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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.

Differential invariants in thermodynamics

Eivind Schneider
University Hradec Kralove
Wednesday, 15. April 2020 - 11:30 to 12:30
ZOOM Meeting
It is well known that contact geometry gives the appropriate framework for formulating thermodynamics: Thermodynamic states can be interpreted as Legendrian submanifolds of a certain contact manifold. The existence of a metric on thermodynamic states has also received some attention in the last decades. The metric can be interpreted as the variance of an underlying probability measure. Less studied is the action of the affine group that appears naturally in this context as the group preserving the variance. We... more

TBA - cancelled - postponed to a later date

Denis Bashkirov
IM, CAS
Wednesday, 8. April 2020 - 11:30 to 12:30
Konirna Seminar room in IM front building, ground floor
TBA

Koszul algebras and one-dependent random 0-1 sequences

Leonid Positselski
IM, CAS
Wednesday, 1. April 2020 - 11:30 to 12:30
https://cesnet.zoom.us/j/239249755 Meeting ID 239-249-755
Koszul algebras are a natural class of graded algebras with
quadratic relations, defined by a series of homological conditions.
To a Koszul algebra over a field with finite-dimensional components,
one can assign a one-dependent stochastic 0-1 sequence, which carries
information about the dimensions of the algebra's grading components.
... more

Cyclic homology for bornological coarse spaces CANCELLED because of COVID-19

Luigi Caputi
Institute of Informatics of the Czech Academy of Sciences, Praha
Wednesday, 25. March 2020 - 11:30 to 12:30
in konirna seminar room of the front IM building, ground floor
Bornological coarse spaces are "large scale" generalizations of metric spaces (up to quasi-isometry). Homological invariants of such spaces are given by coarse homology theories, which are functors from the category of bornological coarse spaces to a stable cocomplete ∞-category, satisfying additional axioms. Among the main examples of coarse homology theories, there are coarse versions of ordinary homology, of topological
and algebraic K-theory. In the talk we define G-equivariant coarse versions of the classical Hochschild and cyclic homologies of algebras. If k is a field, the evaluation at the one point space induces equivalences with the classical Hochschild and cyclic... more

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