Hi guys, here is a preliminary list of schools I am thinking about: MIT, Harvard, Chicago, Columbia, Cal Tech, UCLA, Texas, Georgia Tech, Duke, Indiana, UC Davis. In some regards I feel like I am being way too anxious, but at the same time, I feel a lot of pressure due to my peers. In any case, I would be thankful for any advice and feedback.

Undergrad institution: One of MIT, Princeton, Harvard, or Stanford

Majors: Mathematics

GPA: 3.78 / 4.0 overall and 3.85 / 4.0 in department

Type of student: Domestic white male

Courses taken (+ Planned)

Math courses taken: Accelerated Honors Real Analysis I (A-), Accelerated Honors Real Analysis II- (A-), Topology (A-), Complex Analysis (A-), Differential Geometry (A), Modern Knot Theory (A)

Courses planned for next fall: Algebra, Measure Theory, Additional reading course in low dimensional topology

Recommenders: One giant in the field of low-dimensional topology with whom I took the knot theory course and will complete an undergraduate thesis, one younger faculty member with whom I am doing an REU this summer, one giant in string theory with whom I did undergraduate research last year

Research experience: Completed a semester long research project in Fall 2017 on random matrices and QFT with one recommender, received an A with submission of 20 page paper, though not for publication. Completing an REU this summer at my home institution on Lagrangian Floer homology and knot Floer Homology with the younger recommender. Will complete a year long undergraduate thesis with the remaining advisor, topic will be broadly in low-dimensional topology.

Work experience: Nothing relevant

Awards: None

GRE General: Taking in fall

GRE Math: Taking in fall