Hi everyone. Posting this because I'm not completely sure where to apply & would want some suggestions. I want to do work in grad school related to probability, geometry, and topology but am not completely sure what programs are good. I've put a profile and partial school list below. Any feedback or suggestions would be much appreciated!!

Undergrad Institution: Small Technical School (Top 50 USA, Top 100 USA for mathematics)

Major(s): Mathematics, minor in political science (was political science for fresh/soph year)

Minor(s): none

GPA: 3.9

Type of Student: White Male Domestic Applicant

GRE Revised General Test: No score yet

Q: xxx (xx%)

V: xxx (xx%)

W: x.x (xx%)

GRE Subject Test in Mathematics: No score yet

M: xxx (xx%)

TOEFL Score: N/A

Program Applying: Pure/Applied not completely sure –– want to focus on probability and computational geometry & topology,

Research Experience: Small research project for real analysis, Small seminars on research topics at school, a couple of research projects for classes this semester, internship this summer was focused on algorithm research for biostatistics, but was at a small company, spent a summer doing research bootcamp with Wolfram but nothing came out of it. No publications or presentations (yet, might be doing a small one for a research seminar next semester)

Awards/Honors/Recognitions: General Honors Societies (school level), Who's Who (national, but I think they pretty much give it to everyone)

Pertinent Activities or Jobs: Software Engineering at a Bioinformatics Company, grader for Real Analysis (Undergrad level)

Any Miscellaneous Points that Might Help: Started out as a political

Any Other Info That Shows Up On Your App and Might Matter:

• Started out as political science / humanities major and took pretty much exclusively soft classes up until end of sophomore year (not sure if that will help or hurt the application, but it definitely did help my writing ability!)

• Grad level courses in math (have As in all of them so far )

• Completed: Matrix Analysis, Differential Geometry,

• Currently Taking: Measure Theory, Probability, Research seminar on matrix computations

• Next Semester: Functional Analysis, Complex Analysis, maybe one more

Applying to Where:

Harvard University - Applied Mathematics PhD (Flexible program, have a planned proposed course of study)

Duke University - Mathematics PhD (good for computational topology)

Ohio State University - Mathematics PhD (topology, geometry, data analysis)

Berlin Mathematical School - Mathematics PhD

• Area 3: Probability

• Area 5: Geometry/Topology/Visualization

• Area 6: Numerical Analysis and scientific computing

Central European University (Budapest) - Mathematics PhD (hosted at Alfred Renyi Inst.)

Stanford University - ICME Masters Program (part-time, will only do this if also get a job in the area)

I am also considering taking a year off or two to work before applying. Any feedback from people who have done that and either found it helpful or completely regretted it would be super awesome!

Thanks again everyone!!!