who am i?
i was born on february 19, 1981 in lahore, pakistan, and moved to the u.s. in 1985 with my family. i currently live in austin, tx, after having spent a year living in seattle, wa and eighteen years in sunnyside new jersey. my parents still live in my hometown, bayonne, nj.

princeton
hello elitism. i'm a class of 2003 graduate with a bachelor's degree in mathematics. most of my time was spent doing number theory:

junior seminar: rational points, heights, and the rank of elliptic curves (with a. wiles and s. miller)
junior paper: factorization in number rings (with w. t. gan)
thesis: kloosterman sums and the number variance of the spectra of hyperbolic modular surfaces (with p. sarnak and s. miller)

[note: i make no claims of accuracy or intelligence in the above preprints.]

outside of school, i occasionally did some theater stuff for theatre-intime and pup. i was also involved with the ufo, serving for a year as chairman.

microsoft
after getting my bachelor's, i took a job as a software design engineer at microsoft. i worked on some theoretical computer science for the advanced strategies and policy division, headed by craig mundie, cto of microsoft. in my spare time, i made some incredible friends and had a great time living and working in seattle. between game night, old timer's, the party bus, and the pink door, it was a fantastic year. as i planned, i left microsoft after a year for grad school.

utexas
i am now a fourth year grad student in math at the university of texas in austin, working with fernando rodriguez villegas. i have spent the last couple of years or so computing L-functions of a few families of twisted elliptic curves with chris hall and investigating the resulting data. my current plans for research include investigating open conjectures concerning L-functions numerically, as well as looking at interesting problems about the arithmetic of elliptic curves over function fields. more generally i'm interested in elliptic curves, arithmetic geometry and computational number theory.

teaching

my photo album

links
quotes from math profs through the years
eating cheap in austin
http://news.bbc.co.uk
http://www.arstechnica.com
http://www.aintitcool.com
http://www.theonion.com

information
address:
university of texas at austin
department of mathematics
1 university station c1200
austin, tx 78712

office: rlm 11.114

office hours: 3 - 4:30pm

phone: 512-475-9529

fax: 512-471-9038

email: <first initial><last name>@math.utexas.edu

cv