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I am currently learning modern algebraic geometry (scheme theory) from Ravi Vakil's algebraic geometry in the time of COVID: https://math216.wordpress.com/agitt

by bollu 6y ago

I am currently learning modern algebraic geometry (scheme theory) from Ravi Vakil's algebraic geometry in the time of COVID: https://math216.wordpress.com/agittoc-2020/ https://math216.wordpress.com/agittoc-2020/. It's a great ongoing course that offers amazing intuition into scheme theory. We're divided into "working group(oid)s" where we discuss the mathematics and solve the weekly homework assigned by Ravi. Best of all, anyone [all over the world] can join in on the fun! You get added to a discord and a zulip group, where all the discussion happens. My favourite article about Grothendieck is the one titled "The Grothendieck-Serre Correspondence": https://webusers.imj-prg.fr/~leila.schneps/corr.pdf https://webusers.imj-prg.fr/~leila.schneps/corr.pdf This article describes both the mathematics, and the lives of Grothendieck and Serre through their exchange of letters. It's powerfully written, and provides great insight into both the mathematics and the two as people. The last line of the article is absolutely beautiful.

markhollis 6y ago
I'm also learning some algebraic geometry at the moment: Some resources I have used are: * video lectures by Richard Borcherds * Lecture notes by Andreas Gathmann (https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/alggeom-2002.pdf https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-200...) * This blog: https://rigtriv.wordpress.com/ag-from-the-beginning/ https://rigtriv.wordpress.com/ag-from-the-beginning/ * An infinite large napkin, by Evan Chen (https://venhance.github.io/napkin/Napkin.pdf https://venhance.github.io/napkin/Napkin.pdf) It also found it helpful to learn some (algebraic) number theory, to get a sense of where some of the motivation comes from (e.g. elliptic curves, modular forms). Grothendieck's work is abstract, but he was always motivated by concrete problems (e.g. Weil conjectures).
yeellow 6y ago
Thanks for sharing, it looks really interesting, too bad I did not know about it earlier (but I will still try to watch the lectures). Are there more initiatives like that one? I know Terry Tao had open lectures online, so it is probably popular nowadays.

by bollu 6y ago

markhollis 6y ago

I'm also learning some algebraic geometry at the moment: Some resources I have used are: * video lectures by Richard Borcherds * Lecture notes by Andreas Gathmann (https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/alggeom-2002.pdf https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-200...) * This blog: https://rigtriv.wordpress.com/ag-from-the-beginning/ https://rigtriv.wordpress.com/ag-from-the-beginning/ * An infinite large napkin, by Evan Chen (https://venhance.github.io/napkin/Napkin.pdf https://venhance.github.io/napkin/Napkin.pdf) It also found it helpful to learn some (algebraic) number theory, to get a sense of where some of the motivation comes from (e.g. elliptic curves, modular forms). Grothendieck's work is abstract, but he was always motivated by concrete problems (e.g. Weil conjectures).

yeellow 6y ago

Thanks for sharing, it looks really interesting, too bad I did not know about it earlier (but I will still try to watch the lectures). Are there more initiatives like that one? I know Terry Tao had open lectures online, so it is probably popular nowadays.