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

Place:

in IM building, the blue lecture room, ground floor +ZOOM meeting

Date:

Wednesday, 9. March 2022 - 13:30 to 14:30

Abstract:

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.

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We open the blue lecture room at 13.15 for coffee.

Join Zoom Meeting

https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09

Meeting ID: 995 9841 3922

Passcode: Galois

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.

Join Zoom Meeting

https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09

Meeting ID: 995 9841 3922

Passcode: Galois