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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.

On integral persistence diagrams
Yaroslav Bazaikin
University Hradec Kralove
Wednesday, 27. November 2019 - 11:30 to 12:30
in IM building, ground floor
Persistence diagrams are not stable with respect to high amplitude noise. In the talk the modified 0-dimensional persistence diagram construction will be discussed. Some particular results on stability with respect to high amplitude noise with small enough integral norm will be presented.

On split-octonions
Jiri Vanzura
IM CAS
Wednesday, 20. November 2019 - 11:30 to 12:30
in Konirna seminar room, front IM building, ground floor
We shall study first split-quaternions and then split-octonions. For technical reasons split-quaternions will be constructed by applying the Cayley-Dickson construction to complex numbers and split-octonions by applying this construction to quaternions. Our attention will be devoted to special elements and their properties in these two algebras. We shall classify all subalgebras in split-quaternions and split-octonions and further describe the types of isotropic subspaces in them.

Koszul algebras and one-dependent random 0-1 sequences: CANCELLED because of DOD
Leonid Positselski
MI, CAS
Wednesday, 13. November 2019 - 11:30 to 12:30
in IM building, ground floor
Koszul algebras are a natural class of graded algebras with
quadratic relations, defined by a series of homological conditions.
To a Koszul algebra over with finite-dimensional components, one can
assign a one-dependent stochastic 0-1 sequence, which carries
information about the dimensions of the algebra's grading components.
... more

Commutative cohomology in characteristic 2
Pavel Zusmanovich
University Ostrava
Wednesday, 6. November 2019 - 11:30 to 12:30
in Seminar room Konirna, front IM building, ground floor
Commutative Lie algebras are commutative algebras in characteristic 2 satisfying
the Jacobi identity. This class of algebras is broader than the class of Lie
algebras (which satisfy the stronger alternating identity [x,x] = 0).
The natural cohomology in this class is a variation of the usual
 Chevalley-Eilenberg cohomology, where alternating cochains are
replaced by symmetric ones. This cohomology appears naturally in the
ongoing efforts to advance in classification of simple Lie algebras in
characteristic 2, and its properties resemble cohomology of Lie
superalgebras (in any characteristic) rather than the usual
Chevalley-Eilenberg cohomology. We will discuss some general results,
computations, and open questions. (Based on arXiv:1907.03690).
 

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