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Cohomology in algebra, geometry, physics and statistics

usually takes place every Wednesday Institute of Mathematics of ASCR, Žitná 25, Praha 1
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.

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

Around the noncommutative cross ratio
Georgy Sharygin
Moscow State University Lomonosov
Wednesday, 31. March 2021 - 11:30 to 12:30
ZOOM meeting
The cross-ratio of four points on a projective line is one of the most important projective invariants, which finds most unexpected applications throughout Mathematics from Geometry and Topology to the Integrable systems theory. I will tell, how one can widen the domain on which this invariant is defined so as to allow one consider "projective lines" over noncommutative field. It turns out that there is an approach, which allows one find such... more

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