3,918 reputation
31247
bio website math.uwaterloo.ca/~y28xiao
location Waterloo, ON
age 28
visits member for 4 years, 9 months
seen 3 hours ago

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 power-free values of polynomials. In particular I work on problems involving applications and generalizations of the determinant methods pioneered by Bombieri/Pila, Heath-Brown, and Salberger, including the real analytic determinant method, the approximate determinant method of Heath-Brown, and the global determinant method of Salberger (an extension of the $p$-adic determinant method of Heath-Brown), 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 non-local terms
Aug
3
reviewed Approve Cholesky decomposition of a positive semi-definite