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Cohomology in algebra, geometry, physics and statistics

usually takes place every Wednesday at 11:30 AM Institute of Mathematics of ASCR, Žitná 25, Praha 1, konírna
Chair: 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.

Triangular decoupling of systems of differential equations, with application to separation of variables on Schwarzschild spacetime
Igor Khavkine
IM, ASCR
Wednesday, 29. April 2020 - 11:30 to 12:30
ZOOM Meeting
Certain tensor wave equations admit a complete separation of variables on the Schwarzschild spacetime (static, spherically symmetric black hole), resulting in complicated systems of radial mode ODEs. The spectral theory of these systems has important applications to the stability analysis electromagnetic and gravitational perturbations of the black hole. However, almost none of the important questions about the radial mode equations can be answered in their original form. I will discuss a drastic simplification of these ODE systems to sparse upper triangular form that is directly susceptible to spectral analysis. Essential to this simplification are geometric properties of the original tensor wave equations, ideas from homological algebra and from the theory of ODEs with rational coefficients. Based on [arXiv:1711.00585, 1801.09800].
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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
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.


As usual  we shall  start  coffee  at 11:00    at   ZOOM, Meeting... more

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

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