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Dynamics, Mathematical Analysis & Artificial Intelligence

The University Center of Excellence “Dynamics, Mathematical Analysis & Artificial Intelligence”

Dyrektor Centrum: prof. dr hab. Mariusz Lemańczyk

The thematic scope of the University Center of Excellence “Dynamics, mathematical analysis and artificial intelligence” includes issues related to dynamic systems and ergodic theory. The work of the Center will also cover analytical number theory, computer science, open quantum systems, and quantum information. As part of the research on artificial intelligence, researchers will focus on brain signal analysis, neurodynamics, and machine learning. The Center lists four areas of research:

Dynamics and ergodic theory:

This research topic continues and develops the main trends of modern dynamics and ergodic theory. They involve examining the interrelationship of the two theories with number theory, combinatorics, geometry, and mathematical analysis. Recent significant progress in understanding the relationship between ergodic theory and analytical number theory is worth noting as there are numerous interconnections and possible applications. The Toruń center has also made a significant contribution to the development of research on this subject.

Computer science – formal languages and concurrency:

Research is conducted in informatics in the field of concurrency theory, formal languages, automatics and machine learning, and data mining. These relate in particular to the theoretical and practical modelling and analysis of concurrent systems (including Petri networks and reaction systems) and solving problems with incomplete information by utilising, among other things, methods that border on combinatorics, algebra, topology and modal logic.

Neuroinformatics and artificial intelligence:

Neuroinformatics is a combination of two essential disciplines on the scientific frontline: brain research and artificial intelligence. By applying machine learning and signal processing methods, new theories and algorithms for analysing brain signals are developed, and hypotheses are verified through experiments.

Entangled states and dynamics of open quantum systems:

The theory of open quantum systems describes the dynamics of the quantum system that interacts with the environment. It combines elements of quantum information theory and advanced mathematical methods such as operator algebra or stochastic processes. In researching the mathematical aspects of these main research areas and given the mathematical tools used, the Centre intends to cooperate with other strong mathematical schools in Toruń: algebra, mathematical analysis, and probability theory. Additionally, the Center will collaborate with foreign centers: Aix-Marseille Université in France, Universität Bielefeld in Germany, and the University of Zurich in Switzerland.

 

Prof. dr hab. Mariusz Lemańczyk is currently Head of the Department of Ergoda Theory and Dynamic Systems at the Faculty of Mathematics and Computer Science, Nicolaus Copernicus University. In previous years, Prof. Lemańczyk was Vice-Dean for research of the Faculty of Mathematics and Computer Science, NCU (1999-2005, two terms of office) and Dean of the Faculty of Mathematics and Computer Science, NCU (between 2005 – 2008). Between 1996 – 2014, he was a member of the Scientific Committee of the Institute of Mathematics at the Polish Academy of Sciences. He led three national research grants.

Prof. Lemańczyk was honoured with many prestigious national scientific awards, including:

  • the Award of the Minister of Science and Higher Education for his doctoral dissertation 1986,
  • the Polish Mathematical Society Award for Young Mathematicians 1986,
  • the K. Kuratowski Award of the Polish Mathematical Society 1987,
  • the Award of the Polish Academy of Sciences 1987,
  • the S. Banach Main Award of the Polish Mathematical Society 1998,
  • the Award of the Minister of Science and Higher Education for scientific achievements 1998,
  • the Władysław Orlicz Medal and 24th Special Lecture, 3.03.2017.

His high international scientific status was confirmed by his unique research position at the CIRM (Marseille) – Jean-Morlet Chair between 1.08.2016-31.01.2017. This prestigious position came as the result of recent breakthroughs in the Sarnake hypothesis, which in some aspects closely relates to the famous Riemann hypothesis. This was also the subject matter of the grant (awarded to Prof. M. Lemańczyk together with Prof. M. Radziwiłł of Caltex) funded by the American Institute of Mathematics and the National Science Foundation. Prof. Lemańczyk is a world-famous expert in ergodic theory and dynamic systems and works with many top mathematicians from most prestigious centers of mathematics in the world including Caltex, Hebrew University in Jerusalem, Institute for Advanced Studies (Princeton), Moscow State University, Ohio State University, Technical University in Vienna, Tel Aviv University, Universite d’Aix-Marseille, University of Maryland, University of Zurich. He is a member of the Editorial Board of one of the most recognized international mathematical journals published in Poland – “Studia Mathematica”.

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