Courses

Introduction to polytopes. Bruno Benedetti (University of Miami).

Abstract: Polygons and their higher-dimensional analog (“polytopes”) have been studied since the beginning of mankind. We all have in mind Egyptian or Mayan pyramids, Roman mosaics, or Greek geometry. The investigation of polytopes and of the complexes they form has however made a significant comeback in recent years, thanks to the rise of two huge applications, namely, linear optimization and computer-driven digitalization. This course shall provide a modern overview of the world of polytopes. We will integrate the two standard monographs dedicated to them (by Gruenbaum and Ziegler) with some of the most recent and exciting developments on triangulated spheres and on the Hirsch conjecture.

Asymptotic results in enumerative and algebraic combinatorics. Maciej Dołęga (Polish Academy of Sciences).

Abstract: What is a typical behaviour of a longest increasing subsequence in a random word, when the length of this word is tending to infinity? What can we say about the shape of the Young diagram that is built by a process of adding new cells at random? What is the relation between these problems and other combinatorial problems such as enumeration of discrete surfaces? We will discuss these topics and we will describe several tools that can be used to tackle these sorts of questions. These tools will include the RSK algorithm, counting methods used in probabilistic settings, symmetric functions, and relation between the permutation group and discrete surfaces.

Research in combinatorics using SageMath. Salvatore Stella (University of L'Aquila).

Abstract: SageMath is a free open-source mathematics software system developed by mathematicians for mathematicians which emerged in recent years as an alternative to proprietary solutions. It builds on top of many existing open-source packages (including NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more) giving access to their combined power through a common, Python-based language. One of the areas of mathematics where SageMath is more effective is combinatorics.

In this course we will provide a gentle introduction to using SageMath as an effective tool to support research in combinatorics with a particular eye towards the topics covered in the other courses of the conference: polytopes and symmetric functions.