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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.

G-structures on NQ-manifolds and gauge theory: Cancelled!
Alexei Kotov
Univ. Hradec Kralove
Wednesday, 23. October 2019 - 11:30 to 12:30
Seminar room Konirna, in front IM building, ground floor
An NQ-manifold is a non-negatively graded super manifold  together with
a homological super vector field of degree 1. This talk will be about
compatibility of certain G-structures on such a manifold with the
corresponding Q-field and applications of this formalism to constructing
of gauge sigma-models.

The talk is cancelled because of the health  condition of the speaker.... more

On Legendrian products and twist spuns
Roman Golovko
Charles University
Wednesday, 26. June 2019 - 11:30 to 12:30
in IM building, ground floor
The Legendrian product of two Legendrian knots, as defined by Lambert-Cole,
is a Legendrian torus. We show that this Legendrian torus is a twist spun whenever one of
the Legendrian knot components is sufficiently large. We then study examples of Legendrian
products which are not Legendrian isotopic to twist spuns. In order to do this, we prove a
... more

Hecke algebras
Petr Somberg
MU UK
Wednesday, 19. June 2019 - 11:30 to 12:30
in IM building, ground floor
We explain the notion of a Hecke algebra (operator, correspondence)
 and indicate its connection with various problems in representation
theory, topology and number theory.

Properads and Homotopy Algebras Related to Surfaces
Lada Peksova
Charles University
Wednesday, 12. June 2019 - 11:30 to 12:30
in IM building, ground floor
Barannikov showed how an algebra over the Cobar construction over a
modular operad can equivalently be described as a solution of a master
 equation for certain generalized BV algebra. We give an analogous
description for properads which were first introduced by B. Vallette
 as connected parts of PROPs.

 In short, we introduce properads along with our main examples, the
closed (commutative) Frobenius properad, and the open (associative)
 Frobenius properad. We consider the construction of the Cobar complex
 of a properad as a free properad over its suspended linear dual
equipped with the differential induced by the duals of the structure
 operations. We describe algebras over the Cobar construction in terms
 of solutions of generalized master equations and recover the
 well-known result that the corresponding algebras for closed Frobenius
properad are $IBL_\... more

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