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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.

Boundary conditions and edge modes in gauge theories

Alexander Schenkel
University of Nottingham
Wednesday, 13. January 2021 - 11:30 to 12:30
ZOOM meeting
The fields of a classical gauge theory form a smooth groupoid (aka stack) with morphisms given by gauge transformations. From this perspective, the concept of "equality" of two gauge fields A and A' is not a property but rather additional data given by the choice of a gauge transformation A ---> A' which witnesses that A and A' are "the same". In this talk, I will explain how this higher-categorical point of view is useful to study gauge theories on manifolds with boundaries and defects. In particular, I will show that the additional data witnessing boundary conditions are precisely the famous edge modes from physics. As examples, I will discuss 3d Abelian Chern-Simons theory on manifolds with boundary, which is physically describing the quantum Hall system, and also the 4d holomorphic Chern-Simons theory of Costello and Yamazaki where the edge modes on surface defects... more

Deformations of symplectic foliations

Alfonso Tortorella
KU Leuven
Wednesday, 6. January 2021 - 11:30 to 12:30
ZOOM
In this talk, based on joint work with Stephane Geudens and Marco Zambon, I develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leaf-wise symplectic form. The main result is that each symplectic foliation is attached with an L_\infty algebra controlling its deformation problem. Indeed, we establish a one-to-one correspondence between the small deformations of a given symplectic foliation and the MC elements of the associated L_\infty algebra. Further, we prove that, under this one-to-one correspondence, the equivalence by isotopies of symplectic foliations agrees with the gauge equivalence of MC elements. Finally, we show that the infinitesimal deformations of symplectic foliations can be obstructed.

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Chain models of string topology coming from symplectic geometry

Pavel Hajek
University Hamburg
Wednesday, 16. December 2020 - 11:30 to 12:30
in IM back building, ground floor, blue lecture room + ZOOM meeting
I will recall loop spaces, natural structures on their
homology and the relation to symplectic geometry of the cotangent bundle
(specifically to chain level structures defined by counting holomorphic
curves). I will then zoom in on the equivariant case and a chain model
based on de Rham forms and Chern-Simons theory. I will show some
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Quotients of Classical Symmetric Spaces

Mahir Can
Tulane University
Wednesday, 9. December 2020 - 11:45 to 12:45
ZOOM meeting
In this talk we will discuss some new and old results regarding the wonderful embeddings of classical complex
symmetric spaces. More precisely, we will introduce certain (non-arithmetic)
quotients of  classical symmetric spaces. Then we will describe their combinatorial
and geometric properties in relation with their wonderful embeddings.
Our running example will be on the variety of nondegenerate quadrics.

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The lecture shall      start   at 11.45 AM  Prague time.
Our ZOOM meeting shall be  open at   11.30  at

https://cesnet.zoom.us/j/99598413922?pwd=c2Y0TENuZHdDQ3hDWEkySFI3YWo3QT09

Meeting ID: 995 9841 3922

Passcode:... more

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