3,541 reputation
31145
bio website math.uwaterloo.ca/~y28xiao
location Waterloo, ON
age 28
visits member for 4 years, 7 months
seen 51 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.


Jun
22
reviewed Approve Two vector fields are cojugate but not take orbits
Jun
16
revised The large sieve for primes
added 201 characters in body
Jun
13
asked Do small prime (bounded) gaps imply larger (but still bounded) gaps?
Jun
13
comment Number of twin primes
Yes, in fact one can deduce such results for at least one even integer between 2 and 240 following the recent advances of James Maynard and the subsequent polymath project.
Jun
13
reviewed Approve M is an R-module which is not finitely generated. is it true that $\inf \{ i| H^i_I(M)\neq 0 \}\le ht_M I?$
Jun
7
comment Distribution of Mordell–Weil ranks of higher genus curves
For the elliptic curve case it is conjectured (a comment by Henri Darmon at this conference: crm.umontreal.ca/Counting14/index.php) that the average rank over a number field should increase with the degree of the number field uniformly over all fields of a fixed degree. Thus, one should expect that higher rank curves become more ubiquitous as the fields get larger.
Jun
6
asked A question on exponential sums
Jun
6
answered About the prime divisors of values of polynomials
Jun
4
revised Geometric interpretation of Schmidt rank
added 9 characters in body
Jun
4
asked Geometric interpretation of Schmidt rank
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
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?