Our semester at Columbia started earlier than usual this year, with first classes this week, my first class yesterday. This semester I’m teaching the second half of a year-long course on the mathematics of quantum mechanics. There’s a Youtube channel with the lectures for the first half of the course, and now also for the second half. The course is largely following the textbook I wrote based on teaching this is earlier years. The first lecture yesterday was a summary of a point of view on canonical quantization explained in the first semester and in the book. This point of view is essentially that Hamiltonian mechanics is based on a Lie algebra (functions on phase space with Poisson bracket the Lie bracket), and canonical quantization is all about the essentially unique unitary representation of (a subalgebra of) that Lie algebra. On Thursday I’ll start on the fermionic version of canonical quantization, which has a very much parallel structure, giving a super-Lie algebra and spinors.
A few other items:
- John Baez’s This Week’s Finds in Mathematical Physics was an unprecedented project conducted over 17 years, providing a wealth of fantastic expository material on topics in math and physics. It started in 1993, and on its twentieth anniversary I wrote an appreciation (in an appropriate font) here. John has now announced that this material has been typeset (2610 pages!) and he is editing it, to be released in batches. The first part is now available, on the arXiv as This Week’s Finds in Mathematical Physics (1-50). As I find time, I’m looking forward to reading through these, encourage everyone interested in math and physics to do the same.
- Frank Wilczek has a new book out, and there’s an interview with him at Quanta. You can see a conversation between him and Brian Greene here on Friday.
- Another physicist with a new book is Jesper Grimstrup, whose Shell Beach: The search for the final theory I’ve just finished reading and enjoyed greatly. The book is quite personal and non-technical, with topic Grimstrup’s life as a theorist pursuing a unified theory. His career story is quite interesting, giving insight into the ways academic theoretical physics is challenging for young theorists trying to pursue non-mainstream research programs. Several books have appeared in recent years aimed at putting this kind of physics research in a human and philosophical context, telling you what it has to do with the meaning of life. There’s some of that in this book too, of a much more compelling sort than what you see elsewhere. Grimstrup has a website here, and in recent years has ended up leaving academia and trying to fund his research with donations. I can think of a lot worse things you could do with your money than send him some.
I’m quite sympathetic to the underlying theme that he describes pursuing (together with Johannes Aastrup) in the book, that of bringing together the insights of loop quantum gravity and non-commutative geometry. More recently they’ve been working on some new ideas for formulating QFT non-perturbatively that seem worth investigating. There’s a survey blog post here.
Update: Another bit of private math/physics funding news. The IAS has announced establishment of the Carl P. Feinberg Cross-Disciplinary Program in Innovation
Scientific research at the Institute is traditionally driven by the collaboration and independent projects of a full-time Faculty and a revolving class of more than 200 researchers at various stages in their careers. The Carl P. Feinberg Cross-Disciplinary Program in Innovation will build on this successful model with the recruitment of mid-career scholars who have pioneered foundational developments in new areas. Bringing together scholars with such unique insights—which may not be obviously connected to the existing themes of the past 20 or 30 or 40 years—ensures that IAS will remain agile and responsive to new intellectual developments that do not yet fit the mold of what graduate students and postdocs generally know. In order to close this knowledge gap, the program will feature intense, focused workshops and “master classes.”
“Since its founding, the Institute has served as a world center for investigations into the fundamental laws of nature. We are currently in the middle of a grand symbiosis of ideas, from the equations of general relativity to the quantum information of black holes,” stated Robbert Dijkgraaf, IAS Director and Leon Levy Professor. “This revolutionary program will provide a dedicated space and the necessary flexibility to accelerate these exciting developments, and will surely forge new connections across fields.”
And another interview with Wilczek, doubtless another of many, with Brian Keating, here, https://www.youtube.com/watch?v=prJjVUuDhvg
Congrats to John Baez! Might there be any way to get a “top ten finds” for each year, or even just overall? Thank you!
Peter thank you for highlighting Jesper’s book. I remember the first call for assistance and how pleased I was to help. The book is a lovely “dividend”
Thanks to your suggestion, I’m reading “Shell Beach.” Can you suggest a good book on non-commutative geometry? I’m an engineer who knows some differential and Riemannian geometry, would prefer a reference that brings out the intuition but is not too much geared towards specific problems in physics.
Alain Connes has written various inspirational survey articles and given lectures that give a good introduction to the subject. Many are at his website alainconnes.org
Have a look at
especially the section on survey papers.
Among his talks, there was a very recent survey one at a Harvard seminar, see
the first one listed under
but you might find many of the others valuable.