PhD pure math programs for a non-competitive student

I’m an international student who is majoring in mathematics at a top 15 liberal arts college in the U.S. I have GPA about 3.0~3.2 in mathematics, more than 90 percentile in GRE math, above average LOR, and no publication. Since my school is liberal arts college, I didn’t take any grad-level course, but I took all the upper-division courses offered here. I’m interested in algebraic/differential geometry, higher category theory and string theory. I know many middle-ranked schools which have faculties strong at these areas, but with my stats I can only go to bottom-ranked schools, and among them I know no school which have such faculties. So, I’m looking for lower ranked schools which have relatively high acceptance rate and is located at East or West coast (hopefully California, which is my favorite state). Could you tell me which schools I should consider?

Well you can look at schools like UMass, Virginia Tech, UC Riverside, FSU, NYU Brooklyn, UC Santa Cruz, Delaware, Temple, Miami, etc. I don’t know how many of them have people in your interests (or what their acceptance rates are). Or you could look for a Master’s program to get a near 4.0 GPA and apply for Ph.D. since your stats look pretty good aside from the GPA. Unfortunately, most schools don’t have dedicated Master’s programs in math, it’s just something you can pick up along the way to a Ph.D. But if you can find something, get a publication or two (or at least some research experience), maybe a more recent LOR saying you’re a good grad student in spite of low undergrad GPA.

International students are typically held to a higher standard, but I’m not sure if that’s also the case if they did their undergrad in the US, or just if they studied in their home country.

Thanks for your answer. I’m not really confident that I have chance for these well-known schools you mentioned, but I will definitely apply to them. Especially, UC Riverside and Santa Cruz have faculties whom I’m strongly interested in. I know that Purdue and UIUC have masters programs in pure math, so I will apply to them in the case that I won’t be accepted by any PhD program.