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 DECEMBAR 2022.

PETAK, 02.12.2022. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Nenad Vesić, Matematički institut SANU
MATHEMATICS AND PHYSICS: SIMILARITIES AND DIFFERENCES
Based on methods used in differential geometry, mathematics and physics are connected in this presentation. At the start, necessary definitions of terms from differential geometry are listed. After that, some of the last obtained results about mappings of Riemannian spaces and some formulae corresponded to transformations of metric tensor are listed in the second part of this presentation. In the last section of presentation, we solve a system of linear equations and point what physical interpretations of these solutions may be.

PETAK, 09.12.2022. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Djordje Baralić, Mathematical Institute SANU
SIMPLICIAL COMPLEXES OF POLYOMINO TILINGS
Polyomino shape is a union of unit squares connected edge by edge. In mathematical physics, they are also known as animals in the grid. We define a simplicial complex for a given set of polyomino shapes and a given subset of the square grid in a plane or on a torus. The topological and combinatorial properties of the complex are exciting. They reveal many features of placements of tiles from the given set into the given subset of the grid without overlappings. We will prove that these complexes have high connectivity and that, in some cases, they have the homotopy type of wedge of spheres. Some of their unexpected applications will be discussed.

PETAK, 16.12.2022. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Stefan Ivkovic, Mathematical Institute SANU
SEMI-FREDHOLM THEORY IN C*-ALGEBRAS
Keckic and Lazovic introduced an axiomatic approach to Fredholm theory by introducing the notion of a Fredholm type element with respect to the ideal of finite type elements in a unital C*-algebra. This notion is a generalization of C*-Fredholm operator on the standard Hilbert C*-module introduced by Mishchenko and Fomenko and of Fredholm operator on a properly infinite von Neumann algebra introduced by Breuer. They obtained then that the set of Fredholm type elements in a unital C*-algebra is open in the norm topology and invariant under perturbation by finite type elements. Also, they proved multiplicativity of the index in the K-group and a generalization of the Atkinson theorem. In this talk we shall present the results from semi-Fredholm theory in unital C*-algebras as a continuation of the approach by Keckic and Lazovic. We introduce the notion of a semi-Fredholm type element and semi-Weyl type element with respect to the ideal of finite type elements in a unital C*-algebra. We prove then the set of proper semi-Weyl elements is open in the norm topology, invariant under perturbations by finite type elements and several other results generalizing their counterparts from the classical semi-Fredholm theory of operators on Hilbert spaces. Also, we illustrate applications of our results to the special case of properly infinite von Neumann algebras. In particular, we obtain a generalization of punctured neighbourhood in this case and we describe the relationship between Fredholm spectra of 2 by 2 upper triangular matrices with coefficients in properly infinite von Neumann algebras and their diagonal entries.

PETAK, 23.12.2022. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Ivan Limončenko, HSE University, Russia
PERSISTENT TOR-ALGEBRAS AND THEIR BARCODES
In my talk, I'm going to cover the basics of topological data analysis from the viewpoint of toric topology. Namely, after a reminder on persistent homology, Gromov-Hausdorff distance on pseudo-metric spaces and Wasserstein distance on the space of barcodes, I'll introduce a generalization of the classical barcode via polyhedral products. Finally, we shall discuss different versions of the stability theorem for the bigraded barcode. No previous knowledge of topological data analysis or toric topology will be assumed.
This talk is based on the joint works with Anthony Bahri, Taras Panov, Jongbaek Song, and Donald Stanley.

PETAK, 28.12.2022. u 18:00, Kneza Mihaila 36, sala 301f i On-line
Vladimir Dragović, Univerzitet Teksasa u Dalasu; MISANU
ORTOGONALNE I LINEARNE REGRESIJE, MOMENTI INERCIJE I KONFOKALNE KVADRIKE
Cilj nam je da istaknemo i razvijamo mostove između statistike, mehanike i geometrije. Povezujemo konfokalne pramenove kvadrika i momente inercija sa ortogonalnom i linearnom regresijom. Za zadati sistem tačaka u k-dimenzionom prostoru, koji ne pripadaju nijednoj afinoj hiperravni, konstruišemo konfokalni pramen kvadrika sa sledećim svojstvima: (i) Sve hiperravni u odnosu na koje zadati sistem tačaka ima jednake momente inercije su tangente na jednu te istu kvadriku iz pramena. (ii) Za bilo koju tačku P, među hiperravnima koje je sadrže, najmanji moment je u odnosu na tangentu na kvadriku koja sadrži P, kojoj odgovara najveća Jakobijeva koordinata. Najveći moment je u odnosu na tangentu na elipsiod iz konfokalnog pramena kvadrika, koji sadrži P. Oba rezultata predstavljaju uopštenja fundamentalnog Pirsonovog rezultata kojim je zasnovana ortogonalna regresija. Navodimo primenu dobijenih rezultata u prirodnim primerima u statistici modela sa mernim greškama (EIV) i restrikovanoj regresiji. U konstrukciji konfokalnog pramena kvadrika koristimo tačke u kojima je elipsoid inercije simetričan. Predavanje je zasnovano na zajedničkom radu sa Borislavom Gajićem.
Zajednički sastanak sa Odeljenjem za Mehaniku. Obavezno je nošenje maski i održavanje distance. Broj prisutnih na predavanju ograničen na najviše 10 (uključujući i predavača).

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

Zoran Petric, Odeljenje za matematiku Matematickog instituta SANU