Aryaman Jal - A Clothesline for Numbers: Generating Functions in Analytic Combinatorics

The late combinatorialist Herb Wilf memorably said that a generating function is a clothesline on which we hang numbers. Questions in enumerative combinatorics are often clarified by a close analytic study of this “clothesline”. In this talk, we survey a clutch of techniques in analytic combinatorics that showcase the power of polynomialising an enumerative problem. This circle of ideas involves enumerative combinatorics, complex analysis, and the theory of combinatorial species which serves as the connective tissue between the first two topics. The talk will be accessible to a broad audience and driven by intriguing examples that occur naturally in the combinatorial wildlife.