Various things that may be of interest:<\/p>\n
The technological hurdles for implementing an ICF-based power system are so numerous and formidable that many decades will be required to resolve them\u2014if they can indeed be overcome.<\/p><\/blockquote>\n<\/li>\n
- I’ve been spending some time reading Grothendieck’s R\u00e9coltes et Semailles<\/a>, which is a simultaneously fascinating and frustrating experience. I’ve made it almost to the end of the first part, except that there will be another forty pages or so of notes to go. To get to the first part involved starting by reading through about two hundred pages of four layers of introduction. It seems that basically Grothendieck did no editing. Once he was done writing the first part, as he thought of more to say he’d add notes. He distributed copies to various other mathematicians, and then kept adding new introductions, with various references to how this fit in with more technical mathematical documents he was working on (La \u201cLongue Marche\u201d \u00e0 Travers la Th\u00e9orie de Galois, \u00c0 la poursuite des champs).\n
After the first part, looking ahead there’s the daunting prospect of 1500 pages with the theme of examining his deepest mathematical ideas and what he felt was the “burial” that he and his ideas had been subjected to after his leaving active involvement with the math research community in 1970. Quite a few years ago I did spend some time looking through this part to try and learn more about Grothendieck’s mathematical ideas. I’ll see if I can try again, with the advantage of now knowing somewhat more about the mathematical background.<\/p>\n
Besides the frustrating aspects, what has struck me most about this is that there are many beautifully written sections, capturing Grothendieck’s feeling for the beauty of the deepest ideas in mathematics. One gets to see what it looked like from the inside to a genius as he worked, often together with others, on a project that revolutionized how we think about mathematics. This material is really remarkable, although embedded in far too much that is extraneous and repetitive. The text desperately needs an editor.<\/p>\n
There are various places online one can find parts of the book and other related material, sometimes translated. Two places to look are the Grothendieck Circle<\/a>, and Mateo Carmona’s site<\/a>.<\/li>\n
- For an up-to-date project on reworking foundations of mathematics (with an eye to eliminating analysis…), Dustin Clausen and Peter Scholze are now teaching a course on Condensed Mathematics and Complex Geometry<\/a>, lecture notes here<\/a>.<\/li>\n
- I noticed that the Harvard math department website now has an article on Demystifying Math 55<\/a>. The past couple years this course has been taught by Denis Auroux, and one can find detailed course materials including lecture notes at his website<\/a>.\n
The current version of the course tries to cover pretty much a standard undergraduate pure math curriculum in two semesters, with the first semester linear algebra, group theory and finite group representations, the second real and complex analysis. The course has gone through various incarnations over a long history, and has its own Wikipedia page<\/a>. For various articles written about the course over the years, see here<\/a>, here<\/a> (about a Pavel Etingof version) and here<\/a> (about a Dennis Gaitsgory version).<\/p>\n
I took the course in 1975-76, when the fall semester was taught by mathematical physicist Konrad Osterwalder, who covered some linear algebra and analysis rigorously, following the course textbook Advanced Calculus by Loomis and Sternberg<\/a>. The spring semester was rather different, with John Hubbard sometimes following Hirsch and Smale<\/a>, sometimes giving us research-level papers about dynamical systems to read, and then telling us to read and work through Spivak’s Calculus on Manifolds<\/em> over reading period.<\/p>\n
My experience with the course was somewhat different than that described in the articles above, partly due to the particular instructors and their choices, partly due to the fact that I was more focused on learning as much advanced physics as possible. I don’t remember spending excessive amounts of time on the course, nor do I remember anyone I knew or ran into being especially interested in or impressed by my taking this particular course. What was a new experience was that it was clear the first semester that I was a rather average student in the class, not like in my high school classes. The second semester about half the students had dropped and I guess I was probably distinctly less than average. The current iteration of the course looks quite good for the kind of ambitious math student it is aimed at, and it would be interesting if a new textbook ever gets written.\n<\/li>\n<\/ul>\n
Update<\/strong>: One more related item. This week Chapman University is hosting a conference about Grothendieck<\/a>. Kevin Buzzard has posted his slides here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"
Various things that may be of interest: MSRI in Berkeley has announced a \\$70 million dollar gift from Jim and Marilyn Simons, and Henry and Marsha Laufer. This gift will make up the bulk of a planned endowment increase of … Continue reading