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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.

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

Reduction cohomology on complex manifolds
Alexander Zuevsky
Institute of Mathematics, Czech Academy of Sciences
Wednesday, 24. March 2021 - 11:30 to 12:30
ZOOM meeting
Developing ideas of classical work of Feigin, and its development by Wagemann,
and proceed with a generalization of ideas of above works. We describe the
notion of a cohomology theory of infinite formal series with non-commutative
modes and localization of variables on Riemann surfaces, constructed via
characteristic functions reduction ... more

First BGG operators on homogeneous parabolic geometries
Jan Gregorovic
University Hradec Kralove
Wednesday, 17. March 2021 - 11:30 to 12:30
ZOOM meeting
I will briefly review the theory of BGG operators on parabolic geometries and show, how to construct and find (normal) solutions of first BGG operators on homogeneous parabolic geometries, in detail. In particular, such a solution can be obtained by purely algebraic computations and using representation theory. This simplifies a construction of... more

Diffeological statistical models and diffeological Hausdorff measures
Hong Van Le
Institute of Mathematics of the Czech Academy of Sciences
Wednesday, 10. March 2021 - 11:30 to 12:30
ZOOM meeting
In my  talk I shall   first    explain  the concept  of diffeological  spaces  introduced by Souriau.   Then  I shall   explain  how to use   this  concept   to  endow  natural  smooth structures on  subsets of probability measures  on an arbitrary measurable   space.    I shall   discuss  the concept  of the diffeological   Fisher metric and the  resulting notion of the diffeological   Hausdorff measure   that are   categorically  natural, and meaningful for  statistical   estimations used in statistical physics and data  analysis.  
 My  talk  is based  on  my paper https://doi.org/10.3390/math8020167 and my joint paper  with  Alexei  Tuzhilin https://arxiv.org/abs/2011.13418
... more

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