Goście i wykłady

Herbert Edelsbrunner (Institute of Science and Technology Austria)

To be announced
Abstrakt TBA

More information about our guest: https://pub.ista.ac.at/~edels/

Thomas Wanner (George Mason University)

Combinatorial Topological Dynamics
Abstrakt Topological methods have always been at the heart of the qualitative study of dynamical systems. For example, topological fixed point theorems can guarantee the existence of stationary states, and classical Morse theory establishes a link between gradient dynamics and the topology of the underlying phase space. These ideas have been generalized to Conley's theory of isolated invariant sets and Morse decompositions, which is able to encode the global dynamics of general dynamical systems using topological information. In fact, even more complicated behavior can be studied in this way, for example recurrent and chaotic dynamics.

In recent years, some of the above approaches have been carried over to a discrete, combinatorial setting, thereby opening the door to a purely combinatorial version of dynamical systems. The first step in this direction was Forman's discrete Morse theory on simplicial complexes, and it has found numerous applications in mathematics, computer science, and the applied sciences.

In these lectures, I will present the current state of combinatorial topological dynamics, which generalizes and extends these early results in a number of directions. The notion of multivector fields on Lefschetz complexes will be introduced in detail, as well as an extension of Conley's theory in this setting. This includes topics such as isolated invariant sets, their Conley index, and Morse decompositions. In addition, we address applications of the theory to establishing recurrence in classical dynamics, and describe advanced topics such as connection matrices. Finally, we also touch upon the relation between this combinatorial theory and its classical counterpart.

More information about our guest: https://math.gmu.edu/~wanner/

Bogdan Batko (Jagiellonian University)

More information about our guest: https://matinf.uj.edu.pl/pracownicy/wizytowka?person_id=Bogdan_Batko

Paweł Dłotko (Dioscuri Centre in Topological Data Analysis)

More information about our guest: https://dioscuri-tda.org/members/pawel.html

Michał Lipiński (Jagiellonian University, Institute of Science and Technology Austria)

To be announced
Abstrakt TBA

More information about our guest: https://sites.google.com/view/michal-lipinski/home