I'm applying to pure math PhD programs this winter. Below is an overview of my profile as an applicant and a list of schools I'm considering applying to. For personal/family reasons, it is very important to me that I am able to go to grad school in either the Chicago area or the LA area. I am just wondering whether it seems like I have a shot at getting into at least one school in each of those regions. What do you think?
Undergrad Institution: Small Liberals College (top 30 among LACs)
Majors: Mathematics, Philosophy
GPA: 3.87 overall, 3.83 in mathematics
Type of Student: Domestic White Male
GRE General Test:
Will take this fall. I tend to be a good standardized test-taker and I anticipate doing well on this test.
GRE Subject Test in Mathematics
Will take in September. I plan on doing nothing but studying for it until then. I am willing to re-take in October if things don't go so hot.
Program Applying: Pure mathematics PhD. I am interested in studying combinatorics, geometry, and topology.
Research Experience: I am doing research at my home institution this summer in computational geometry/applied algebraic topology. I plan on completing an honor's thesis this year in combinatorics. I have also completed two "capstone" level projects in hypergraph theory and algebraic topology; I plan on completing two more of these, one each in representation theory and functional analysis.
Awards/Honors/Recognitions: Dean's list/honor roll, merit scholarship.
Pertinent Activities or Jobs: Graded and held office hours for Calc II, Calc III, and Abstract Algebra. Supplemental instructor (i.e. I am present in class and hold additional recitation sessions outside of class) for Discrete Math. Math tutor for private company.
Misc.: Studied in Budapest; took hard classes and got A-'s. I am very close with my letter writers; students who have worked with my letter writers have been admitted to programs I am considering; some of my letter writers know people at some of the programs I am applying to. I am good at teaching and very enthusiastic about it. I have taken (or will take) all of the highest-level courses available at my school.
Other: I am also a philosophy major and have written several philosophy+math papers. A philosophy professor who knows me well and loves me is willing to write a rec letter iff it would help me stand out.
Chicago (or "Chicago Enough") Schools:
University of Illinois - Chicago
University of Illinois - Urbana-Champaign
University of Chicago
University of Minnesota
LA (or "LA Enough") Schools:
University of California - Los Angeles
University of California - San Diego
University of California - Irvine
University of California - Santa Barbara
University of Southern California
Carnegie Mellon (ACO)
University of California - Davis
Iowa State University