Contact Information

Name: Anton Geraschenko
Web: http://stacky.net
Email: geraschenko@gmail.com
Phone: 617 275 1573 (cell), 626 395 4328 (office)
Office: 374 Sloan Hall
Work: Mathematics 253-37, Caltech, Pasadena, CA 91125 (map)
Home: 1115 Cordova St. #110, Pasadena, CA 91106 (map)

Research Interests

Algebraic geometry, algebraic stacks, moduli, algebraic groups, representation theory.

Appointments

Harry Bateman Research Instructor, Caltech, September 2011-present.

Education

University of California, Berkeley, California USA

Ph.D.May 2011, Dissertation Topic: "Toric Stacks", Adviser: Vera Serganova

Brandeis University, Waltham, Massachusetts USA

B.A. May 2004, Summa Cum Laude Physics and Mathematics with Highest Honors

Honors and Awards

National Science Foundation Graduate Research Fellowship, 2005-2008
Arnold Shapiro Prize in Mathematics, 2004

Publications

MathOverflow; Joint with Scott Morrison and Ravi Vakil. Opinion piece for Notices of the AMS, June/July 2010. http://www.ams.org/notices/201006/rtx100600701p.pdf
Toric Stacks I: The Theory of Stacky Fans; Joint with Matthew Satriano. http://arxiv.org/abs/1107.1906
Toric Stacks II: Intrinsic Characterization of Toric Stacks; Joint with Matthew Satriano. http://arxiv.org/abs/1107.1907
Torus Quotients as Quotients by Finite Groups; Joint with Matthew Satriano; in preparation.
The Grothendieck Existence Theorem for Good Moduli Spaces; Joint with David Zureick-Brown; in preparation.

Synergistic Activities

MathOverflow; (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 many 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. Many 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 will give a brief presentation about the site at the 2011 Open Science Summit.

Caltech Algebraic Geometry Seminar; (Fall 2011) co-organizer.
Toric Geometry Student Seminar; (Fall 2011) faculty sponsor/organizer.
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?

UCSD Algebraic Geometry Seminar. (10-26-2011)
Claremont Algebra, Number Theory and Combinatorics Seminar. (10-25-2011)
WAGS (poster session). (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 II

Student Algebraic and Arithmetic Geometry Seminar. (Spring 2008)

Introduction to Toric Varieties I

Student Algebraic and Arithmetic Geometry Seminar. (Spring 2008)

EGA IV \S 11 and the Valuative Criterion for Flatness

Clay sponsored EGA seminar. (Summer 2008)

EGA I \S\S3--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 $U_q(\mathfrak{g})$ II

Berkeley student representation theory seminar. (Fall 2006)

An overview of $U_q(\mathfrak{g})$ I

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.
- Algebraic Spaces and Algebraic Stacks (Caltech, Math 193a), Fall 2011
- (expected) Algebraic Geometry (Caltech, Math 163b), Winter 2011
- (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.
- Introduction to Number Theory (UC Berkeley, Math 115), Summer 2010

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
- Multivariable Calculus (UC Berkeley, Math 53), Fall 2008
- Linear Algebra and Differential Equations (UC Berkeley, Math 54), Fall 2010

Software Skills

Proficient in Sage, Python, and Bash.

References

Vera Serganova	Department of Mathematics	University of California Berkeley	Berkeley, CA 794720-3840	serganov@math.berkeley.edu
Martin Olsson	Department of Mathematics	University of California Berkeley	Berkeley, CA 94720-3840	molsson@math.berkeley.edu
Ravi Vakil	Department of Mathematics	Stanford University	Stanford, CA 94305	vakil@math.stanford.edu
Tom Graber	Department of Mathematics 253-37	California Institute of Technology	Pasadena, CA 91125	graber@caltech.edu