# Seminars:

The Centre is running a virtual seminar during the pandemic on Wednesdays, 11am to 12:30pm via Zoom. The Meeting-ID is 390 769 7241. Please contact Pawel Dlotko to obtain the passcode.

If you would like to give a talk as part of our seminar series please contact Pawel Dlotko.

If you are interested in research talks by members of the center, see below.

- 02/12/2020

Artem Dudko: On computability and computational complexity of Julia sets.

**Abstract:**In this talk I will give an introduction to computability and computational complexity of sets with the focus on Julia sets of polynomials. For a polynomial p(z) its Julia set is the set of points on a complex plane near which the iterations of p(z) behave chaotically. Roughly speaking, a set is called computable if there is an algorithm which can produce an approximation of this set (by a finite set of pixels) with any given precision. Computational complexity measures how hard it is to produce such approximations. In the talk I will show that already in the class of Julia sets of quadratic polynomials there are various interesting computational phenomena, including:

- large classes of functions having Julia sets of low (polynomial) computational complexity;

- functions with non-computable Julia sets;

- large classes of functions having Julia sets of arbitrarily high computational complexity. - 25/11/2020

John Harvey (Swansea University): Estimation of dimension

**Abstract:**I will survey various established and new techniques to estimate the dimension of a submanifold of Euclidean space from a sampled point cloud, how we might investigate underlying assumptions of the estimators, and how they relate to testing for manifoldness - 18/11/2020

Pawel Dlotko (Dioscuri TDA, Warsaw): Mild introduction to TDA

**Abstract:**In this talk I will provide a general introduction to methods of TDA - concentrated mostly on persistent homology and mapper algorithm. I will present the basic theory, highlight the main application. But, I will mostly encourage questions and discussion. - 11/11/2020

**No seminar due to public holiday!** - 04/11/2020

Niklas Hellmer (Dioscuri TDA, Warsaw): Nonembeddability of Persistence Diagrams with p>2 Wasserstein Metric.

**Abstract:**To apply kernel methods on persistence diagrams, they are mapped into a Hilbert space. The question is how much information we lose by doing so. I present recent work by Alexander Wagner that shows that persistence diagrams with p-Wasserstein metric do not admit a coarse embedding into a Hilbert space for p>2.

### Talks of center members in other seminars

- 26/02/2021

Niklas Hellmer: "Discrete Prokhorov Metric for Persistence Diagrams" at APATG.