MISANU

PROGRAM

ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU

PROGRAM ZA DECEMBAR 2020.

Petak, 11.12.2020. u 14:15, sala 301f, MISANU, Kneza Mihaila 36
Stevan Gajović, University of Groningen
KRIVE ZA KOJE SE DOSTIŽE JEDNAKOST U KOLMANOVOJ NEJEDNAKOSTI
Pre dokaza Faltingsove teoreme, Šaboti je za određenu klasu krivih dokazao da imaju konačno mnogo racionalnih tačaka. Kolman je konstruisao metod koji za tu klasu krivih daje gornju ocenu o broju racionalnih tačaka. Korišćenjem metoda Šaboti-Kolmana uz neke druge metode, veoma često možemo da odredimo racionalne tačke na krivama iz te klase. Međutim, u samoj Kolmanovoj nejednakosti se jednakost jako retko dostiže. Na ovom predavanju ćemo se baviti konstrukcijom primera krivih za koje se dostiže jednakost.

Četvrtak, 17.12.2020. u 14:15, Live stream Beograd
Nikolai Erokhovets, Moscow State University
CANONICAL GEOMETRIZATION OF 3-MANIFOLDS REALIZABLE AS SMALL COVERS
Roughly speaking geometrization conjecture of W.P. Thurson (finally proved by G.Perelman) says that any oriented 3-manifold can be canonically partitioned into pieces, which have a geometrical structure of one of the eight types. In the seminal paper by M.W. Davis and T. Januszkiewicz (1991) there is a sketch of the proof that such a decomposition exists for 3-manifolds realizable as small covers over simple 3-polytopes. It should be noted, that in this sketch the notion of a nontrivial 4-belt, which plays an important role in the decomposition, is not mentioned. Moreover, it can be shown that in general, a decomposition of a 3-polytope along 4-belts may be done in many inequivalent ways. We present a solution to the following problem: to build an explicit canonical decomposition. At tools we use the notion of an almost Pogorelov polytope, retractions of moment-angle complexes to subspaces corresponding to full subcomplexes, and the construction by A.Yu. Vesnin and A.D. Mednykh of manifolds from right-angled polytopes.
The talk is based on joint works with V.M. Buchstaber and T.E. Panov. Details can be found in Nikolai Erokhovets, Canonical geometrization of 3-manifolds realizable as small covers, arXiv:2011.11628 https://arxiv.org/abs/2011.11628

Petak, 18.12.2020. u 14:15, Live stream Beograd
Mehmetcik Pamuk, Middle East Technical University, Ankara
PERSISTENT HOMOLOGY
Topological data analysis (TDA) is a recent field that emerged from various works in applied algebraic topology and computational geometry. TDA provides a new approach of understanding patterns in your data that are associated with its shape. The main goal of TDA is to apply topology and develop tools to study features of data.
One of the powerful methods in TDA is called persistent homology (PH). It studies qualitative features of data that persist across multiple scales. In this talk, I will define PH, talk about some theoretical background and applications.

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