- Which university offers strong PhD program related to probability theory? What I know is that most of the top 10 schools offer great programs, but I am also wondering what other universities have good program in probability other than the top 10s for reaches and safer choices.

- Which university offers a great degree of freedom regarding the fields I can study? I also wish choosing the advisor is flexible. As most applicants, I'm not firmly decided on my research field and I have a huge interest in nonstandard analysis and differential geometry as well(though I got a very bad grade in the subject due to some reasons...) As far as I can see,
*Cornell*offers diverse opportunities by offering three faculty members to one student, and they can be changed as I progress and my subject of interest is changed. I want to know more universities with such flexibility.

- Which university do you think is a reach and a safe bet for my profile listed below? I am mainly thinking of applying for probability at the moment. Or do you think I should opt for statistics as well?

- Should I pre-contact some of the potential advisors? There are some researching areas I am interested but I doubt I am qualified to make a good comment about it.

**Undergrad Institution**: Top 3 in my country.

**Majors**: Mathematics, Economics.

**GPA**: 3.76/4.0

**Type of Student**: International (Asian)

**Awards/Honors**: Graduated with High Honors. Bunch of honors and scholarships (within the university).

**Math/Statistics Grades**: Mostly got As. Took some statistics classes as well(mathematical statistics, Bayesian statistics). Also took stochastic process but received B+. Not bad in analysis but very strong in algebra including mathematical logic and algebraic combinatorics.

**GRE General Test**: 166V, 169Q, 4.5W.

**GRE Subject Math Test**: Waiting for the result. Expecting higher than 90% minimum.

**Programs Applying**: Probability.

**Research Experience:**None...

**Working Experience**: Quantitative researcher in a fintech startup company (1 year). My researching area was asset allocation with weight constraints, and I actually implemented the program using quadratic programming in Python. Working experience in Python and ML. Developed several low frequency trading algorithms. I have done so much since it was a small startup, working with a statistician in finance(Master) and a mathematician(PhD, probability and PDE).

**Hobbies**: Analyzing old classics games, finding the optimal strategy using probability theory and sometimes Python. Fun stuff. This is what got me the job.

**Letters of Recommendation**: I doubt they will be particularly strong but I doubt they will be detrimentally bad either. 1 from my set theory and mathematical logics professor, 1 from my linear algebra and abstract algebra professor, and 1 from my probability professor.

Thank you in advance sincerely for your advice.