MISANU

PROGRAM

Predavanja na Logičkom seminaru možete uživo pratiti preko linka
https://miteam.mi.sanu.ac.rs/asset/iYxPidYtFqBC9sT7a.
Ukoliko želite i da učestvujete u diskusiji, to možete preko linka
https://miteam.mi.sanu.ac.rs/asset/oaqCm4EyPhHR6kM6N
na kome prethodno treba napraviti nalog, t.j. popuniti registracioni formular koji se pojavi nakon klika.
Neulogovani korisnici mogu pratiti prenos predavanja na ovom linku (ali ne mogu postavljati pitanja osim putem chata):
https://miteam.mi.sanu.ac.rs/call/8HX5pHW3fhfr2vFnF/Sud4M5nyx6-CCpaW4etWS1ZEM4wCvSsPuSxPAQ9Yfs6

Četvrtak, 06.06.2024. u 14:00, Kneza Mihaila 36, sala 301f i On-line
Adam Skalski, Mathematical Institute of the Polish Academy of Sciences, Warsaw
WHAT IS A GOOD DEFINITION? IN SEARCH OF QUANTUM GROUPS
Definitions form a fundamental part of the mathematical study. I will discuss the requirements that mathematicians put on 'good' definitions and explain how such definitions develop, based on the notion of a locally compact quantum group, originating in 1970s and 1980s, and reaching a (possibly?) final form in the work of Kustermans and Vaes in 2000. Later developments will also be mentioned, but in general the talk will be accessible to general mathematical audience.
Zajednički sastanak sa Odeljenjem za matematiku i Seminarom za verovatnosne logike.

Petak, 07.06.2024. u 16:15, On-line
Somayeh Chopoghloo, Institute for Research in Fundamental Sciences, Teheran
LOGICS FOR PROBABILISTIC DYNAMICAL SYSTEMS
In this talk, we will investigate (discrete-time) Markov processes augmented by a dynamic mapping from the modal logic point of view. These structures, which we call dynamic Markov processes, are of the form ⟨Ω,A,T,f⟩ where ⟨Ω,A⟩ is a measure space, T:Ω × A → [0, 1] is a Markov kernel and f:Ω → Ω is a measurable function.
Our presentation is divided into two parts. The first part is devoted to introducing the finitary dynamic probability logic (DPL), as well as its infinitary extension DPLω1. Both these logics extend the (modal) probability logic (PL) by adding a temporal-like operator ⃝ which describes the dynamic part of the system. We subsequently provide Hilbert-style axiomatizations for both DPL and DPLω1. We show that while the proposed axiomatization for DPL is strongly complete, the axiomatization for the infinitary counterpart supplies strong completeness for each countable fragment A of DPLω1.
The second part is allocated to investigating (frame) definability of natural properties of dynamic Markov processes. We show that some dynamic properties such as measure-preserving, ergodicity, and mixing are definable within DPL and DPLω1. Moreover, we consider the infinitary probability logic with initial distribution (InPLω1) by disregarding the dynamic operator. This logic studies Markov processes with initial distribution, i.e. structures of the form ⟨Ω,A,T,π⟩ where ⟨Ω,A,T⟩ is a Markov process and π:A → [0, 1] is aσ-additive probability measure. We show that the strong expressive power of InPLω1 would allow us to define n-step transition probabilities T^n of Markov kernel T. From this, we conclude that many natural stochastic properties of Markov processes such as stationary, invariance, irreducibility, and recurrence can be stated within InPLω1.
This is based on my recent joint work with Prof. Massoud Pourmahdian in S. Chopoghloo and M. Pourmahdian. Dynamic probability logics: axiomatization & definability, 2024. https://arxiv.org/pdf/2401.07235.pdf.

Petak, 28.06.2024. u 16:15, Kneza Mihaila 36, sala 301f i On-line
Jeffrey Bergfalk, University of Barcelona
CONDENSED MATHEMATICS AND INFINITARY COMBINATORICS
Around 2019, Dustin Clausen and Peter Scholze undertook the systematic development of an approach to “doing algebra with objects carrying a topology” which they term *condensed mathematics*, work which actively continues today. After a brief introduction to this approach, we survey some of its connections to infinitary combinatorics, both via derived functor computations and set theoretic forcing. Connecting these two prongs in turn is an analysis of Whitehead’s problem (does Ext(A,Z)=0 imply that A is free?) in the setting of condensed abelian groups. This work is joint with Chris Lambie-Hanson and Jan Saroch.
Zajednički sastanak sa Odeljenjem za matematiku.

OBAVEŠTENJA:

Ukoliko zelite mesecne programe ovog Seminara u elektronskom obliku, obratite se: tane@mi.sanu.ac.rs. Programi svih seminara Matematickog instituta SANU nalaze se na sajtu: www.mi.sanu.ac.rs

Beograd,
Srdacan pozdrav,
Predrag Tanovic
rukovodilac seminara