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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.

TBA

Jan Gregorovic
University Hradec Kralove
Wednesday, 17. March 2021 - 11:30 to 12:30
in IM building, ground floor
TBA

Diffeological statistical models and diffeological Hausdorff measures

Hong Van Le
Institute of Mathematics of the Czech Academy of Sciences
Wednesday, 10. March 2021 - 11:30 to 12:30
ZOOM meeting
In my  talk I shall   first    explain  the concept  of diffeological  spaces  introduced by Souriau.   Then  I shall   explain  how to use   this  concept   to  endow  natural  smooth structures on  subsets of probability measures  on an arbitrary measurable   space.    I shall   discuss  the concept  of the diffeological   Fisher metric and the  resulting notion of the diffeological   Hausdorff measure   that are   categorically  natural, and meaningful for  statistical   estimations used in statistical physics and data  analysis.  
 My  talk  is based  on  my paper https://doi.org/10.3390/math8020167 and my joint paper  with  Alexei  Tuzhilin https://arxiv.org/abs/2011.13418
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TBA-cancelled

Yaroslav Bazaikin
University Hradec Kralove and University Novisibirsk
Wednesday, 3. March 2021 - 11:30 to 12:30
ZOOM meeting
 TBA

(MODULI) SPACES OF RIEMANNIAN METRICS

Wilderich Tuschmann
Karlsruhe Institute of Technology
Wednesday, 24. February 2021 - 11:30 to 12:30
ZOOM meeting
Consider a smooth manifold with a Riemannian metric satisfying some sort of curvature constraint like, for example, positive scalar curvature, non-negative Ricci or negative sectional curvature, being Einstein, Kähler, Sasaki, etc. A natural question to study is then what the space of all such metrics does look like. Moreover, one can also pose this question for corresponding moduli spaces of metrics, i.e., quotients of the former by (suitable subgroups of) the diffeomorphism group of the manifold, acting by pulling back metrics.

These spaces are customarily equipped with the topology of smooth convergence on compact subsets and the quotient topology, respectively, and their topological properties then provide the right means to measure 'how many'... more

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