## Video URL

http://pirsa.org/23020057# Symplectic groupoid and log-canonical coordinates on the Teichmueller space of closed genus two surfaces.

### APA

Shapiro, M. (2023). Symplectic groupoid and log-canonical coordinates on the Teichmueller space of closed genus two surfaces.. Perimeter Institute for Theoretical Physics. http://pirsa.org/23020057

### MLA

Shapiro, Michael. Symplectic groupoid and log-canonical coordinates on the Teichmueller space of closed genus two surfaces.. Perimeter Institute for Theoretical Physics, Feb. 24, 2023, http://pirsa.org/23020057

### BibTex

@misc{ scitalks_PIRSA:23020057, doi = {}, url = {http://pirsa.org/23020057}, author = {Shapiro, Michael}, keywords = {Mathematical physics}, language = {en}, title = {Symplectic groupoid and log-canonical coordinates on the Teichmueller space of closed genus two surfaces.}, publisher = {Perimeter Institute for Theoretical Physics}, year = {2023}, month = {feb}, note = {PIRSA:23020057 see, \url{https://scivideos.org/PIRSA/23020057}} }

Michael Shapiro Michigan State University (MSU)

## Abstract

The coordinate functions on a Poisson variety are log-canonical if the Poisson bracket of two coordinate functions equals a constant times the product of these functions. We consider the symplectic groupoid of unipotent upper-triangular matrices equipped with canonical Poisson bracket. We described a system of log-canonical coordinates and the corresponding cluster structure. As a bonus, we discovered a system of log-canonical coordinates on Teichmueller space of closed genus 2 surfaces. This is joint work with L. Chekhov.

Zoom link: https://pitp.zoom.us/j/94716952708?pwd=R2RiQWRpcHFMYlJLMlB0UjlPVGZkQT09