bio  website  math.uwaterloo.ca/~y28xiao 

location  Waterloo, ON  
age  28  
visits  member for  4 years, 9 months 
seen  3 hours ago  
stats  profile views  3,183 
PHD Candidate in Pure Mathematics, University of Waterloo. I am being advised by Professor Cameron Stewart, FRSC.
I am interested in analytic number theory, prime number theory, transcendence theory, and powerfree values of polynomials. In particular I work on problems involving applications and generalizations of the determinant methods pioneered by Bombieri/Pila, HeathBrown, and Salberger, including the real analytic determinant method, the approximate determinant method of HeathBrown, and the global determinant method of Salberger (an extension of the $p$adic determinant method of HeathBrown), as well as other potential variants.
2d

comment 
Avoiding the range of a bivariate integer function or Diophantine function
I am not sure what your asking? If the $\mathbb{Z} \setminus \text{range}(f)$ is an infinite set, then surely it is possible to define an (infinite) sequence which avoids the range of $f$. Therefore you must have something else in mind when you want to define such a sequence/function. What is it? Or are you asking whether or not the quadratic polynomial $f(x,y)$ represents all but finitely many integers? 
Aug
24 
revised 
Does the Galois group of a Pisot polynomial contain the alternating group?
minor grammar fixing 
Aug
23 
comment 
Rank of the Jacobian of twists of hyperelliptic curves
@JoeSilverman: I do want an upper bound, perhaps with finitely many exceptions. And yes I do mean the rank of the Jacobian over the rationals. 
Aug
23 
reviewed  Approve Polynomials with roots in convex position 
Aug
23 
revised 
Rank of the Jacobian of twists of hyperelliptic curves
deleted 1 character in body 
Aug
23 
reviewed  Approve Intuition behind the following theorem of Reeb? 
Aug
23 
revised 
Dickson/determinant type polynomial (updated)
added 2 characters in body 
Aug
23 
comment 
Dickson/determinant type polynomial (updated)
I made a small edit to reflect the fact that $a_1 x_1 + \cdots + a_k x_k$ is a linear form, not a monomial. Further, by $\mathbb{Z}_2$ do you mean the $2$adic integers or the field $\mathbb{F}_2$? 
Aug
23 
revised 
Dickson/determinant type polynomial (updated)
added 3 characters in body 
Aug
23 
asked  Rank of the Jacobian of twists of hyperelliptic curves 
Aug
22 
reviewed  Approve Minimum size of the union of sets 
Aug
21 
accepted  Hyperelliptic curves with fixed genus and many rational points 
Aug
21 
comment 
Hyperelliptic curves with fixed genus and many rational points
@MichaelStoll: Yes I think your comments are very satisfying 
Aug
20 
comment 
Hyperelliptic curves with fixed genus and many rational points
@MichaelStoll: Thank you for your post! That was helpful. The example you gave is quite impressive. 
Aug
19 
asked  Hyperelliptic curves with fixed genus and many rational points 
Aug
18 
reviewed  Approve Reference/proof for parabolic Holder spaces property 
Aug
15 
revised 
Prime divisors of values of a polynomial on an infinite set
added 57 characters in body 
Aug
15 
answered  Prime divisors of values of a polynomial on an infinite set 
Aug
7 
reviewed  Approve Possible lower bound in quantum many body system with nonlocal terms 
Aug
3 
reviewed  Approve Cholesky decomposition of a positive semideﬁnite 