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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.

Geometry of gauge PDEs I

Alexei Kotov
University Hradec Kralove
Wednesday, 13. May 2020 - 11:30 to 12:30
ZOOM Meeting
I will show how jet spaces and Q-bundles can be incorporated into an invariant mathematical description of gauge theories.

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We shall start at 11 AM at ZOOM for   a   coffee

Join Zoom Meeting

https://cesnet.zoom.us/j/99598413922?pwd=Ym4velNHckh2TlNxK2R2SzRpVXRhdz09

 

Meeting ID: 995 9841 3922

Password: 097923

  After the end of seminar we still have 30... more

Shock waves in Euler flows of gases

Mikhail Roop
Moscow State University
Wednesday, 6. May 2020 - 11:30 to 12:30
ZOOM Meeting
We study non-stationary 1-dimensional flows of gases described by a quasilinear system of differential equations including Euler equation and continuity equation. We show that equations in question essentially depend on thermodynamics of the medium. We represent the system by means of 2-forms on zero-jet space and get some exact solutions by means of such a representation. The solutions obtained are multivalued, we find caustics and shock wave front. The method can be applied to any thermodynamic state of the medium as well as to any thermodynamic process. The talk is based on our joint paper with Valentin Lychagin, arXiv:2004.05015.
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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

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