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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.

KP integrability of triple Hodge integrals

Alexander Alexandrov
Center for Geometry and Physics, IBS Pohang, South Korea
Wednesday, 2. December 2020 - 11:30 to 12:30
ZOOM meeting
In my talk I will describe a relation between the Givental group of rank one and Heisenberg-Virasoro symmetry group of the KP integrable hierarchy. In particular I will show that only a two-parameter family of the Givental operators can be identified with elements of the Heisenberg-Virasoro symmetry group. This family describes triple Hodge integrals satisfying the Calabi-Yau condition. Using identification of the elements of two groups it is possible to prove that the generating function of triple Hodge integrals satisfying the Calabi-Yau condition and its $\Theta$-version are tau-functions of the KP hierarchy. This generalizes the result of Kazarian on KP integrability in case of linear Hodge integrals. I will also describe the relation of this family of tau-functions with the generalized Kontsevich matrix model. My talk is based on two papers, arXiv:2009.01615 and arXiv:2009... more

Convergence of the Kähler-Ricci flow on varieties of general type

Tat Dat To
Wednesday, 18. November 2020 - 11:30 to 12:30
ZOOM meeting
We study the Kähler-Ricci flow on varieties of general type. We show that the normalized Kähler-Ricci flow exists at all times in the sense of viscosity, is continuous in an open Zariski set and converges to the singular Kähler-Einstein metric. This gives an answer to a question of Feldman-Ilmanen-Knopf.

Our ZOOM meeting shall be opened at 11.15 at

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Gluing bundles over noncommutative flag varieties

Zoran Skoda
University of Zadar and University of Hradec Kralove
Wednesday, 4. November 2020 - 11:30 to 12:30
ZOOM meeting
Localization functors may be used to define local covers in some
examples from noncommutative geometry. In an earlier work, I have used
this technique to treat
gluing of bundles over quantum flag varieties with applications to quantum group
coherent states and representation theory. A non-flat version of this technique
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Formally integrable complex structures on higher dimensional knot spaces

Domenico Fiorenza
Università di Roma “La Sapienza”
Wednesday, 21. October 2020 - 11:30 to 12:30
ZOOM meeting
By the Brown-Gray’s classification, there are four classes of Riemannian manifolds M with parallel r-fold vector cross products: r = 1 and M a Kähler manifold, r = dim M − 1, r = 2 and M a G_2-manifold, r = 3 and M a Spin(7)-manifold. For the first three classes it has been proven by Brylinski, LeBrun, and Verbitsky, via ad hoc arguments for each of these classes, that the higher knot spaces for M carry a natural formally Kähler structure. More recently, Henrich provided a new proof for the r = dim M − 1 case. In a recent work with Hông Vân Lê (arXiv:1912.05175), we show how a variant of Henrich's construction can be used to provide a uniform proof for all four classes. In particular, this provides a proof for the previously unknown case of Spin(7)-manifolds.
ZOOM meeting shall be opened at 11.15 at
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