MISANU

ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU

Predavanja možete pratiti i online putem MITEAM stranice Odeljenja za matematiku:
https://miteam.mi.sanu.ac.rs/asset/WbsehnSL4ZeTPJo6r

PROGRAM ZA APRIL 2026.

Petak, 03.04.2026. u 14:15, Kneza Mihaila 36, sala 301f i Online
Pavle Blagojević, Matematički institut SANU
IGRAJUĆI BILIJAR
Izučavanje osobina matematičkih bilijara je klasična tema matematičke mehanike, koja na jednom mestu kombinuje metode različitih oblasti, na primer iz geometrije i topologije.
U ovom predavanju otkrivamo kako ekvivarijantna topologija konfiguracionih prostora odgovara na pitanje o minimalnom broju periodičnih trajektorija bilijara u strogo glatkom konveksnom telu proizvoljne dimenzije.
Bazirano na zajedničkom radu sa Harisonom, Tabačnikovim i Ciglerom.

Petak, 17.04.2026. u 14:15, Kneza Mihaila 36, sala 301f i Online
Stanislav Speranski, Steklov Mathematical Institute of RAS
WEAK ARITNMETIC FROM THE VIEWPOINT OF MONADIC SECOND-ORDER LOGIC
By a weak arithmetical structure we shall mean a structure on the natural numbers such that: a) all the corresponding predicates and functions are computable; b) its elementary (that is, first-order) theory is decidable. Among the structures of this kind are Presburger's and Skolem's arithmetics, viz. the natural numbers with equality and either addition or multiplication. We are going to discuss monadic second-order definability in weak arithmetical structures and related complexity issues. Here `monadic' means that only predicate variables of arity 1 — which range over unary predicates on the natural numbers — are allowed. In effect, in second order logic, it is often natural to focus on monadic formulas. We shall examine in detail the case of Presburger arithmetic, and somewhat less explicitly, the case of Skolem arithmetic and its reducts.
Zajednički sastanak sa Seminarom iz matematičke logike i Seminarom za računarsku logiku.

Petak, 24.04.2026. u 14:15, Kneza Mihaila 36, sala 301f i Online
Evgeny Spodarev, Institute of Stochastics, Ulm University, Germany
SPECTRAL PROPERTIES OF FULLERENES, GRAPHENE, AND NANOTUBES
This talk discusses recent advances in the spectral theory of carbon allotropes, focusing on adjacency spectra, closed walk counts, and limiting spectral distributions.
We begin with the spectral clustering of fullerene isomers. Fullerenes are finite 3-regular planar graphs containing twelve pentagons and n/2−10 hexagons. By analyzing adjacency spectra and associated Newton polynomials, we quantify structural similarity among isomers and show how spectral data encode the combinatorial structure of their facet graphs. This leads naturally to asymptotic questions concerning the empirical spectral distributions of large fullerenes. The discussion then turns to the infinite hexagonal (graphene) and dual triangular lattices. The numbers of closed walks of length k at a vertex define the moment sequence of a probability measure, identified as the spectral measure (random eigenvalue) of the lattice. We derive explicit expressions for the corresponding density, characteristic function, and moment generating function. The analysis builds on a new integral identity for a series involving 3rd powers of modified Bessel functions, revealing connections with planar random flights. Finally, we investigate infinite dual (p,q)-nanotubes constructed by periodic identification of the triangular lattice. Random eigenvalues are expressed explicitly in terms of independent uniform random variables; moments and their generating functions are computed, and weak convergence of their spectral distributions to that of graphene is established as p+q→∞. We close with open problems, notably the conjectured Benjamini–Schramm convergence of random fullerenes to the hexagonal lattice and the resulting convergence of their empirical spectral distributions.
This is joint work with A. Bille, V. Buchstaber, S. Coste, P. Ievlev, S. Kuriki, and S. Novikov.

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