, Matematički fakultet, Beograd
SYMPLECTIC CIRCLE ACTIONS ON MANIFOLDS WITH A CONTACT TYPE BOUNDARY
In this talk we consider circle actions on symplectic manifolds that have a (convex) contact type boundary. The most natural examples from classical mechanics are cotangent bundles with their natural actions induced by an action on the base manifold. We show that many of the key ideas of Morse-Bott theory, used for closed symplectic manifolds, could also be applied in the boundary case. However, in contrast to the closed symplectic case, we show that any symplectic circle action on a symplectic manifold with a contact type boundary is always Hamiltonian. We further show several results about the topology of these symplectic manifolds. In particular, we show that the contact type boundary is connected if the dimension of the symplectic manifold is 4.
This talk is based on a joint work with Klaus Niederküger.

PETAK, 16.06.2023. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Andreja Tepavčević, Matematički institut SANU
KARAKTERIZACIJA GRUPA PREKO MREŽE SLABIH KONGRUENCIJA
R. Schmidt u knjizi "Mreže podgrupe grupa" iz 2011. godine, kao jedan od "najuzbudljivijih otvorenih problema" u ovom kontekstu, spomenuo je mrežno teorijsku karakterizaciju rešivih grupa. Rešive grupe su od posebnog značaja jer su u vezi sa rešenjima polinomnih jednačina i teorijom Galoa. U seriji radova objavljenih u poslednje 1-2 godine, mi smo dali mrežno-teorijsku karakterizaciju ne samo rešivih grupa već i mnogih drugih klasa grupa, poput Hamiltonovih, nilpotentnih, Abelovih, superrešivih, i drugih preko mreža slabih kongruencija. Slabe kongruencije su simetrične i tranzitivne relacije saglasne sa operacijama na algebrama. Mreža slabih kongruencija je algebarska mreža koja u sebi sadrži kao intervale i mreže kongruencija i podalgebri, kao i mreže kongruencija na svim podalgebrama. U ovom predavanju predstavićemo rezultate o mrežama slabih kongruencija grupa. Jedan od prvih rezultata u ovom pravcu bila je karakterizacija Dedekindovih grupa preko modularnih mreža slabih kongruencija. Teorija grupa je matematički aparat koji se u fizici intenzivno koristi za proučavanje simetrija, kao i ponašanja fizičkih sistema pod određenim transformacijama; grupe se koriste u proučavanjima interakcija čestica kao i u fizici kondenzovane materije. Nadamo se da će u ovom kontekstu naši rezultati imati primenu i u teorijskoj fizici.
Rezultati koji će biti predsatvljani su zajednički rad sa Milanom Grulovićem, Jelenom Jovanović i Branimirom Šešelja.

PETAK, 23.06.2023. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Tatjana Davidović, Matematički institut SANU
PATH RELINKING - A VERY USEFUL OPTIMIZATION TOOL
In the optimization field it is necessary to find at least one extreme value of the objective function, as well as the corresponding set of arguments. Especially interesting and extremely hard are problems with the discrete domain, like Traveling Salesman Problem (TSP), Vehicle Routing Problem (VRP), Scheduling, Clustering, etc., that appear in the everyday life. As it is impossible to find the optimal solutions, various heuristic methods are developed to obtain high-quality sub-optimal solutions. One of these methods is Path Relinking (PR), that is classified as an evolutionary heuristic although it is deterministic and explores mathematical principles more than natural evolution. The main idea of PR is to build a path between two solutions, by performing successive modifications that transform one solution into the other. All intermediate solutions are evaluated and the best among them is adopted for further exploration. The number of intermediate solutions is determined by the distance between the initial solutions, indicating that PR needs a properly defined metric. More often than a standalone method, PR is used as an auxiliary step in other optimization methods, metaheuristics in particular. After a brief review of PR and recent applications within various metaheuristics, our experience with using PR within discrete Symbiotic Organisms Search (SOS) for TSP will be presented.
This is a joint work with Vladimir Ilin, Raka Jovanović, and Dragan Simić.

PETAK, 30.06.2023. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Luka Milićević, Matematički institut SANU
PRIBLIŽNI KVADRATNI VARIJETETI
Prvi netrivijalan rezultat o približnim algebarskim strukturama u aditivnoj kombinatorici je Frajmanova teorema. U kontekstu Furijeove analize višeg reda, sledeća opštija verzija te teoreme pojavljuje se prirodnije: kada god skup $A\subseteq\mathbb{F}_p^n$ ima bar $c|A|^3$ aditivnih četvorki, onda postoji potprostor $U$, veličine $|U|\leq O_c(|A|)$, takav da je $|U\cap A|\geq\Omega_c(|A|)$. (Kao što je uobičajeno, pod aditivnom četvorkom nazivamo četvorku elemenata $(a_1,a_2,a_3,a_4)\in(\mathbb{F}_p^n)^4$ takvu da je $a_1+a_2=a_3+a_4$). Dakle, o skupu $A$ sa ovim svojstvom možemo razmišljati kao o približnom potprostoru. Motivisani drugim približnim algebarskim strukturama koje se pojavljuju u Furijeovoj analizi višeg reda, u ovom predavanju ćemo se baviti kvadratnom verzijom ove teoreme. Naime, razmatraćemo koji bi to kombinatorni uslovi bili adekvatni za definiciju približnih kvadratnih varijeteta, a koji bi nam pritom omogućili da dokažemo kvadratnu Frajmanovu teoremu.
Predavanje se odlaže i održaće se početkom jeseni.

Odeljenje za matematiku je opsti matematicki seminar namenjen sirokoj publici. Predavanja su prilagodjena matematicarima i onima koji zele da to postanu.

Zoran Petrić, Odeljenje za matematiku Matematickog instituta SANU