A fractal spectrum of tales
- Four Golden Lessons
The recent death of Steven Weinberg, winner of the Nobel prize in Physics and one of the most brilliant scientists of our times, made many people look back to his incredible production. In addition to some incredible eulogies, this has allowed a lot of little gems to resurface. Here I want to share one of them.
In 2003, Weinberg wrote a short note to PhD students in physics: “Four Golden Lessons”.
1 min read - Jul 26, 2021 - Material from Hamiltonian Mechanics 2021
During the current incarnation of the course in Hamiltonian Mechanics I have collected some amount of material to share with the students. To avoid losing it in the guts of our teaching CMS, I leave it here for posterity, practically copy-pasting it without edits because I am really tired :D
The books on SpringerLinks linked below are accessible from our students for free via the university proxy but in general (unfortunately) not open access.
5 min read - Mar 26, 2021 - Lecture notes on Analysis on Manifolds
In the previous academic term I had the pleasure to teach Analysis on Manifolds, essentially an introduction to differential geometry for third year students.
In the course I tried to address the topic with the perspective that some of the students would be joining also my master course in Hamiltonian Mechanics later on next year. So many of the topics go in the direction of introducing the prerequisites for studying flows, symplectic geometry and sub-Riemannian geometry.
1 min read - Mar 25, 2021 - Steven Strogatz ask me anything video
This is a follow up from the previous post. I have stumbled upon a wonderful recent video by Steven Strogatz on Twitter which I believe could be extremely helpful for current and prospective PhD students in STEM, and for their advisors!
I think it is worth every minute of it:
Consider also listening to Strogatz’ The Joy of x podcast, it gives a beautiful, humane and informative snapshot into what research and researchers are like.
1 min read - Mar 25, 2021 - On doing a PhD (in STEM)
I was asked a few times in the recent past if doing a PhD is worth the effort. Since then, I have been thinking of writing what I think on my blog but, as usual, I could never find the time for it. Not long ago, Jacopo Bertolotti shared his thoughts on the same matter in a nice twitter thread.
Since that really resonated with what I had to say, I’ll let him speak also for me and add a few more comments at the end.
5 min read - Dec 4, 2020 - Micro Course in Spectral Sub Riemannian Geometry
Recently, I have had the pleasure and honour to give a “micro” course on spectral sub-Riemannian geometry for the Dutch Differential Topology and Geometry seminar. Given the current global circumstances, the course was given via Zoom and the organizers and participants have been kind enough to have it recorded and published online.
You can access the recordings of the first and second lecture on the YouTube Channel of the DDT&G. The slides are also available (beware, they are 99Mb of handwritten pdf!).
1 min read - Oct 13, 2020 - Lecture notes on Hamiltonian mechanics (update)
I have just released a small update to the Hamiltonian Mechanics lecture notes here. This contains some edits to improve the english and fix a few typos. The lecture notes have also been approved to appear in the AMS Open Math Notes, which seems to be a very nice initiative, full of very interesting and high quality content.
1 min read - Oct 11, 2020 - Lecture notes on Hamiltonian mechanics
In the last academic term, I had the great pleasure to teach Hamiltonian Mechanics, an optional master course for mathematics and physics students. Even though the course was based on Arnold’s beautiful book, my plan for the course was to give a panoramic on the modern theory of integrable systems and perturbation theory. Of course, my grand plan, was way to optimistic. And between the time available, a bad flu and then the pandemic landing, we were able to do much less than what I hoped for.
2 min read - Apr 20, 2020 - First steps with Category Theory and OCaml
# Introduction
Category theory is an abstrac mathematical framework that had a huge influence on pure functional programming design patterns. The abstractions and laws that come bundled with the mathematical concepts allow us to write safer and composable interfaces, very prone to equational reasoning, at the price of a steeper learning curve. If you attempt to write some relatively modern Haskell code, you will inevitably have to deal with Monoids, Functions, Monads, Lenses and whatnot typeclassopedia. Also, if you are using modern OCaml libraries, you will find fingerprints of these constructs all over the place, even though there they are less prominent.
34 min read - Jun 4, 2017 - On teaching mathematics - By V. I. Arnold
This is an extended text of the address at the discussion on teaching of mathematics in Palais de Découverte in Paris on 7 March 1997.
Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
The Jacobi identity (which forces the heights of a triangle to cross at one point) is an experimental fact in the same way as that the Earth is round (that is, homeomorphic to a ball). But it can be discovered with less expense.
19 min read - Feb 6, 2015