The eleven residents who have been part of this stay have offered activities in schools and high schools, but also a day dedicated to a group of students highly motivated by mathematics.
“We arrived at Faber knowing a bit what to expect, since about a year ago we had already spent two weeks in Olot. Being the only Catalan participant who stayed for the whole period (the other Catalan resident, Xavier Guitart, stayed only for three days) had put me in the position of a host to the others. Of course, this was an easy task: the natural beauty surrounding us, a comfortable atmosphere in the hotel and, of course, the great team at Faber. But what we didn’t expect the sunny and warm day when we arrived was that we would be able to enjoy snow as we did! It snowed for almost two full days, which changed completely the view from the room where we met to work. It was so entertaining to see, that we were careful in choosing those seats offering the best views! At the end, we got a lot of work done. Some of us learned how to start developing code for Sage (an open-source mathematics software project), some exchanged ideas on how to contribute code, and some fixed bugs and added features. We are looking forward to another edition of this beautiful residence.”
The writer of these lines is Marc Masdeu, Ramón y Cajal scholar, who contacted us in 2016 to see if they could collaborate with Faber. The projects would be nothing without the people who animate and lead them and that is why the presence of Marc Masdeu, Jean-Philipe Labbé, Vincent Delecroix and Aurel Page, the residents who already made a working stay during February 2017, was so important. They have come again this year to develop their project together with Nick Howell, Charles Fougeron, Xavier Guitart, Simon Drewitz, Bertrand Rémi, Irene Pasquinelli and Vít Tucek.
Mathematical projects are always difficult to describe, because we should start by saying that it is a joint project between GAP, PARI and Sage, and that the main theme of the work is “Subgroups and lattices of Lie groups”. In a first level of translation I would say that the aim of the residency is that all experts work in algebra, hyperbolic geometry, symmetric spaces, grids and Coxeter groups and that, next to them, there are programmers who can improve the functionality of open source packages. In other words, they work in programming architectures applied to complex geometric processes.
The characteristics of these mathematicians’ stays are special. The group work is combined with the individual work, the work is constant and has a specific schedule. Residents meet in the apartment or in the conference room. Of course, work is partly private, and everyone has their own projects, but everyone ends up converging in the development of joint work, almost uninterruptedly, there are many hours of work, almost all of them, except for meals. There has been space for other things that have not been group or personal work, activities of all kinds, walks, bike rides and even an excursion to the castle of Colltort. We must also say, by way of an anecdote, that Irene Pasquinelli one day prepared some wonderful pizzas with Pescara recipe.
As always, and thankfully, the residents have shown the best willingness to collaborate with the educational centers in the area and have done all kinds of activities. Vincent Delecroix went to Castell d’Estela high school, in Amer: “During my talk I talked about algorithms and probabilities. It’s always hard to talk to young students. We need to know what their math background is in order to make the talk understandable and to keep them interested. Some of the questions some of the students asked were about the content of the talk, but also about my studies.”
Xavier Guitart, who curiously was a student years ago at Castell d’Estela hig school where Vincent Delecroix went to talk about algorithms, gave a talk on cryptography to the students of the Little Stem of Olot and also to those of the Pia school. He says: “During the talks the students were interested and also curious to understand how information is encrypted in the digital communications we use in our daily lives, whether it’s when we send messages via WhatsApp or when we log into our Facebook account.”
Finally, Marc Masdeu went to Cor de Maria school and Garrotxa high school: “The main point was that the students should realize that before ‘solving’ an equation we need to decide in which group we look for solutions (whether in natural, rational or real numbers…) and what kind of answer we are looking for. Changing these parameters can turn a ‘trivial’ problem into an ‘impossible’ one, and different choices apply in different situations. The second part of the talk focused on equations in two (polynomial) variables and how problems become much more difficult.
The highlight of the activities was Saturday 27th February. We have welcomed 14 students from different schools in Olot and Besalú, from 4th year of ESO to 2nd year of Batxillerat, and we have proposed seven projects for research during the day. The students have signed up for the project they liked best, and have ended up forming four groups to work in. In the first group, they experimented to discover what the drawings that can be made without lifting the pencil from the paper have in common. The second group has been devoted to the study of detector and error-corrector codes, which are used today both on DVD and BluRay and in WiFi networks. The third group has analyzed a combinatòric game that can be used to divide the price of renting a flat with three different rooms among three people so that everyone is satisfied. Finally, the fourth group studied how to calculate the area of a polygon drawn on a grid, simply by counting the grid points inside the polygon and those on the border.
After spending the whole day working —except for a while to have lunch in the sun on the terrace— they have prepared some posters to explain the results they have found, which they have been able to present to the rest of the participants.
It’s been a great community of practice. The human and professional group that has been created will leave an indelible memory in Faber. We know that we are talking about residents and professionals, but also about friends. It has been a pleasure to receive Marc Masdeu, Jean-Philipe Labbé, Vincent Delecroix, Aurel Page Nick Howell, Charles Fougeron, Xavier Guitart, Simon Drewitz, Bertrand Rémi, Irene Pasquinelli and Vít Tucek, and collaborate one more time with Pia school, Cor de Maria school, Garrotxa high school and Petit Plançó school. For many years to come!