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.

Lorentzian Symmetry Predicts Universality Beyond Power Laws

Stephen Watson

University of Glasgow

Wednesday, 24. June 2020 - 11:30 to 12:30

ZOOM meeting

The statistical physics governing phase-ordering dynamics following a symmetry breaking first-order phase transition is an area of active research. The Coarsening/Ageing of the ensemble of phase domains, wherein irreversible annihilation or joining of domains yields a growing characteristic domain length, is a omniprescent feature whose universal characteristics one would wish to understand. Driven kinetic Ising models and growing nano-faceted crystals are theoretically important... more

Vertex algebra cohomology of foliations on Riemann surfaces

Alexander Zuevsky

Institute of Mathematics, Czech Academy of Sciences

Wednesday, 17. June 2020 - 11:30 to 12:30

ZOOM meeting + the blue lecture room in the rear building, Zitna 25

In the transversal basis formalism, we construct a vertex algebra
cochain complex, show its independence on coordinates and choice of basis, and
define the vertex algebra cohomology for a foliation on a smooth complex curve.
The first cohomologies are determined in terms of connections and classes of extensions of
the vertex algebra. We will introduce the... more

Cyclic homology for bornological coarse spaces

Luigi Caputi

Institute of Informatics of the Czech Academy of Sciences, Praha.

Wednesday, 10. June 2020 - 11:30 to 12:30

ZOOM meeting + blue lecture room on the ground floor of the rear building Zitna 25

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 homology of k. In the equivariant setting, the G-equivariant coarse Hochschild (cyclic) homology of the discrete group G agrees with the classical Hochschild (cyclic) homology of the associated group algebra k[G].

... more

An approach to the representation theory of symmetric groups

Petr Somberg

Charles University Prague

Wednesday, 3. June 2020 - 11:30 to 12:30