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, Romain 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).

Course Notes and exercises

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).

Files

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 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.

Exercise session: Thursday

Usual Classroom (Stella)

Martina Costa Cesari

Nathanaël Hassler

Catarina Pacheco

Maddalena Pismataro

Alessandro Tedeschi

Eliana Tolosa Villarreal

Eduardo Venturini*

***

Riccardo Biagioli

Sabrina Botticchio

Solal Gaudin

Alessandro Iraci*

Menghao Qu

Roberto Riccardi

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Classroom on the left (Benedetti)

Alessandra Caraceni

Elena Hoster

Giovanni Interdonato

Inês Legatheaux Martins

Alessio Sgubin

Viola Siconolfi*

Alexander Stewart

***

Jhon Bladimir Caicedo Portilla

Fabrizio Caselli

Sabino Di Trani

Iqra Khan

Anthony Lazzeroni

Vassilis Dionyssis Moustakas*

Divya Setia

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Classroom on the right (Dołęga)

Luca Fiorindo

Katerina Kalampogia-Evangelinou

Lorenzo Noè

Marino Romero*

Antonije Subotić

Maurizio Zanardo

***

Michele D'Adderio*

Danai Deligeorgaki

Alice Dell’Arciprete

Paola Malatacca

Lorenzo Perrone

Tommaso Punis

Elisa Sasso

Exercise session: Wednesday