MPI Lectures 2026

This is the website for the lecture series An Invitation to Analytic Combinatorics at the Max Planck Institute for the Mathematical Sciences from June 9 – June 11.

The majority of the material is covered in the undergraduate lecture notes An Invitation to Enumeration or the textbooks An Invitation to Analytic Combinatorics and Analytic Combinatorics in Several Variables.

Each lecture also links to a SageMath Jupyter notebook working through the code presented in the slides. Some of the notebooks also require the ore_algebra, sage_acsv, and sage_periods packages to be installed.

• Lecture 1: Combinatorics Basics and Rational GFs

  • The slides for Lecture 1 are here.
  • The corresponding Sage notebook is here (static HTML).

• Lecture 2: Analytic Combinatorics + Algebraic and D-Finite GFs

  • The slides for Lecture 2 are here.
  • The corresponding Sage notebook is here (static HTML).

• Exercise Session 1

  • The problems are available here.

• Lecture 3: Diagonals and Polynomial Amoebas

  • To come.

• Lecture 4: Smooth Analytic Combinatorics in Several Variables

  • To come.

• Exercise Session 2

  • To come.

• Lecture 5: Automating ACSV and Limit Theorems

  • To come.

• Exercise Session 3

  • To come.

• Lecture 6: Non-Smooth ACSV and a Geometric Framework

  • To come.