University of Washington, Fall 2021, Winter 2022, Spring 2022

Math 581, 582, 583 -- Non-archimedean geometry

Instructor:

Lecture time and address:

Lecture notes:

I will scan and share my handwritten notes.

All students will participate in scribing notes on GitHub.

Description:

The main goal is to introduce Berkovich's theory of analytic spaces. This generalizes the notion of complex manifolds, where complex numbers is replaced by a general valued field, including p-adic numbers or formal Laurent series.

The general theory has applications in various fields, including tropical geometry, arithmetic/Arakelov geometry, combinatorics, complex geometry, dynamics, local Langlands program, etc. If time permits, some of these applications will be discussed (especially the first three in this list, which are close to the instructor's research). Students can also study some of these applications as a course project (during winter quarter). In any case, we hope to cover enough of the basic concepts and constructions so that participants can start studying advanced research papers on the subject.

During the Fall quarter, some general theory of valued fields and the basics of Berkovich's theory will be covered.

References:

There is no official textbook. We use various sources, including some research papers.

Disability Resources and Accommodations:

Reasonable accommodations will be provided to students who have a documented disability that may affect their ability to participate in course activities or to meet course requirements. Students with disabilities are encouraged to contact the office of Disability Resources for Students (DRS).

Religious Accommodations::

Washington state law requires that UW develop a policy for accommodation of student absences or significant hardship due to reasons of faith or conscience, or for organized religious activities. The UW's policy, including more information about how to request an accommodation, is available at Religious Accommodations Policy. Accommodations must be requested within the first two weeks of this course using the Religious Accommodations Request form.

Academic Integrity:

Each student in this course is expected to abide by the University of Washington's code of academic integrity. Any work submitted by a student in this course for academic credit will be the student's own work. More information about this code is available here.

Intellectual Property and Copyright:

All course materials are intellectual property belonging to the author. Students are not permitted to share any course materials without the expressed permission of the instructor.