bio | website | math.uwaterloo.ca/~y28xiao |
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location | Waterloo, ON | |
age | 28 | |
visits | member for | 4 years, 4 months |
seen | 59 mins ago | |
stats | profile views | 2,884 |
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 |