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 OKTOBAR 2023.

Petak, 06.10.2023. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Pavle Blagojević, Matematički institut SANU
CONVEX PARTITIONS OF SECTIONS OF POLYTOPES VIA FIBREWISE CONFIGURATION SPACES
The classical problems of mass partitions, like Grünbaum-Hadwiger-Ramos and Nandakumar & Ramana-Rao problems, ask for the existence of a partition of a Euclidean space into parts of the prescribed type in such a way that the quantities, given in advance, are equalised on the parts of this partition.
Motivated by the classical questions it is natural to study a more general class of problems where we consider a family of Euclidean spaces, parametrised by a topological space, and a family of quantities defined on them. We ask for the existence of at least one Euclidean space in this family which possesses a partition of the prescribed type such that all quantities are equalised on the parts of this partition.
In this lecture we will present results on the Nandakumar & Ramana-Rao partition problem for families of Euclidean spaces.
Based on the PhD thesis of Tatiana Levinson and joint work with Michael Crabb and Tatiana Levinson.

Petak, 13.10.2023. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Dušanka Janežič, University of Primorska, Slovenia
NEXT-GENERATION ProBiS AND ITS APPLICATION IN THE MILLION-PROTEIN Space
We have developed a suite of protein binding site tools, collectively known as ProBiS, which includes web servers, databases, and algorithms for predicting protein binding sites and ligands. These tools are based on a graph theoretic algorithm that we developed, which uses a fast and improved maximum clique algorithm to identify the largest fully connected subgraph in a protein graph.
The next-generation ProBiS represents a significant step forward in our ability to understand protein structures within the vast space of millions of proteins. To achieve this, we have developed new computational tools that utilize graph theoretical approaches and molecular simulations to analyze the entire human structural genome for protein-ligand binding in drug discovery.

Petak, 20.10.2023. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Nenad Vesić, Matematički institut SANU
DIFFERENTIAL GEOMETRY, COSMOLOGY, QUANTUM MECHANICS AND FUTURE RESEARCH
This presentation is focused on results prepared for soon submission to a journal. The presentation is divided on three parts. In the first part of presentation, differential geometry with torsion is reviewed. In the second part of presentation, different fields are recognized with respect to applications in cosmology. In the third part of presentation, we will talk about basics of classical and quantum mechanics covered by complex and real non-symmetric metric tensor.
Zajednički sastanak sa Seminarom za matematičku analizu i primene.

Petak, 20.10.2023. u 16:15, Kneza Mihaila 36, sala 301f i On-line
Stanislav Speranski, Steklov Mathematical Institute, Moscow
ELEMENTARY THEORIES OF CLASSES OF PROBABILITY SPACES
We shall be concerned with a two-sorted probabilistic language, denoted by QPL, which contains quantifiers over events and over reals. It is obtained by combining the elementary language of Boolean algebras and that of ordered fields in a natural way, and can be viewed as an elementary language for reasoning about probability spaces. The fragment of QPL containing only quantifiers over reals (but not over events) is a variant of the well-known `polynomial' probability logic from [Fagin, Halpern, Megiddo 1990: Section 6]. First we prove that the QPL-theory of the Lebesgue measure on [0, 1] is decidable, and moreover, all atomless spaces have the same QPL-theory. Then we introduce the notion of elementary invariant for QPL, and use it to translate the semantics for QPL into the setting of elementary analysis. This allows us to obtain further decidability results as well as to provide exact complexity upper bounds for a range of interesting undecidable theories.
Zajednički sastanak sa Seminarom za Logiku.

Petak, 27.10.2023. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Filip Marić, Matematički fakultet, Beograd
ŽIRO-GRUPE I NjIHOVA ULOGA U FORMALIZACIJI HIPERBOLIČKE GEOMETRIJE
U sklopu predavanja biće ukratko predstavljena teorija žiro-grupa i žiro-vektorskih prostora koje je matematičar Abraham Ungarn predložio kao algebarsku osnovu za izučavanje Ajnšajnove teorije relativnosti, ali i izučavanje hiperboličke geometrije. Naime, uvođenje vektora u hiperboličku geometriju predstavlja problem, jer su uobičajene operacije sabiranja vektora u opštem slučaju neasocijativne i nekomutativne. Uvođenjem posebne operacije zvane žiracija, koja je inspirisana Tomasovom precesijom eksperimentalno otkrivenoj u fizici, rađa se struktura žirogrupa, a zatim i žirovektorskih prostora, koje predstavljaju uopštenja klasičnih algebarskih struktura i koje predstavljaju odličan algebarski okvir za formalizaciju hiperboličke geometrije u kom se većina formula sintaksički poklapa sa odgovarajućim formulama u Euklidskoj geometriji.

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