Jerry's webpage

Xiaoheng Jerry Wang

Princeton Math Department
Fine Hall, Washington Road
Princeton, NJ 08544
xw5@math.princeton.edu


I recently graduated from Harvard university under the supervision of Professor Benedict Gross. I am now a Postdoctoral Reseach Fellow and an Instructor at Princeton University.

I am interested in number theory, algebraic geometry and diophantine approximation. My primary research interest is the arithmetic aspects of hyperelliptic curves.

Here is my CV, research statement and teaching statement.

Papers

Odd degree binary forms taking square values.
With Manjul Bhargava. In preparation.

Squarefree values of polynomial discriminants.
With Manjul Bhargava and Arul Shankar. In preparation.

Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces.
With Manjul Bhargava and Arul Shankar. Preprint.

Geometry-of-numbers methods over global fields II: Coregular representations.
With Manjul Bhargava and Arul Shankar. In preparation.

A positive proportion of locally soluble hyperelliptic curves over Q have no rational points over any odd degree extension.
arXiv:1310.7692. With Manjul Bhargava and Benedict Gross. [pdf] (Appendix by Tim and Vladimir Dokchitser.) To appear in J. Amer. Math. Soc.

Arithmetic invariant theory II: Pure inner forms and obstructions to the existence of orbits.
arXiv:1310.7689. With Manjul Bhargava and Benedict Gross. [pdf] To appear in Progress in Mathematics, Representations of Lie Groups: In Honor of David A Vogan, Jr. on his 60th Birthday.

Rational points on hyperelliptic curves having a marked rationl non-Weierstrass point.
arXiv:1307.3531. With Arul Shankar. [pdf]

Maximal linear spaces contained in the the base loci of pencils of quadrics.
arXiv:1302.2385. [pdf]

Pencils of quadrics and Jacobians of hyperelliptic curves.
Version 1.5 of my thesis. [pdf]

Extensions of Atanassov's methods for Halton sequences.
Monte Carlo and Quasi-Monte Carlo Methods 2010, Springer, 2012, pp.345-362. With Henri Faure and Christiane Lemieux. [pdf]

MAT345 Algebra I teaching stuff

Lecture notes. [pdf]

Homework 1. [pdf][sol]

Homework 2. [pdf][sol]

Homework 3. [pdf][sol]

Homework 4. [pdf][sol]