I have one year remaining and want to improve my profile in anyway I can for next year. If anyone sees any weaknesses, which I'm sure exist, I would totally appreciate any feedback or criticisms. What texts/courses would you recommend I look into for the summer and next year. Of course I will approach faculty and ask if they can supervise a reading course.

I'm aiming for Top 10 graduate programs for Homotopy Theory, Algebraic K-Theory and Algebraic Geometry.

Undergraduate Institution: Top 40 in Mathematics

GRE Scores:

V: 31%

Q: 94%

W: 60%

Math Subject: 73%

GPA:

Cumulative: 3.45

Major: 3.6

Program Applying: (Pure Math, specifically Homotopy Theory and Algebraic Geometry)

Research Experience: Never did research but have given a presentation on Category Theory and Sigma-Algebras.

Awards/Honors/Recognitions: Bernard Kurtin ($1000 to top 3 undergrads)

Pertinent Activities or Jobs: Former TA for Introduction to Proofs course. Tutor a few hours per week

Any Miscellaneous Points that Might Help: 4 grad classes: Algebra 1 and 2, Algebraic Topology (Category Theory and Homological Algebra heavy so far), and Measure Theory. Some of my recommendation writers are world famous but they don't know me very well so it's very hard to tell if this will work into my favor.

Any Other Info That Shows Up On Your App and Might Matter: Honestly, what I wrote above is literally what I'm relying on.