Одељење за математику, 17. и 18. децембар 2020.

Нареднижа два састанка Семинара биће одржани у четвртак, 17. децембра и петак 18. децембра 2020, у сали 301ф Математичког института САНУ са почетком у 14:15.

Четвртак, 17. децембар 2020, 14:15.

Предавач: Nikolai Erokhovets, Moscow State University


Апстракт: 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

Петак, 18. децембар 2020, 14:15.

Предавач: Mehmetcik Pamuk, Middle East Technical University, Ankara


Апстракт: 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.

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