# 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.

### Formal integrability of geometric structures

##### Francesco Cattafi
KU Leuven
Wednesday, 14. October 2020 - 11:30 to 12:30
ZOOM meeting
A Γ-structure on a manifold is a maximal atlas whose changes of coordinates take values in a Lie pseudogroup Γ. Various geometric structures (e.g. symplectic, complex and contact structures) fit in this framework, but there is no general definition of almost Γ-structure (e.g. almost symplectic, almost complex and almost contact structures) in terms of Γ. In this talk we are going to fill this gap by introducing the general definition of an almost Γ-structure, and presenting a characterisation of its formal integrability. This will be obtained by introducing the concept of principal Pfaffian bundle. We will draw inspiration from the theory of PDEs, from Poisson geometry, as well as from similar results in the theory of G-structures, which we recover as particular cases. This is joint work with Marius Crainic.

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### On the different perspective of the Casals-Murphy criterion of looseness

##### Roman Golovko
Charles University
Wednesday, 7. October 2020 - 11:30 to 12:30
ZOOM meeting
We show that inside a trivial open book $\partial (W\times D^2)$ with page being a Weinstein manifold $(W, d\theta)$, any Legendrian which is contained entirely inside a page and which intersects some cocore disc transversely in a single point is loose. This leads to the alternative proof of Casals-Murphy criterion of looseness. This is joint work with Georgios Dimitroglou Rizell.

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ZOOM  meeting  shall be opened at  11.20  at

https://cesnet.zoom.us/j/99598413922?pwd=Ym4velNHckh2TlNxK2R2SzRpVXRhdz09

Meeting ID: 995 9841 3922

Passcode: 097923

and closed  at 13.00
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### Lorentzian Symmetry Predicts Universality Beyond Power Laws

##### Stephen Watson
University of Glasgow
Wednesday, 24. June 2020 - 11:30 to 12:30
ZOOM meeting
The statistical physics governing phase-ordering dynamics following a symmetry breaking first-order phase transition is an area of active research. The Coarsening/Ageing of the ensemble of phase domains, wherein  irreversible annihilation or joining of domains yields a growing characteristic domain length, is a omniprescent feature whose universal characteristics one would wish to understand. Driven kinetic Ising models and growing nano-faceted crystals are theoretically important... more

### Vertex algebra cohomology of foliations on Riemann surfaces

##### Alexander Zuevsky
Institute of Mathematics, Czech Academy of Sciences
Wednesday, 17. June 2020 - 11:30 to 12:30
ZOOM meeting + the blue lecture room in the rear building, Zitna 25
In the transversal basis formalism, we construct a vertex algebra
cochain complex, show its independence on coordinates and choice of basis, and
define the vertex algebra cohomology for a foliation on a smooth complex curve.
The first cohomologies are determined in terms of connections and classes of extensions of
the vertex algebra. We will introduce the... more