3,284 reputation
31143
bio website math.uwaterloo.ca/~y28xiao
location Waterloo, ON
age 28
visits member for 4 years, 5 months
seen 4 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.


1d
revised Examples of polynomials $x_1(t), x_2(t)$ such that $(x_1(t))^4 + (x_2(t))^4$ has a double root
added 190 characters in body
1d
comment Examples of polynomials $x_1(t), x_2(t)$ such that $(x_1(t))^4 + (x_2(t))^4$ has a double root
How did you come up with this example?
1d
accepted Examples of polynomials $x_1(t), x_2(t)$ such that $(x_1(t))^4 + (x_2(t))^4$ has a double root
1d
comment Examples of polynomials $x_1(t), x_2(t)$ such that $(x_1(t))^4 + (x_2(t))^4$ has a double root
Yes; I forgot to include that in the body of the question. Thank you for pointing that out.
1d
revised Examples of polynomials $x_1(t), x_2(t)$ such that $(x_1(t))^4 + (x_2(t))^4$ has a double root
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1d
asked Examples of polynomials $x_1(t), x_2(t)$ such that $(x_1(t))^4 + (x_2(t))^4$ has a double root
Apr
9
comment What's the minimum amount of knowledge to start doing research?
Perhaps a situation which fits with the OP's question is the bounded gap problem. When Goldston, Pintz, and Yildirim showed in their seminal paper (annals.math.princeton.edu/wp-content/uploads/…) that one can obtain bounded gaps if the level of distribution in the Bombieri-Vinogradov theorem can be slightly increased, it was thought that the problem would be intractable for another generation. Yitang Zhang shattered this expectation; most likely because he is an 'outsider'. The later improvements by Maynard are also along these lines.
Apr
8
reviewed Approve Positivity of logarithmic energy of certain measures
Apr
4
reviewed Approve Decide two indices of Ext functor
Apr
4
asked A question on Pythagorean triples
Apr
2
reviewed Approve Counting number of points in a lattice with bounded sup norm
Mar
28
reviewed Approve Merging / combining categories
Mar
27
reviewed Reject A classic cardinal characteristic of the continuum in disguise?
Mar
27
revised Square-free sieve over number fields
added 118 characters in body
Mar
27
asked Square-free sieve over number fields
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