TBA

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.

University Hradec Kralove

Wednesday, 17. March 2021 - 11:30 to 12:30

in IM building, ground floor

TBA

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

... more

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

... more

University Hradec Kralove and University Novisibirsk

Wednesday, 3. March 2021 - 11:30 to 12:30

ZOOM meeting

TBA

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

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