3,376 reputation
31145
bio website math.uwaterloo.ca/~y28xiao
location Waterloo, ON
age 28
visits member for 4 years, 6 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.


May
24
awarded  Popular Question
May
23
awarded  Proofreader
May
23
reviewed Edit Is the product of two supermodular functions supermodular?
May
23
revised Is the product of two supermodular functions supermodular?
Improved formatting
May
22
comment A not-so-weak Goldbach's conjecture
I think your 'definition' of 'natural' is too restrictive. The squares (which are the thickest of perfect powers) are too thin to apply the known arguments ins analytic number theory. It is possible that Helfgott's improvements can be applied to prove a 'weak Goldbach' for a set whose density is $O(x^\delta)$ with $\delta$ very close to one, but I doubt any such set would fit your definition of 'natural'.
May
22
comment A not-so-weak Goldbach's conjecture
I am not sure if the question is well posed. It should be fairly easy to adapt Helfgott's arguments to apply to a subset of the primes say, defined by congruence conditions. Also, it is known that the number of exceptions to Goldbach's conjecture, up to $x$, is $O(x^\delta)$ for some positive $\delta < 1$, so it certainly is possible to adjoin a set of density $O(x^\delta)$ to remove the exceptions.
May
22
revised A not-so-weak Goldbach's conjecture
added 44 characters in body
May
20
comment Numbers represented by inhomogeneous forms
I am not sure what kind of answer you are looking for. In general one cannot expect a simple description for the set of numbers represented by a specific function. Are you looking for things like whether a given polynomial represents all numbers?
May
15
answered Long gaps between primes
May
7
revised Distribution of smooth values of polynomials
added 10 characters in body
May
7
asked Distribution of smooth values of polynomials
May
4
asked Concentration of large prime factors of polynomials
May
1
reviewed Approve Is there an introduction to probability theory from a structuralist/categorical perspective?
Apr
27
asked Factoring a polynomial in a specific manner
Apr
26
asked Density of polynomials which are soluble with respect to a set of primes
Apr
25
comment Density of polynomials with a prescribed number field extension
I modified the question to be more precise and non-trivial.
Apr
25
revised Density of polynomials with a prescribed number field extension
added 111 characters in body
Apr
25
asked Density of polynomials with a prescribed number field extension
Apr
23
reviewed Reject Singular projective variety where the Cartan homomorphism is not an isomorphism?
Apr
22
asked When is it appropriate to name something a 'fundamental lemma'?