Uniformizing Lee-Yang singularities

Motivated by the search for QCD critical point, we discuss how to obtain singular behavior of a thermodynamic system near namely Lee-Yang singularities, from limited amount local data generated in different region phase diagram. We show that using number Taylor series coefficients, it is possible reconstruct equation state past radius convergence, particular region. Furthermore also extend this reconstruction go crossover first-order transition diagram, uniformizing map pass between Riemann sheets. illustrate these ideas via chiral random matrix model and Ising model.