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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.

Deformed Donaldson-Thomas connections
Kotaro Kawai
Gakushuin University, Tokyo
Wednesday, 19. May 2021 - 11:30 to 12:30
ZOOM meeting
The deformed Donaldson-Thomas (dDT) connection is a Hermitian connection of a Hermitian line bundle over a $G_2$-manifold satisfying certain nonlinear PDEs. This is considered to be the mirror of a calibrated (associative) submanifold via mirror symmetry. As the name indicates, the dDT connection can also be considered as an analogue of the Donaldson-Thomas connection ($G_2$-instanton). 
In this talk, after reviewing these backgrounds, I will show that dDT connections indeed have properties similar to associative submanifolds and $G_2$-instantons. I would also like to present some related problems. This is joint work with Hikaru Yamamoto. 
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We shall  open ZOOM  at 11.15 and close at 13.00

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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
geometries.

TBA
Martel Jules
Max-Planck-Institute for Mathematics, Bonn
Wednesday, 6. October 2021 - 11:30 to 12:30
ZOOM meeting
TBA

TBA
Kaoru Ono
RIMS, Kyoto
Wednesday, 20. October 2021 - 11:30 to 12:30
ZOOM meeting
TBA

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