Institute of Mathematics of the Academy of Sciences of the Czech Republic

Learnability can be undecidable

Obor “machine learning” se zabývá zhruba otázkou, co se lze o nějakém objektu dozvědět z omezeného množství dat; v extrémním případě, jestli k uchopení daného problému vůbec stačí konečné množství dat, a pokud ano, kolik. To je dnes zajímavé hlavně kvůli počítačům, ale dalo by se to vnímat i jako studium možností lidského mozku. Ukázali jsme, že poměrně přirozená úloha v tomto oboru je nerozhodnutelná ze základních matematických axiomů. To je zase jiná větev matematiky, matematická logika, která ukazuje, že pravdivost některych tvrzení nelze rozhodnout ze základních axiomů. Klasický příklad je hypotéza kontinua, kdy je nerozhodnutelné, jaká je mohutnost reálných čísel. Podobně my ukazujeme, že obecná otázka, co se lze naučit z konečného množství dat, je nerozhodnutelná. Článek byl publikován v časopise Nature Machine Intelligence.

Paper

Naši pracovníci se podíleli na nalezení nového typu černé díry

Vědečtí pracovnící našeho ústavu V. Pravda a A. Pravdová ve spolupráci s kolegy R. Švarcem a J. Podolským z MFF UK nalezli statické, sféricky symetrické řešení polních rovnic kvadratické gravitace s nenulovou kosmologickou konstantou popisující černou díru. Tato teorie tedy kromě všeobecně známé Schwarzschildovy černé díry připouští navíc ještě další statickou, sféricky symetrickou černou díru. Ve své práci navázali na práce týmu z USA, Velké Británie a Číny, který s použitím numerických výpočtů existenci této nové černé díry v roce 2015 předpověděl (avšak pouze v případě s nulovou kosmologickou konstantou).
Čeští autoři využili svého předchozího výsledku, ve kterém ukázali, že sféricky symetrické statické prostoročasy jsou vždy konformní ke Kundtovým prostoročasům. Dále také využili toho, že dodatečné členy kvadratické gravitace lze zkombinovat do Bachova tenzoru, který se při konformních transformacích velmi jednoduše transformuje. Tento nový konformní přístup jim umožnil provést podstatnou část potřebných výpočtů "na pozadí" daleko jednoduššího Kundtova prostoročasu a vedl ke dramatickému zjednodušení výsledných polních rovnic kvadratické gravitace. To následně umožnilo zkoumat tyto rovnice analytickými metodami. Ukázalo se, že tato nová černá díra má kromě hmotnosti ještě jeden další parametr, který odpovídá hodnotě Bachova tenzoru na horizontu. V práci bylo také ukázáno, že tento nový parametr má mimo jiné vliv na pohyb testovacích částic obíhajících tuto černou díru.
Práce byla publikována ve špičkovém časopise Americké fyzikální společnosti Physical Review Letters.

Exact black holes in quadratic gravity with any cosmological constant (Physical Review Letters)

Exact black holes in quadratic gravity with any cosmological constant (arXiv)

Eduard Čech Distinguished Visitor Programme

The programme has been established with the aim to significantly enhance the creative environment in the Institute of Mathematics by bring here highly distinguished mathematicians for prolonged periods. The Eduard Čech Distinguished Visitor for 2018/2019 is Prof. Vojtěch Rödl from the Emory University, Atlanta. For the details of the programme see the corresponding

regulation

The Czech Mathematical Society Prize for Young Mathematicians

The Czech Mathematical Society is awarding the Prize for Young Mathematicians. The Prize is given every fourth year to up to four Czech mathematicians or groups of mathematicians under 35 for their excellent publications. On Monday 12th February, the Prize 2018 was awarded to Michal Doucha and Václav Mácha from the Institute of Mathematics CAS, and to Martin Branda and Jan Šaroch from the Charles University.

Higher Structures – a new journal

M. Markl, together with M. Batanin and R. Kaufmann, founded the journal Higher Structures. It is an all-electronic, refereed journal on the theory of higher structures and its applications in the mathematical sciences. The journal publishes articles that make significant new contributions to mathematical science using higher structures, or that significantly advance our understanding of the foundational aspects of the theory of such structures. The scope of the journal includes: higher categories, operads and their generalisations, and applications of these to Algebra, Geometry, Topology, Combinatorics, Logic and Mathematical Physics.

M. Křížek, L. Somer, M. Markl, O. Kowalski, P. Pudlák, and I. Vrkoč received the 2018 Josef Hlávka Prize

Every year, the Foundation of Josef, Marie and Zdeňka Hlávka awards the Josef Hlávka Prize for scientific literature. In the ceremony held at the Castle Lužany on June 17, 2019, M. Křížek, L. Somer, M. Markl, O. Kowalski, P. Pudlák, and I. Vrkoč recieved the 2018 Josef Hlávka Prize for their book Abelova cena – nejvyšší ocenění za matematiku (The Abel Prize – the Highest Achievement in Mathematics) published by Academia Publishing House in 2018. The book surveys the major results of the recipients of the first fifteen Abel Prizes. The Prize which is considered a mathematics counterpart of the Nobel Prize is awarded by the King of Norway every year to one or two mathematicians for their lifetime achievement.

Book cover

M. Křížek and L. Somer in front of Josef Hlávka statue in Lužany

Commemorative Medal of Masaryk University in Brno

On the occasion of Centennial of Masaryk University in Brno, the Commemorative Medal has been awarded on June 13, 2019 to the Institute of Mathematics as a recognition of the long-term collaboration with the Faculty of Science especially in the field of ordinary differential equations, algebraic topology and differential geometry, for membership in boards and commissions, important joint grant projects and doctoral programme.

Award

Complete list of awarded partners

Tomáš Vejchodský appointed as the new director

President of the Czech Academy of Sciences Professor Eva Zažímalová, accompanied by the Vice President Professor Jan Řídký, appointed Tomáš Vejchodský as director of the Institute of Mathematics of the CAS for the period from 1 May 2019 to 30 April 2024. The ceremony held in the Institute of Mathematics on April 30, 2019, was attended by members of the Board of the Institute and of the Supervisory Board, and many employees of the institute. Mrs. President thanked Jiří Rákosník, the outgoing director, and wished the institute and its new director good luck.

Diderot Mathematical Forum: Mathematics and Architecture, 8 June 2019

The cycle of conferences Diderot Mathematical Forum was introduced by the European Mathematical Society in 1996. Each conference takes place simultaneously in three European cities exchanging information by videoconferences, addresses a specific topic, and has both a research and a public component. The venues of the Diderot Mathematical Forum 2019 are Helsinki, Porto and Prague.
The lectures in Prague will take place in the Main Lecture Hall of the Institute of Mathematics CAS on 8 June 2019 from 9 a.m. The speakers include Henri Achten (Czech Technical University), Robert Aish (University College London), Juhani Palasmaa (University of Helsinki), Daniel Piker (Foster and Partners), José Pedro Susa (University of Porto), Christopher Williams (Chalmers University).
All interested are welcome.

Programme

Poster

Jiří Neustupa received the Honorary Medal of the Czech Mathematical Society

On 23 April 2019 there was a workshop in the occasion of 70th birthday of Professor Jiří Neustupa. During the workshop, the President of the Czech Mathematical Society Luboš Pick presented the Honorary Medal for Mathematics to Jiří Neustupa for his lifelong contribution to the development of the Czech mathematics, international collaboration in research, and education of the new generation of mathematicians.

Miloslav Feistauer and Antonín Novotný received the Honorary Bernard Bolzano Medal for Merits in Mathematical Sciences

President of the Czech Academy of Sciences Prof. Eva Zažímalová awarded Prof. RNDr. Miloslav Feistauer, DrSc., dr. h. c., from the Charles University, and Prof. RNDr. Antonín Novotný, CSc., from Université de Toulon, the Honorary Bernard Bolzano Medal for Merits in Mathematical Sciences. The ceremony took place on 6th February 2019 in the Institute of Mathematics of the CAS. M. Feistauer, member of the Learned Society of the Czech Republic, is a renowned specialist in development and analysis of numerical methods for solving partial differential equations. A. Novotný is a renowned specialist in theory of partial differential equations and their applications in mathematical description of fluid mechanics. Both have a long-term broad collaboration with the colleagues from the Institute of Mathematics of the CAS.
The ceremony was followed with the workshop Antonín Novotný and his contribution to PDEs on 6th February and the seminar Current Problems in Numerical Analysis on 8th February dedicated to M. Feistauer.

Laudation for Miloslav Feistauer (Michal Křížek)

Laudation for Antonín Novotný (Eduard Feireisl)

Photo gallery (Jana Plavec, SSČ AV ČR)

Jan Grebík received the Josef Hlávka Prize

On 16 November, the eve of the Students' Day of Fight for Freedom and Democracy, The Foundation of Josef, Marie and Zdeňka Hlávka is traditionally awarding the Josef Hlávka Prize for the best students of the Prague public universities and Brno Technical University and for young talented researchers in the Czech Academy of Sciences. Among this year's awardees was Jan Grebík, Ph.D. student of David Chodounský.

Photogalery

The fifteenth Eduard Čech Lecture: Prof. Vojtěch Rödl, Emory University, Atlanta

Quasi-Randomness and the Regularity Method in Hypergraph

Thursday, 6 December 2018 at 10:30 a.m., in the main lecture hall of the Institute of Mathematics CAS
For abstract see the invitation below. The distinguished Eduard Čech Lectures held to commemorate one of the most eminent Czech mathematicians and founder of the Institute are directed to a general mathematical audience.
Professor Vojtěch Rödl is the second Eduard Čech Distinguished Visitor. The fifteenth Eduard Čech Lecture will be part of his research programme in the Institute of Mathematics.

Invitation to the Eduard Čech Lecture

The Academic Award – Praemium Academiae for Martin Markl

The President of the Czech Academy of Sciences Prof. Eva Zažímalová presented the most prestigious Academic Award – Praemium Academiae 2018 to three researchers of the Academy's institutes. One of them was Dr. Martin Markl, member of the Department of Algebra, Geometry and Mathematical Physics in the Institute of Mathematics. The Academic Award is a rigorously selective instrument for the financial and moral support of scientific excellence at the Czech Academy of Sciences. The most generous grant in the country providing a support for six years is intended to assist outstanding scientific figures who are the bearers of research at the top international level and create for them such conditions in which they can better develop their potential in the benefit of the Czech Academy of Sciences and all of Czech science. This is already the second Academic Award in the institute; the winner of the first one was E. Feireisl in 2007.

A short video portrait of M. Markl

Dny otevřených dveří v Matematickém ústavu AV ČR | Open Houses in the Institute of Mathematics CAS

Tradiční Dny otevřených dveří v Matematickém ústavu AV ČR jsou součástí Týdne vědy a techniky Akademie věd ČR, nejrozsáhlejšího vědeckého festivalu v ČR pořádaného Akademií věd ČR ve spolupráci s dalšími institucemi ve dnech 5.–11. listopadu 2018. Široká veřejnost a především studenti středních škol mají možnost nahlédnout do pracoven, laboratoří a knihoven a poznat, jak se dělá věda. Badatelé z výzkumných pracovišť AV ČR připravují širokou nabídku exkurzí, přednášek, výstav a diskusních večerů, ve kterých představí své výzkumné projekty, předvedou nejmodernější vědecké přístroje a experimenty a přiblíží návštěvníkům nejnovější trendy v oblasti vědy. V Matematickém ústavu AV ČR se Dny otevřených dveří uskuteční na pražském pracovišti ve dnech 5.–9. listopadu 2018.
Traditional Open Houses in the Institute of Mathematics CAS was held as part of the Week of Science and Technology, the most extensive scientific festival in the Czech Republic, organized by the Czech Academy of Sciences in cooperation with other institutions from 5th to 11th November 2018. The scientists from the research workplaces of the Academy of Sciences prepare a wide offer of lectures, presentations, panel discussions, seminars, excursions, exhibitions and discussion evenings, in which they present their research projects, the most modern scientific apparatuses and outline the latest trends in the areas of science in the Czech Republic and the world. The Prague departments in the Institute of Mathematics will be open to public from 5th to 9th November 2018.

Nabídka přednášek v MÚ AV ČR | Lectures offered in the Institute of Mathematics

Aktuální program přednášek | Current program of lectures

Michal Doucha received the Otto Wichterle Award for young researchers

President of the Czech Academy of Sciences Prof. Eva Zažímalová awarded the Otto Wichterle Award for young researchers to Dr. Michal Doucha, member of the Department of Topology and Functional Analysis. The award has been established in 2002 to encourage and support young promising researchers in institutes of the Czech Academy of Sciences. It is connected with a financial premium in the subsequent three years. Michal Doucha is one of 23 laureates in this year.

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