Title: Deformation theory of log canonical Poisson brackets
Abstract: A log canonical Poisson bracket is a bracket of the form $\{ x_i, x_j \} = lambda_{ij} x_i x_j$. I will describe how to deform such brackets to more complicated Poisson brackets. This will involve discussing the infinitesimal deformations, given by the Poisson cohomology, and presenting a key unobstructedness result akin to the Bogomolov-Tian-Todorov theorem. I will introduce a class of decorated graphs that serve as a tool to encode the obtained deformations, providing a systematic framework for understanding them. Examples of Poisson brackets arising from this approach will be discussed, with a focus on the standard Poisson brackets on Bott-Samelson varieties. The talk is based on joint projects with Brent Pym, Travis Schedler and Jiang-Hua Lu.