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Cohomology in algebra, geometry, physics and statistics

usually takes place every Wednesday Institute of Mathematics of ASCR, Žitná 25, Praha 1
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.


ZOOM meeting shall be opened at 11.15 and closed at 1 PM. Join Zoom Meeting
Meeting ID: 995 9841 3922
Passcode: Galois

Using second Galois cohomology to search for a real point in a real homogeneous space

Mikhail Borovoi
Tel Aviv University
Wednesday, 13. October 2021 - 11:30 to 12:30
ZOOM meeting
Let G be a real algebraic group and Y be its real homogeneous space, say an orbit of the complex group G(C), stable under the complex conjugation, in a linear representation of G. We wish to find a real point in Y or to prove that Y contains no real points. We arrived at this problem when classifying trivectors on R^9. I will explain a method of solving it using second (nonabelian) Galois cohomology.
No preliminary knowledge of Galois cohomology (first or second, abelian or nonabelian) is assumed.


ZOOM meeting shall be opened at 11.15  and closed at  1 PM.

Join Zoom Meeting

Meeting ID: 995 9841 3922

Passcode: Galois

Modules of quantized Lie algebras and their braiding from homology of configuration spaces

Jules Martel-Tordjman
University of Burgundy
Wednesday, 6. October 2021 - 11:30 to 12:30
ZOOM meeting
From any semi-simple Lie algebra, Drinfel'd has defined an associated quantized version called a quantum group. The theory of modules over quantum groups has been widely used to produce topological invariants in low dimension such as: braid groups representations, the famous Jones polynomial for knots or topological quantum field theories à la Witten--Reshetikhin--Turaev (providing representations of mapping class groups of surfaces expected to have rich properties and 3-manifold invariants).
All these constructions rely on the algebraic background surrounding quantum groups so that their topological content is often mysterious in the end, and finally the subject of many conjectures in this field called quantum topology.
We are able to recover quantum groups modules from homology of configuration spaces, and it gives a homological model for quantum braid group representations and knot invariants such as the ones arising from the Jones family.

In this talk I'll... more

Symmetry, holonomy and special geometries

Petr Zima
Charles University
Wednesday, 26. May 2021 - 11:30 to 12:30
ZOOM meeting
Various types of geometrical structures can be described via their so
called structure group. This becomes especially apparent when studying
homogeneous spaces. Those spaces are of the form G/H where G is a
transitive symmetry group and H is the isotropy subgroup which plays the
role of structure group. A natural question is to ask whether we can
enlarge or reduce the structure group while preserving the geometrical
structure. Particular answer is given by the notion of holonomy that
provides the smallest possible structure group H. We will review these
notions and demonstrate them by examples of special Riemannian

We open ZOOM at 11.15 and close  at 13.00
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