From physics to math:Fall 2022 PhD admission

[decadewong]

Hello everyone, I am an international master student in mathematical physics. I have a background in Physics and I want to apply pure math PhD in 2022. The following is my profile:

Major:physics
Undergraduate GPA:3.2/4.0(overall)
Math course taken:Calculus(A-), linear algebra(A-), multivaraible calculus I(B+), math method for physics(A-)(including ODE,multivariable caculus II),topology(B), math method I(A-,solving pde), math method II(B, including most part of complex analysis)

Graduate GPA:~3.53/4.0(German Grade 1.47)
Math course taken: Geometry of manifolds(A), representation theory(A), mathematical quantum theory(A/A-), mathematical relativity(A), mathematical statistical physics(A-/B+)
Math course taking:functional analysis,algebraic topology introduction of commutative algebra and algebraic geometry
Math course planned to take: Introduction to real analysis, introduction to abstract algebra

Research experience: I have worked as an mphil student in physics for 3 years. It is a theoretical physics research project so not many pure math involved. I am now working on my dissertation on C* algebra.
Working experience: 2 year as TA.
Awards: 2 year full time scholarship for master degree(not the degree I am doing).
Letter of recommendation: one from my thesis advisor, two from professors which I get A in his/her courses
GRE: Not taken(may take it in 2021)
GRE math: Not taken(may take it in 2021)

School planned to apply: UC Berkeley, UCSD, UCLA, U of Chicago, Penn state (top choice), Purdue, Texas A&M Ohio state, Iowa, Vanderbilt, Nebraska-Lincoin

I know I am not traditional student, or a strong background student. How is my chance to get into any of the above programs. What can I do in 2021 to increase my chances? Any advice will be appreciated!

[raremeatsandcheeses]

I am an undergraduate student (younger than you), so take what I say with some caution, but: I think a large portion of your applications are going to very competitive schools. You might want to consider a couple more safety schools.

[decadewong]

I am an undergraduate student (younger than you), so take what I say with some caution, but: I think a large portion of your applications are going to very competitive schools. You might want to consider a couple more safety schools.

Thank you for your advice, how do I know which schools are safe? Since what I am doing now is checking the QS ranking from top to the bottom, do school ranked lower than 300 safe?

[raremeatsandcheeses]

I am an undergraduate student (younger than you), so take what I say with some caution, but: I think a large portion of your applications are going to very competitive schools. You might want to consider a couple more safety schools.

Thank you for your advice, how do I know which schools are safe? Since what I am doing now is checking the QS ranking from top to the bottom, do school ranked lower than 300 safe?

The QS ranking is probably a decent metric, but I do not know much about it. Personally, I go through many posts in the '20XX Applicant Profiles and Admissions Results' threads pinned on this forum's front page, and that gives me some perspective on schools vs. stats. I would recommend you do that to.

Compared to a lot of students, you are very strong, so I do not mean your stats are comparable to people who DONT get into many of their reaches/targets. Hope that was clear.