1, 5, 14, 28, 47, 71, 100, 134, 173, 217, 266, 320, 379, 443, 512, 586, 665, 749, 838, 932, 1031, 1135, 1244, 1358, 1477, 1601, 1730, 1864, 2003,...*

I was a Project NExT Fellow for 2005-2006. It's been incredible! It consists of attending meetings and exchanging emails with other new (and some more experienced) mathematics professors. I'm learning a tremendous amount about teaching through this program of the MAA, and it has made me more enthusiastic than ever about teaching!


The math website I (used to) visit most often is the AG Algebraic Geometry page at the Front for the Mathematics ArXiv . It lists the most recently released papers (eprints) in algebraic geometry, and can be searched for articles dating back to about 1992. Here is a list of my papers posted on the ArXiv. MathSciNet is also very useful for seeing where papers are published and looking up older works. See more math links here.

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Examples of past teaching web pages

Here are some seminars I have organized or participated in. Expository talk example
Why is O(1) called the twisting sheaf?   dvi version    postscript version     pdf version
(These versions do not include images.)


Graduate Study and Research

My areas of specialization are moduli of stable maps and Gromov-Witten theory, or more generally, algebraic geometry. I also enjoy doing algebra, set theory, point set topology, and complex analysis in my (nonexistent?) free time.


Zhu, Sheldon, Mutaz, and me at the Park City Math Institute in July 2001.
Zhu and Mutaz are Sheldon's other two students who moved with him from OSU to the University Illinois.
As of summer 2005, all of us have now graduated!

My adviser Dr. Sheldon Katz took a position at University of Illinois-Urbana-Champaign starting in August 2001. (Before that he was at 0SU.) I moved there to join him in December 2001. I was jointly enrolled at both universities for 2.5 years, but my degree still came from OSU.

I passed my oral qualifying exam on August 9, 2001. It covered the paper Notes on Stable Maps and Quantum Cohomology by William Fulton and Rahul Pandharipande. In September 2001, Dr. Katz assigned me a thesis problem: Calculate the Chow ring of \bar{M}_g,n(P^r,d), the moduli space of stable curves from n-pointed, genus g curves into projective space with image of degree d. This was pretty broad and ambitious; I chose to concetrate on certain small values for m, g, n, and/or d. The case g=0, n=0, d=2 had recently been solved by Behrend and O'Halloran. I hoped to finish by May 2003, but it took longer than I thought. I ultimately found the Chow ring for the case g=0, n=2, d=2, r=1 and graduated in July 2004. This was the first known presentation for a Chow ring of stable maps of degree greater than one with more than one marked point. As of this writing, Mustata and Mustata have just announced their discovery of the presentation for the general g=0 case (with n, d, and r arbitrary)! This vastly generalizes my result.

Courses I took at OSU:

Advanced Linear Algebra
Modern Algebra I & II
Advanced Calculus II
Complex Analysis I
Complex Analysis II See a chronological description of what a doctoral course is like! This was a fun class.
Teaching Seminar
Several Complex Variables (Independent Study)
Real Analysis I & II
Geometric Topology
Algebraic Topology
Fourier Analysis
3-Manifold Topology
Algebra I & II
Functional Analysis I & II
Super Mathematics
Algebraic Geometry (reading course using Harris)
Algebraic Curves and Riemann Surfaces
Algebraic Geometry I (using Hartshorne)
Complex Geometry (reading course using Griffiths & Harris)
Analysis Learning Seminar
Algebraic Geometry II (using Hartshorne)
Commutative Algebra
Research and Thesis (Many hours!)
Analytic Number Theory
* This is the sequence of Betti numbers of the moduli space of degree 2 stable maps from 2-pointed rational curves to infinite-dimensional projective space. (from my dissertation)

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