18.787: Topics in Number Theory (MIT, Fall 2007)

This was the web page for the course 18.787 (Topics in Number Theory), taught at MIT in the fall 2007 semester. The topic was p-adic differential equations, including their relationship to complex differential equations, a broad development of intrinsic properties (following Dwork, Robba, Christol, Mebkhout, et al.), and some applications in arithmetic geometry.

The chief product of the course was a stack of lecture notes, which I later redacted into a book manuscript to be published by Cambridge University Press. See here for more details.

For historical purposes, you will also find here, in unmodified form:

• the lecture calendar, including links to the original course notes;
• the course syllabus and course poster.
• the compiled notes which I assembled at the end of the semester. Although these include significant edits to the original notes, they still needed more work; see above for the current version.