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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.

An approach to the construction of virtual fundamental cycle/chain with integer coefficients

Kaoru Ono
RIMS, Kyoto
Wednesday, 20. October 2021 - 11:30 to 12:30
ZOOM meeting
Around 2000, Kenji Fukaya and I proposed the construction of 
virtual fundamental cycle/chais with integer coeffients under the condition that 
the moduli spaces carry consistent  (relative) stable complex structures.  Starting with
the construction of virtual fundamental cycle/chains with rational coefficents, 
I will explain our ideas for the construction with integer coefficients.

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ZOOM meeting shall be opened at 11.15 and closed at 1 PM. Join Zoom Meeting
https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09
Meeting ID: 995 9841 3922
Passcode: Galois
 

On the differential geometry of groups of diffeomorphisms and of non-formal pseudo-differential operators

Jean-Pierre Magnot
University d'Angers, France
Wednesday, 27. October 2021 - 11:30 to 12:30
ZOOM meeting
Summary:
After reviewing a class of infinite dimensional groups based on the central extension of a group of diffeomorphisms by a group of pseudo-differential operators (PDOs), I will explain:
1) how the action of the group of diffeomorphisms generates the dressing operator of a KP hierarchy, which is shown to be well-posed in a class of NON FORMAL PDOs
2) How renormalized traces enables to define pseudo-Riemannian metrics on some of these groups of PDOs, different from the classical sobolev metrics present in the literature
3) how the geodesic equation of one of these metrics admit an infinite number of independent  integrals of the motion
Part of the results of this talk are obtained from works in collaboration with Enrique G. Reyes. Arxiv identifiers of related publications/preprints are: 2104.08159 ; 2007.00387 ; 1808.03791 and 1407.1427... more

TBA

Arthur J. Parzygnat
IHES, Paris
Wednesday, 3. November 2021 - 11:30 to 12:30
ZOOM meeting
TBA

TBA

Dmitri Alekseevsky
Institute for Information Transmission Problems, Moscow
Wednesday, 10. November 2021 - 11:30 to 12:30
ZOOM meeting
TBA

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