What was the question?
The challenge for the students was to find applications of the Flower Theorem in the context of data that we could gather in the city of Toronto.
Unfortunately, we were interrupted midway by the COVID-19 pandemic and the project got quite disrupted.
What motivated me?
I wanted to do a project that was less of a reading course and engaged more with actual research process. I did want the students to struggle with the idea of doing research work by themselves.
The probabilistic method is an idea that I find incredible and to see the Sunflower Theorem proven in this way was very spectacular. I got this idea from this post on Quanta.
What did the students do?
They understood the examples of sunflowers and the idea of proof of some basic cases. For this they had to study what the probabilistic method was and read from some papers the ideas of basic cases of sunflowers. Finally, they suggested ideas of how to look for sunflowers in data from Facebook. This last part unfortunately was not done because of the pandemic lockdowns.
Special moments I remember 🙂
When the pandemic started everything was upside down for both the students and myself. I lost contact with them for around a month and a half due to this. I thought the project would be a mess, but they proved me wrong! They kept working by themselves (and online!) and they had managed to do a good final work given their conditions, despite the fact that I could not be with them due to the separation. I was very proud of them.
Outcomes of the work
The students presented a work on the sunflower lemma, the proof of some basic cases and ideas they had to apply it in an online event at the end of the term.
Malors 