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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.

Algebraic geometry and number theory applications of vertex operator algebras
Alexander Zuevsky
Institute of Mathematics, Czech Academy of Sciences, Praha 
Wednesday, 24. October 2018 - 11:30 to 12:15
in IM building, ground floor
We continue our series of lectures concerning vertex operator algebras and their applications in algebraic geometry and number theory. In particular, we consider a construction and properties of characters for vertex operator algebras on Riemann surfaces.

Volokitina's computation of Gelfand-Fuks cohomology on ...
Hong Van Le
IM CAS, Zitna 25, Praha 
Wednesday, 17. October 2018 - 11:30 to 12:30
in IM building, ground floor
I report on Volokitina's works on Gelfand-Fuks cohomology on the orbifold ...

Vertex algebras and foliations associated to CFT correlation functions
<strong>Sasha Zuevsky</strong>
<span style="background-color:rgb(255, 255, 255); color:rgb(153, 153, 153); font-family:arial,helvetica,sans-serif; font-size:12.096px">IM CAS, Praha</span>
Wednesday, 10. October 2018 - 11:00 to 15:00
in IM building, ground floor
<span style="background-color:rgb(255, 255, 255); font-family:arial,helvetica,sans-serif; font-size:13.44px">We recall the notion of CFT/vertex operator algebras, their modules, construction of CFT correlation functions on Riemann surfaces of various genus, and their relations to modular forms. Using properties of vertex algebra intertwining operators and characters, we show how to construct a foliation associated to a grading-restricted vertex algebra. A short synopsis of the proof for coordinate-independence of the construction will be given. Finally, we will shortly discuss cohomology and characteristic classes of grading-restricted vertex algebras and corresponding foliations.</span>

Vertex algebras and foliations associated to CFT correlation functions
Sasha Zuevsky
IM CAS, Praha
Wednesday, 3. October 2018 - 11:00 to 12:30
konirna room, ground floor, front building
We recall the notion of CFT/vertex operator algebras, their modules, construction of CFT correlation functions on Riemann surfaces of various genus, and their relations to modular forms. Using properties of vertex algebra intertwining operators and characters, we show how to construct a foliation associated to a grading-restricted vertex algebra. A short synopsis of the proof for coordinate-independence of the construction will be given. Finally, we will shortly discuss cohomology and characteristic classes of grading-restricted vertex algebras and corresponding foliations.

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