bio | website | math.uwaterloo.ca/~y28xiao |
---|---|---|
location | Waterloo, ON | |
age | 28 | |
visits | member for | 4 years, 7 months |
seen | 51 mins ago | |
stats | profile views | 3,071 |
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 Mordellâ€“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? |