The definition of the Reeb foliation depends upon two real functions satisfying certain conditions. All these foliations are pairwise homeomorphic and have trivial Godbillon-Vey class. We construct explicit examples of the Reeb foliations that are not diffeomorphic. For this purpose we show that a modified Godbillon-Vey class defined by Losik is non-trivial for some Reeb foliations and trivial for some other Reeb foliations. This characteristic class takes values in the second order frame bundle of the leaf space of the foliation. This is a joint work with Ya. Bazaikin and P. Gumenyuk.
Cohomology in algebra, geometry, physics and statistics
usually takes place every Wednesday Institute of Mathematics of ASCR, Žitná 25, Praha 1Chair: Anton Galaev, Roman Golovko, Igor Khavkine, Alexei Kotov, Hong Van Le and Petr Somberg
In this seminar we shall discuss topics concerning constructions and applications of cohomology theory in algebra, geometry, physics and statistics. In particular we shall discuss in first four seminars the relations between vertex algebras and foliations on manifolds, Gelfand-Fuks cohomology on singular spaces, cohomology of homotopy Lie algebras. The expositions should be accessible for all participants.
Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class
Anton Galaev
University Hradec Kralove
Wednesday, 22. April 2020 - 11:30 to 12:30
ZOOM, Meeting ID:895-276-2498
Differential invariants in thermodynamics
Eivind Schneider
University Hradec Kralove
Wednesday, 15. April 2020 - 11:30 to 12:30
ZOOM Meeting
It is well known that contact geometry gives the appropriate framework for formulating thermodynamics: Thermodynamic states can be interpreted as Legendrian submanifolds of a certain contact manifold. The existence of a metric on thermodynamic states has also received some attention in the last decades. The metric can be interpreted as the variance of an underlying probability measure. Less studied is the action of the affine group that appears naturally in this context as the group preserving the variance. We... more
TBA - cancelled - postponed to a later date
Denis Bashkirov
IM, CAS
Wednesday, 8. April 2020 - 11:30 to 12:30
Konirna Seminar room in IM front building, ground floor
TBA
Koszul algebras and one-dependent random 0-1 sequences
Leonid Positselski
IM, CAS
Wednesday, 1. April 2020 - 11:30 to 12:30
https://cesnet.zoom.us/j/239249755
Meeting ID 239-249-755
Koszul algebras are a natural class of graded algebras with
quadratic relations, defined by a series of homological conditions.
To a Koszul algebra over a field with finite-dimensional components,
one can assign a one-dependent stochastic 0-1 sequence, which carries
information about the dimensions of the algebra's grading components.
... more
quadratic relations, defined by a series of homological conditions.
To a Koszul algebra over a field with finite-dimensional components,
one can assign a one-dependent stochastic 0-1 sequence, which carries
information about the dimensions of the algebra's grading components.
... more