Warning: This page is not yet stable! All contents subject to change without warning until the start of the course, although things should settle down by mid-summer.
Course description: The topic for this course is condensed mathematics. This term refers to a collection of techniques starting with an analogue of ordinary set theory in which the role of finite sets is instead played by compact Hausdorff topological spaces (notably including profinite sets). This can then be used to build up a form of commutative algebra for topological rings that smoothly adapts concepts from ordinary commutative algebra, where a more naive approach would run into the basic incompatibility between topology and certain algebraic operations. This proves to be particularly useful in analytic geometry in both its archimedean and nonarchimedean forms.
This course will be offered in a "pandemic-style" hybrid format. Lectures will be given in-person and streamed over Zoom. Course communication (including Zoom links) will take place in a Zulip discussion forum. Office hours will be offered in both in-person and remote formats.
Handwritten slides, lecture recordings, and detailed lecture notes will be made available publicly via this website. In addition, I will make the livestream and Zulip available for unofficial remote participation; please fill out the Google Form (link to be added later) to get access to there.
Environment: I aim to create a conducive learning environment for all students, particularly those who do not see themselves reflected in the mathematical profession at present or have experienced systemic bias affecting their mathematical education. I insist that all participants do their part to maintain this environment. I also pledge all reasonable effort to address accessibility issues that come to my attention.
Instructor: Kiran Kedlaya, kedlaya [at] ucsd [etcetera].
Lectures: MWF 9-10:20am in B402A, plus a Zoom livestream. Note the disagreement with the officially posted lecture times; in practice we will meet roughly twice per week, but the schedule of lectures will be a bit irregular (see below). Slides and recordings will be posted to this website.
Office hours: Each lecture will be followed by 30 minutes of hybrid office hours. Additional office hours will be announced over Zulip (timings of these will vary).
Homework: A short writeup (expected length 2-3 pages) of a topic not to be covered in lecture.
Final exam: None. Disregard any information from the UCSD Registrar to the contrary.
Grading: 100% homework.
Textbook: None; I will post lecture notes in HTML and PDF formats (generated using PreTeXt.
Prerequisites: None; however, familiarity with algebra at the level of Math 200A-C, and global and local fields at the level of Math 204A, is strongly recommended. At times, familiarity with algebraic geometry at the level of Math 203A-C may also be helpful.
Topics by date (with videos, references, and boards): Note: the course meets only on the indicated dates.