3,259 reputation
31143
bio website math.uwaterloo.ca/~y28xiao
location Waterloo, ON
age 28
visits member for 4 years, 4 months
seen 59 mins 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.


Mar
23
accepted Are there dense sets of positive but not full measure?
Mar
20
comment Isomorphisms between different models of elliptic curves
@joro yes, the motivation behind $f(x)$ is that it is `generic'.
Mar
20
asked Isomorphisms between different models of elliptic curves
Mar
20
comment Are there dense sets of positive but not full measure?
My apologies, I intended to not consider trivial sets which contain intervals
Mar
20
revised Are there dense sets of positive but not full measure?
added 55 characters in body
Mar
20
asked Are there dense sets of positive but not full measure?
Mar
19
reviewed Approve Commutation of tensor products with inverse limits in a specific case
Mar
16
comment A question on polynomial heights
I believe you are right. I think the question is more reasonable if one supposes some sort of structure on the $F_{i,j}$'s. One way to think about it is to consider an integral basis $c_1, ..., c_d$ of the ring of integers in $\mathcal{O}_K$, then take a dual basis $\omega_1, \cdots, \omega_d$. Then one can write $F_j = \sum_{i=1}^d \lambda_i \operatorname{Tr}(F_j \omega_i)$. One can hopefully get a bound in terms of $F_j$ and the basis.
Mar
12
asked A question on polynomial heights
Mar
11
revised Special linear sections of a hypersurface
added 103 characters in body
Mar
10
comment Sparse sets of numbers with the Goldbach property
Erdos showed that there are sets $S$ with density as low as $O(n^{1/2 + \epsilon})$ are actually additive bases; meaning every large positive integer lies in $2S$. For concrete sets, it should be accessible to prove that semi-primes of finite order (say, numbers with at most $k$ prime factors) have the Goldbach property, and they are not much denser than the primes themselves.
Mar
10
asked Polynomial congruences with respect to a large prime (power)
Mar
10
reviewed Approve Vanishing of top local cohomology when $R$ is domain
Mar
5
reviewed Approve Projective Plane of Order 12
Mar
2
revised Density of numbers whose prime factors all come from a fixed congruence class
added 2 characters in body
Mar
2
asked Density of numbers whose prime factors all come from a fixed congruence class
Jan
30
reviewed Approve Examples of Brody hyperbolic affine varieties which are not Kobayashi hyperbolic
Jan
25
asked Coefficients of Hilbert polynomials
Jan
25
reviewed Approve How to topologize X(R) when R is a topological ring?
Jan
20
reviewed Approve Lusternik-Schnirelmann Theorem