The Grothendieck Existence Theorem for Good Moduli Spaces; Joint with David Zureick-Brown; in preparation.
Synergistic Activities
; (Fall 2009-present) founder and moderator.
MathOverflow is a website for mathematicians to ask and answer research-level questions. It has about 1500 active users who post about 40 new questions every day.
MathOverflow has been responsible for many fruitful collaborations, and has helped mathematicians overcome technical obstructions in their research. For many professional mathematicians, it has become an extension of how they do mathematics. At the same time, the site is extremely useful for developing mathematicians since it has become a repository for "professional secrets," insights revealed by experts which are for one reason or another difficult to communicate in other media. It is not unusual for an answer to a question to come from the founder of the field!
Notably, much of MathOverflow's traffic comes from small institutions where individual researchers are are alone in their field. Such mathematicians have told me that MathOverflow has made them happier and more productive. The site has also served an important social role for developing mathematicians since it allows them to freely interact with other mathematicians at all stages in their careers. In this way, the site has filled an important niche, allowing mathematicians to effectively network by doing mathematics together rather than "networking."
Though MathOverflow is a professional forum not targeted at the general public, several general-interest articles have been written about it (for example, a featured article of the Simons Foundation, another in the Atlantic, the San Jose Mercury, as well as posts on several mathematical blogs). In addition to administering, moderating, and participating in MathOverflow, I have done interviews for these articles because I believe it is important to promote mathematics as a whole. In the same spirit, I gave a brief presentation about the site at the 2011 Open Science Summit (slides).
Berkeley Student Representation Theory Seminar; (Fall 2006 -- Spring 2007) organizer.
Seminar Presentations
When is a variety a quotient of a smooth variety by a finite group?
BIRS workshop. Algebraic Stacks: Progress and Prospects. (03-26-2012) (video)
Emory Algebraic Geometry Seminar. (03-20-2012)
UCSD Algebraic Geometry Seminar. (10-26-2011)
Claremont Algebra, Number Theory and Combinatorics Seminar. (10-25-2011)
WAGS (poster session; my poster). (10-01-2011)
University of Michigan Postdoc Algebraic Geometry Seminar. (09-12-2011)
Rice University Algebraic Geometry Seminar. (08-30-2011)
Toric Stacks
USC Algebra Seminar. (02-07-2011)
UW Madison Algebraic Geometry Seminar. (01-21-2011)
Stanford Algebraic Geometry Seminar. (10-29-2010)
Geometry, Representation theory, And Some Physics (GRASP) Seminar, UC Berkeley. (Fall 2010)
Moduli of Representations of Unipotent Groups
UW Madison Number Theory Seminar. (01-20-2011)
Lie Groups, Lie Algebras and their Representations Workshop. (Fall 2010)
Geometry, Representation theory, And Some Physics (GRASP) Seminar, UC Berkeley. (Spring 2010)
Introduction to Toric Varieties I & II
Student Algebraic and Arithmetic Geometry Seminar. (Spring 2008)
EGA IV §11 and the Valuative Criterion for Flatness
Clay sponsored EGA seminar. (Summer 2008)
EGA I §§3--4 Products and Immersions of Schemes
UC Berkeley EGA seminar. (Summer 2008)
The Salamader Lemma
Many Cheerful Facts (UC Berkeley graduate student colloquium). (Fall 2007)
Introduction to D-modules
D-modules seminar at UC Berkeley. (Summer 2007)
An overview of $U_q(\mathfrak{g})$ I & II
Berkeley student representation theory seminar. (Fall 2006)
Category Theory
Many Cheerful Facts (UC Berkeley graduate student colloquium). (Spring 2006)
Bruhat-Tits spaces and the exponential map
Many Cheerful Facts (UC Berkeley graduate student colloquium). (Fall 2005)
Buckyballs, glass, and origami
Many Cheerful Facts (UC Berkeley graduate student colloquium). (Fall 2005)
Teaching Experience
California Institute of Technology, California USA. Instructor. Organized courses, gave lectures, held office hours, wrote and graded exams.
(expected) Geometry and Topology (Caltech, Math 109c), Spring 2012
University of California, Berkeley, California USA. Graduate Student Instructor. Organized course (syllabus and text), gave lectures (8 hours per week), wrote and graded midterms and final, held office hours.
University of California, Berkeley, California USA. Graduate Student Instructor. Led discussion sections (3 hours per week per section, 2 sections). Wrote weekly quizzes, graded quizzes and exams, and held office hours.
Calculus II (UC Berkeley, Math 1B), Fall 2004
Multivariable Calculus (UC Berkeley, Math 53), Spring 2004
; (Fall 2009-present) founder and moderator.