Algebra and topology for analytic combinatorics in several variables

The course will cover the basics of the modern approach to multivariate analytic combinatorics dealing with asymptotic expansions of generating functions. These expansion on one hand provide a very powerful tool in handling otherwise difficult problems arising in a variety of adjacent areas (from analysis of algorithms to statistical physics); on the other hand they rely on tools from topology and analysis on complex algebraic varieties.

Sources: I will be relying on Pemantle and Wilson’s “Analytic Combinatorics in Several Variables“, Melczer’s “An Invitation to Analytic Combinatorics” and several research articles.

Modality: the course will be conducted online (Zoom link); the recordings and lecture notes, will be posted after the lectures at the diary page.

Schedule: Tuesdays 6:40 – 8:10pm (Illinois)=Wednesdays 8:40-10:10am (Kyushu). First lecture: June 8/9.