# 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 and Hong Van Le

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.

### Structure functions and Spencer cohomology in zero and positive characteristics

##### Pasha Zusmanovich
University of Ostrava
Wednesday, 29. May 2019 - 11:30 to 12:30
in IM building, ground floor
Structure functions are obstructions to integrability of G-structures, where G is a Lie group,
on a real or complex manifold. These well known invariants are
expressed in terms of Spencer
cohomology of the corresponding graded Lie
algebra. Many important particular cases of structure
functions are known under
the names of Riemann tensor, Nijenhuis tensor, etc.
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### Almost formality of manifolds of low dimension

##### Lorenz Schwachhoefer
TU Dortmund
Wednesday, 5. June 2019 - 11:30 to 12:30
in IM building, ground floor
This is based on work with Domenico Fiorenza, Kotaro Kawai and Hong Van Le.

A classical result by Miller states that any $(k-1)$-connected closed oriented manifold of dimension $\leq 4k-2$ is formal. More recently, Crowley and Nordstr\”om defined the  Bianchi-Massey tensor and showed that its vanishing is the only obstruction to the formality of a $(k-1)$-connected closed oriented manifold of dimension $\leq 5k-3$. Moreover, recently Chan-Karigiannis-Tsang showed that closed $G_2$-manifolds are almost formal, meaning that their deRham algebra is equivalent to a DGA whose differential vanishes in all but one dimension.

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### TBA

Charles University
Wednesday, 12. June 2019 - 11:30 to 12:30
in IM building, ground floor
TBA

### TBA

##### Petr Somberg
MU UK
Wednesday, 19. June 2019 - 11:30 to 12:30
in IM building, ground floor
TBA