# Archives

## 2017

**Prof. Richard Smith (University College Dublin): Approximation of norms on Banach spaces.**

**Miroslav Olšák (MFF UK): Weakest nontrivial idempotent equations.**

An equational condition is a set of equations in an algebraic language, and an algebraic structure satisfies such a condition if it possesses terms that meet the required equations. We will explore a single nontrivial equational condition which is implied by *any nontrivial idempotent * equational condition.

**Tomáš Kroupa (ÚTIA AV ČR): Pravděpodobnostní algebry ve dvou-sortové varietě.**

## 2016

**Matěj Dostál (katedra matematiky FEL ČVUT): Sémantika přirozeného jazyka uchopená kategoriálně.**

**RNDr. Jan Buša, CSc. (Technická univerzita v Košiciach): Open source systém počítačovej algebry wxMaxima.**

## 2015

**Miroslav Korbelář (katedra matematiky FEL ČVUT): Symmetries in finite-dimensional quantum mechanics.**

Finite-dimensional quantum mechanics is a concept where the usual real configuration space is substituted by an abelian group that is discrete and finite (in a more general approach then locally compact). The basic operator structures here are the finite Heisenberg groups. I will talk about their symmetries and related problems (e.g. connection with mutually unbiased bases).

**Jan Hladký (Matematický ústav AV ČR): Limits of dense graphs.**

Borgs, Chayes, Lovasz, Szegedy, and Vesztergombi realized around 2004 that there is a natural compactification of the space of all finite graphs. At around the same time, Razborov developed his theory of "flag algebras" which offers an alternative viewpoint on some aspect of the theory of graph limits. These theories have found numerous applications in the theory of random graph and extremal graph theory, leading to solutions of several central problems in these fields. After giving an overview of these developments I will talk about my recent work with Dolezal and Mathe [arXiv:1510.02335]. The talk will be self contained.

**Prof. Thomas Schlumprecht (Texas A&M University): On the closed subideals of the space of operators on l**_{p}⊕l_{q}.

In this joint work with Andras Zsak we solve a problem of A.Pietsch and we show that there are uncountably many subideals of *L*(*l _{p}*⊕

*l*) .

_{q}## 2014

**Jiří Velebil (katedra matematiky FEL ČVUT): Let's have fun with Geometric algebra.**

Geometric algebra, the subject known to pure mathematicians for about 140 years, has recently found its applications in, e.g., physics (geometry of spacetime) and computer graphics, robotics, etc (interesting and efficient algorithms). In this talk, in a rather relaxed and informal way, we will go through the basic concepts of Geometric algebra. No prior knowledge is needed (perhaps, apart from some grammar school geometry).

**Miroslav Korbelář (katedra matematiky FEL ČVUT): Open problems in commutative semirings.**

Semirings (a generalization of rings, where the subtraction is in general not available) are fairy basic objects (e.g. the semiring of natural numbers) and they appear naturally in many branches of mathematics and informatics. Apart of the rings, the structure of semirings is more complicated and some basic structural properties of even the most common ones are not known (e.g. the structure of subsemirings of Q^{+} - the semiring of all positive rational numbers). Classification of the simple commutative semirings (El Bashir et al, '01) motivated a series of conjectures about idempotency in finitely generated commutative semirings. We make an overview about this topic, related ideas and the current state of the conjectures.

**Petr Zizler (Mount Royal University): Some Remarks on the Non-Abelian Fourier Transform in Crossover Designs in Clinical Trials.**

Let *G* be a non-abelian group and let *l ^{2}(G)* be a finite dimensional Hilbert space of all complex valued functions for which the elements of

*G*form the (standard) orthonormal basis. In our paper we prove results concerning

*G*-decorrelated decompositions of functions in

*l*. These

^{2}(G)*G*-decorrelated decompositions are either obtained using the

*G*-convolution by the irreducible characters of the group

*G*or by an orthogonal projection onto the matrix entries of the irreducible representations of the group

*G*. Applications of these

*G*-decorrelated decompositions are given to crossover designs in clinical trials, in particular the William's 6×3 design with 3 treatments. In our example, the underlying group is the symmetric group

*S*.

_{3}**András Zsák (University of Cambridge): Renorming Banach spaces with greedy bases.**

We consider the problem of renorming spaces with greedy bases in order to improve the greedy or democracy constant. We prove that every greedy basis can be renormed to be almost 1-democratic, and every bidemocratic greedy basis can be renormed to be almost 1-greedy. These results answer questions of Bill Johnson. (Joint work with Dilworth, Kutzarova, Odell and Schlumprecht.)

## 2013

**Jarno Talponen (University of Eastern Finland): Convexity properties of the quasihyperbolic metric on domains of Banach spaces.**

Quasihyperbolic (QH) metric is a weighted metric on a path connected metric space motivated by looking at invariants of Möbius transforms of the unit disk. In this talk the metric is given on an open path-connected non-trivial subset of a Banach space. It turns out that many properties of the underlying Banach space are visible in the QH geometry. We discuss the convexity of quasihyperbolic balls and look at some geometric examples.

**doc. RNDr. Jiří Spurný, Ph.D. (MFF UK Praha): Baireovské třídy L**_{1}-preduálů a C^{*}-algeber.

**Petr Zizler (Mount Royal University): On Spectral Properties of Group Circulant Matrices.**

Let *G* be a finite group (typically non-abelian) and let *l ^{2}(G)* be a finite dimensional Hilbert space of all complex valued functions (usual inner product) for which elements of

*G*form the (standard) orthonormal basis. We study group circulant matrices,

*C=C*, induced by the convolution operator on

_{G}(ψ)*l*by the function

^{2}(G)*ψ ∈ l*. Unlike the abelian case, non-abelian group circulant matrices are typically non-normal and possibly even non-diagonalizable. We obtain results on geometric properties of eigenspace decompositions and diagonalizations (or Jordan decompositions) of group circulant matrices. Results in this context are obtained for dihedral circulant matrices where the underlying group is the dihedral group

^{2}(G)*D*with

_{n}*n*even.

**Prof. Jiří Adámek (TU Braunschweig): Minimalizace nedeterministických automatů.**

**Prof. Thomas Schlumprecht (Texas A&M University): Bases formed by translates of one element in L**_{p}(R).

Let 1*< p <∞.* We prove that a sequence of translates of a fixed function *f∈ L _{p}*(R) cannot be an unconditional basis of

*L*(R). If

_{p}*p=*1 then such a sequence cannot even be

*L*(R).

_{1}## 2012

**prof. Mgr. Petr Hájek, DrSc. (katedra matematiky FEL ČVUT): Extenze hladkých operátorů do biduálu.**

**Assoc. Prof. Katherina Roegner (TU Berlin): Multimedia in a blended-learning context.**

The MUMIE (MUltimedia Mathematics Education for Engineers) is an open-source learning and teaching platform that can be used flexibly in STEM courses. This educational tool has been appllied to the first-semester course „Lineare Algebra for Engineers“ at the Technical University Berlin, which is offered as a blended-learning course to over 3500 students per year. The basic goal of the didactical concept developed especially for this course is that the students are supported in their transition from school to university mathematics. Resources were created for each unit not only for students, but also for tutors to aid in activating students and to enhance students' thinking processes in tutorials. Typical problems and some ideas for alleviating these are discussed within this setting.

## 2010

**Daniela Petrisan (University of Leicester): Universal algebra over nominal sets**In theoretical computer science nominal sets are regarded as a powerful mathematical model for formal languages involving binding constructors. A nominal set is just a set equipped with an action of a group of permutations on a countable set of names, satisfying some additional properties of `finite supportedness'. I will discuss several characterisation of the category of nominal sets and I will present some results concerning universal algebra in this setting, such as an HSP-like theorem characterising equationally definable classes of algebras over nominal sets. (This is based on joint work with Alexander Kurz and Jiri Velebil.)

**Miloslav Čapek (katedra teorie elektromagnetického pole FEL): Rojová optimalizace v Matlabu**

**Jiří Velebil (katedra matematiky FEL): Logické konexe a modální logika ve světech mimo množiny**-
**Jiří Cigler (katedra řídicí techniky FEL): Kvadraticky optimální systémy s předepsanými póly** -
**Jiří Velebil (katedra matematiky FEL): Sémantika kvantového programovacího jazyka**

## 2009

**Prof. J.D.M. Wrigh (Oxford): On classifying small monotone complete C*-algebras.**