# 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. https://pirsa.org/23020057

### MLA

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

### BibTex

@misc{ pirsa_PIRSA:23020057, doi = {10.48660/23020057}, url = {https://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}, year = {2023}, month = {feb}, note = {PIRSA:23020057 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

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