Hello everyone. I'm a master's student, and I'll be applying to PhD programs this cycle. I'd really like to know if it seems like I have a chance to get into a top 10 school for graph theory. Any feedback or tips for how to improve my application would be appreciated. Thanks!

Graduate Institution: Decent Canadian school with some well-known graph theorists

Major(s): Graph theory

GPA: All A's and A+'s

Type of Student: White American male

GRE Revised General Test:

Q: 169 (96%)

V: 170 (99%)

W: 6.0 (99%)

GRE Subject Test in Mathematics:

M: 860 (88%)

Program Applying: Pure math - graph theory

Research Experience: I've written some papers. I have one single-author paper published in Discrete Mathematics. I have a lot of preprints with others that are just about done and that can probably go in journals at least as good. Specifically, I have two preprints with my advisor, two preprints with a postdoc at my school, one preprint with another grad student I met at a conference that I contributed to significantly, and one preprint with a professor I met at a conference where they just added a small idea of mine in the middle of their paper. I've also given some talks. I've given two talks at the discrete math seminar at my school, and I've given two talks at national-level discrete math conferences.

Awards/Honors/Recognitions: A paper that I wrote was selected as one of about eight student papers to be presented at a conference. I didn't end up winning a prize with this paper, but I was a finalist in the competition.

Pertinent Activities or Jobs: I've worked as a TA for the past year, and I always get good reviews from students.

Any Miscellaneous Points that Might Help: One of my letter writers is famous, and I may also be able to get him as an author on one of my preprints. He seems to like me, and I think he'll write me a good letter.

Any Other Info That Shows Up On Your App and Might Matter: I taught math in a high school in China for two years. I speak several languages, including Spanish, Korean, Mandarin, and Cantonese.