Hello everyone, I would like to apply math PhD fro fall 2022. I don't have a traditional background, therefore I would like someone evaluate my profile. Since there's a lot of uncertainty in 2021, much of the information here have their uncertainty as well. However I will update the information when the things are certain. Also any advice is appreciated.
Undergraduate institution: East asian university in top 20 of qs ranking
Major: Physics
GPA: 3.25/4.0(overall)
Math course: Calculus(A-), engineer maths(A), multivaraible calculus(B+/A-), Linear algebra (A-), topology(B)
Graduate: One of the German Universities Excellence Initiative
Major: Master of Mathematical physics
Grade:1.47(German grading, 1 is the best, 5 is fail)
Math course: Geometry of manifolds(1), representation theory(1), mathematical quantum theory(1.3), mathematical relativity(1), mathematical statistical physics(2), algebraic topology(taking), introduction to commutative algebra and algebraic geometry(taking), functional analysis(taking)
Course plan to take in 2021: Introduction to real analysis, introduction to abstract algebra
Research experience: 1. Working as a master student(research oriented) in my alma mater in theoretical physics for three years. 2. Undergraduate project on physics. 3. Working on master dissertation right now (C* algebra)
LoR: My plan is one letter form my supervisor, two letters from the course I get 1.
GRE: Not taken(may take it in 2021)
GRE math: Not taken(may take it in 2021)
Award: Two year scholarships for full time master student in my alma mater.
type of student: International Asian male
Type of PhD: Mathematics
Research interest: Operator algebra, noncommutative geometry
School I am planning to apply: UC Berkeley, UCLA, UCSD, Ohio State, Penn State, Purdue, Texas A&M, Vanderbilt U, U of Chicago
Am I too weak for these schools? Anything I can do in 2021 to increase my chance? Thank You in advance!