Colloquial Talk for professor appointment procedure - April 10, 2pm, lecture room M1 PDF Print

A colloquial talk for professor appointment procedure, April 10, from 2pm, lecture room M1

Jan Paseka

Title: Quantales and related structures

In this talk we survey, first, the development in the theory of quantales and quantale-like structures, and, second, the work of Brno quantale research group.
We will start with a definition of a quantale (a complete lattice equipped with an associative binary operation that distributes over arbitrary suprema) and related examples. Then, we will go to the origins of quantale theory. After it, we switch to up-to-date sources of our research – theory of operator algebras, many-valued and non-commutative topologies, computer science, and logic.
In the second part of our talk we will discuss our joint work we have done in this area. We conclude with directions for further research. The talk will be accessible to any graduate student.

Last Updated on Thursday, 04 April 2019 07:52
Colloquial Talk - September 25, 4pm, lecture room M1 PDF Print

Colloquial talk - Fall 2018 - TUESDAY, September 25, M1, 16:00

John P. D'Angelo  (Professor at University of Illinois, PhD from Princeton, 1976)

Title: Rational CR maps between spheres: a compressed sensing problem.

I will discuss aspects of the theory of proper holomorphic mappings between balls and connections with other branches of mathematics. Such mappings arise for several reasons; one is that the unit sphere admits many symmetries, and many mappings exist, especially when the target dimension is large compared with the domain dimension. When the source dimension is at least two, and a proper map is smooth up to sphere, it must be a rational mapping. Classification of such rational mappings is difficult; this problem  leads to group theory, algebraic combinatorics, compact operator theory, and so on. The primary focus of the talk will be on the degree estimate problem in two or more dimensions; the idea is to bound the degree of such a rational mapping in terms of an explicit function of the source and target dimensions. Equivalently, one could seek a lower bound for the target dimension given the degree. Doing so leads to a problem in compressed sensing. The sharp bounds are known only in the case of monomial maps. I will discuss joint work I have done on this problem with two Czech co-authors. The talk will be accessible to advanced undergrads, because I will spend most of the time in source dimension two.

Last Updated on Friday, 21 September 2018 15:27
Recorded colloquial Talk - Stano Katina - What is important for the future of (applied) Czech science: Complex examples from biostatistics and data science PDF Print

Colloquial talk took place at the Institute of Mathematics and Statistics, No.8 building within the Faculty of Science, Kotlarska 2, Brno

Time and place:  Wednesday, May 9, 4pm, lecture hall M1

Stano Katina

What is important for the future of (applied) Czech science: Complex examples from biostatistics and data science


What is statistics? What is data analysis? Is it good to question what a statistic is telling you? Are statistics an aid for your intelligence and judgement, or a replacement for them? What is bias? What has been measured? Is it important for applied scientist to learn basic statistical concepts? Is the statistics mirroring the process of building a house or is it reflecting only its decoration? What is a difference between statistician of 20th and 21st century? What is a difference between applied scientist of 20th and 21st century?

During the colloquium we will ask many of these sort of questions and learn some basic concepts of statistics of 19th, 20th and 21st century. We will learn that even though data never lies, it is far too easy to be tricked by it, and even though we just said that data never lies, the way it is generated and collected can create deceptive conclusions. We also find out that the benefit of studying statistics is in gaining a skill set that is transferable to other research methods, disciplines and walks of life.

Some of the concepts will be applied on data from different medical fields, e.g. knee replacement surgery, electroencephalography, electrocardiography, magnetic resonance imaging, and facial modelling.

Record available HERE.

Last Updated on Thursday, 10 May 2018 14:44
Colloquium - Hervé Gaussier - 11.4.2018 PDF Print

Wednesday 11.4.2018, 16.00, M1

Hervé Gaussier (Institute Fourier - Grenoble)

On the Schwarz Lemma and metrics in complex geometry.

Abstract. I will explain how the geometric approach of the Schwarz Lemma due to Ahlfors opened new perspectives in the metric geometry of complex manifolds and will present current problems in the theory.

Last Updated on Monday, 09 April 2018 16:16
Colloquial Talk - Aleksey Kostenko - On Infinite Quantum Graphs PDF Print

Colloquial talk take place at the Institute of Mathematics and Statistics, No.8 building within the Faculty of Science, Kotlarska 2, Brno

Time and place: December 6, 4pm, lecture hall M1

Aleksey Kostenko (Vienna/Ljubljana)

On Infinite Quantum Graphs


The notion of quantum graph refers to a graph considered as a one-dimensional simplicial complex and equipped with a differential operator (“Hamiltonian”). From the mathematical point of view, quantum graphs are interesting because they are a good model to study properties of quantum systems depending on geometry and topology of the configuration space. They exhibit a mixed dimensionality being locally one-dimensional but globally multi-dimensional of many different types.
We will review basic spectral properties of infinite quantum graphs (graphs having infinitely many vertices and edges). In particular, we will discuss recently discovered fruitful connections between quantum graphs and discrete Laplacians on graphs.
Aleksey Kostenko is a renown expert in spectral theory, publishing in journals like Inventiones (2016) and his standard collaborators include Gerald Teschl of Vienna.

Last Updated on Thursday, 30 November 2017 18:05
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