Mathematical Colloquium
PROGRAM
ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU
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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/WbsehnSL4ZeTPJo6r.
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 NOVEMBAR 2024.
Petak, 08.11.2024. u 14:15, Kneza Mihaila 36, sala 301f i Online
Ivan Damnjanović, Elektronski fakultet, Niš
ON THE SPECTRAL RADIUS OF THRESHOLD GRAPHS
The spectral radius of a graph is the spectral radius of its adjacency matrix. A threshold graph is a simple graph whose vertices can be ordered as $v_1$, $v_2,\ldots$, $v_n$, so that for each $2 \leq i leq n$, vertex $v_i$ is either adjacent or nonadjacent to all of $v_1$, $v_2,\ldots$, $v_{i-1}$. Brualdi and Hoffman initially posed and then partially solved the extremal problem of finding the simple graph with a given number of vertices and edges that has the maximum spectral radius. This problem was subsequently completely resolved by Rowlinson. Here, we deal with the similar problem of maximizing the spectral radius over the set of connected simple graphs with a given number of vertices and edges. As shown by Brualdi and Solheid, each such extremal graph is necessarily a threshold graph. We investigate the spectral radii of threshold graphs by relying on computations involving lazy walks. Furthermore, we obtain certain lower and upper bounds on the spectral radius of a given threshold graph.
This is a joint work with Peter Csikvari, Dragan Stevanović and Stephan Wagner.
Petak, 15.11.2024. u 14:15,
Online
Sonja Petrović, Illinois Institute of Technology
PROBABILITY AND RANDOMNESS IN NONLINEAR ALGEBRA
Many problems in symbolic computation with polynomials have high worst-case complexity. At the same time, in many areas of computational mathematics, significant improvements in efficiency have been obtained by algorithms that involve randomization, rather than deterministic ones. This talk will overview a randomized sampling framework from geometric optimization to applied computational algebra, and demonstrate its usefulness on two problems, including solving large (overdetermined) systems of multivariate polynomial equations.
Petak, 29.11.2024. u 14:15, Kneza Mihaila 36, sala 301f i
Online
Đorđe Baralić, Matematički institut SANU
MOD p BUHŠTABEROVA INVARIJANTA
Buhštaberova invarijanta je jedna od centralnih tema torusne topologije i predstavlja kombinatornu osobinu simplicijalnog kompleksa. Koristeći jedan od opisa klasičnih Buhštaberovih invarijanta preko univerzalnih kompleksa baza od
Zn i
Z2n, za svaki prost broj
p definiše se odgovarajući univerzalni kompleks od
Zpn i mod p Buhštaberova invarijanta. Pokazuje se da su ove invarijante u opštem slučaju različite i da su same po sebi interesantne već i na najednostavnijim primerima skeletona od simpleksa. Na predavanju ćemo dati i prikaz rezultata koji su dobijeni u zajedničkim radovima sa Alešom Vavpetičom i Aleksandrom Vučićem.
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
