报告人：Cyril Banderier

邀请人：胡怡宁

报告题目：An introduction to Analytic Combinatorics

报告时间：2020年11月28日（星期六）18:00-19:30

报告地点：：https://bbb.lipn.univ-paris13.fr/b/ban-kpe-96w

报告摘要："Analytic Combinatorics" is the name of a wonderful field, mostly developed these last 40 years by Philippe Flajolet and his school (extending ideas of Euler, Ramanujan, Pólya, ...) and nicely presented in his book with Robert Sedgewick.Its aim is the enumeration and asymptotics of combinatorial structures. Many combinatorial structures have a recursive definition which can be translated into a functional equation for the corresponding generating function.By considering the landscape of this function in the complex plane,one benefits from powerful tools in complex analysis,which offer us access to closed form formulas, asymptotics, limit laws, etc. What is the number of trees of size n?What is the link between their typical height and Mandelbrot's fractal?What is the probability to have an irreducible polynomial in a finite field?These questions are easily answered with tools from analytic combinatorics, which I will illustrate via different applications in combinatorics, probability theory, statistical mechanics, chemistry, bioinformatics, economy, computer algebra, language theory, computer science, number theory.

报告人简介：Cyril Banderier is a CNRS researcher at the university of Sorbonne Paris Nord. He is one of the world experts in analytic combinatorics, which he likes to apply to different fields, as seen by his publications in Ann. Probab., Algorithmica, J. Phys. A, Disc. Math., Random Structures & Algorithms, etc.