Logic Seminar

Please note that the time is PST

Techniques in measurable combinatorics for solving graph labeling problems almost everywhere on a Borel graph are often adaptable to solve these problems on a comeager set. For example, Brandt, Chang, Grebík, Grunau, Rozhoň, and Vidnyánszky showed that every locally checkable labeling problem (LCL) admitting a mod-null solution on any d-regular acyclic Borel graph also admits a mod-meager solution on every such graph. Also, some results showing that measure-expansive pmp graphs have measurable perfect matchings have analogs in the Baire-measurable setting.

Despite this, there is an LCL which always admits a measurable solution on any Schreier graph of a free Borel action of Z2 but does not always admit a Baire measurable solution. This talk will discuss the methods used in these Baire measurable construction and obstruction results as well as the method of rectangular toast for constructing measurable labelings on grids. This includes joint work with Alexander Kastner as well as with Katalin Berlow, Anton Bernshteyn, and Felix Weilacher.