slideshow 3

Cohomology in algebra, geometry, physicsand statistics

Lie algebra of operators on moduli space of Riemann surfaces

Speaker’s name: 
Alexander Zuevsky
Speaker’s affiliation: 
Institute of Mathematics of the Czech Academy of Sciences


in IM building, the blue lecture room, ground floor +ZOOM meeting
Wednesday, 9. March 2022 - 13:30 to 14:30
We recall variational formulas for holomorphic elements on Riemann surfaces
with respect to arbitrary local coordinates on the moduli space of complex structures.
These formulas are written in terms of a canonical element on the  moduli space
which corresponds to the pairing between the space of quadratic differentials and
the tangent space to the  moduli space. Next, we recall the notion of continual
Lie algebras introduced by Saveliev and Vershik and provide several classical examples.
We show that canonical differential operators on moduli space $\mathcal M_{n, 3g-3}$
of Riemann surfaces form a continual Lie algebra with the base field given by domains
of points on $\mathcal M_{n, 3g-3}$, where $n$ is the number of punctured points.
General formulation of exactly solvable models associated to continual Lie algebras
will be given. As an application, we provide explicit formulas for solutions to solvable equations.

We open the blue   lecture room at 13.15 for  coffee.

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Meeting ID: 995 9841 3922
Passcode: Galois