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Explore log-canonical coordinates and their significance in Poisson geometry during this 59-minute conference talk. Delve into the simplification of quadratic Poisson brackets through rational transformations and understand the role of log-canonical coordinates in constructing cluster structures on Poisson varieties. Examine a detailed construction of log-canonical charts on Poisson-Lie groups and Poisson homogeneous spaces associated with R-matrices from the Belavin-Drinfeld classification. Discover the crucial Poisson map connecting a simple Lie group with standard Poisson-Lie structure to the same group equipped with a non-trivial Belavin-Drinfeld Poisson bracket. This talk, part of the Workshop on the Role of Integrable Systems dedicated to John Harnad, presents collaborative research with M. Shapiro and A. Vainshtein, offering valuable insights into advanced topics in mathematical physics and geometry.
