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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.

Hertz potentials and the decay of higher-spin fields
Jérémie Joudioux
Albert Einstein Institute, Golm
Wednesday, 28. April 2021 - 11:30 to 12:30
ZOOM meeting
The purpose of the talk is to illustrate how differential complexes can be used in relativity. Electromagnetism and linearized gravity (more generally higher-spin fields) are governed by hyperbolic systems of partial differential equations. Solutions to these systems can be generated by the mean of potentials (here, Hertz potentials) satisfying a wave equation. It is possible to recast the problem of representing a solution to these higher-spin fields by Hertz potentials in the context of the initial value problem. Initial data for higher-spin fields satisfy constraint equations, and cannot be chosen freely. The integrability conditions for these constraints are described by elliptic complexes. These elliptic complexes also happen to be those describing the relation between initial data for higher-spin fields and those for their Hertz potentials. The problem of describing the asymptotic behavior of generic solutions to higher-spin fields can then be completely deduced from the... more

Filtered expansions in general relativity
Michael Reiterer
Hebrew University of Jerusalem
Wednesday, 21. April 2021 - 11:30 to 12:30
ZOOM meeting
I will review the BKL (Belinskii-Khalatnikov-Lifshitz) proposal for singularities in general relativity, for spatially homogeneous and spatially inhomogeneous spacetimes. Then I will discuss a construction of formal power series solutions, for one BKL bounce, which is a building block for the BKL proposal. I will in particular highlight the algebraic tools that we use, namely Maurer-Cartan perturbation theory and a filtration that organizes the calculations. Joint with Eugene Trubowitz, see arxiv.org/abs/1905.09026 and arxiv.org/abs/2005.03390.

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We open  ZOOM  at 11.15 and close  at 13.00

Join Zoom Meeting

https://cesnet.zoom.us/j/99598413922?pwd=ZGM0TTJ6VWxyYzZLWENjU01LN1p4QT09

Meeting ID: 995 9841 3922

Passcode: Einstein

Smooth 1-dimensional algebraic quantum field theories
Marco Benini
INFN Genoa and Genoa University
Wednesday, 14. April 2021 - 11:30 to 12:30
ZOOM meeting
Algebraic quantum field theory (AQFT) axiomatizes quantum field theories (QFTs) as functors A assigning to each spacetime M an algebra A(M), interpreted as the algebra of observables of a QFT over the spacetime M. To support this physical interpretation, certain physical axioms are imposed on the functors A. None of these... more

The de Finetti theorem in categorical probability
Tobias Fritz
University of Innsbruck, Austria
Wednesday, 7. April 2021 - 11:30 to 12:30
ZOOM meeting
While probability theory is traditionally based on measure theory and Kolmogorov's axioms as a foundation, the  recently proposed
formalism of Markov categories constitutes a potential alternative approach in which a (modest) number of classical theorems of probability
and statistics have already been... more

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