I'm a first-year mathematics Ph.D. Student at Duke University. I completed my undergraduate degree in mathematics at the University of Maryland. Click here for my full CV.

I have a philosophy that there are no fields of math that I "dislike" or that I "like more than others." At the end of the day, 99% of mathematics (PDE, probability, topology, harmonic analysis, geometry, abstract algebra,  functional analysis, etc.) is the study of some function spaces over some sets with some structure. Other than preferring the teaching style of one professor in one subject over another professor in a different subject, there's no good reason for me to "like" one abstract function space (e.g., the collection of smooth maps from one manifold to another) more than another (e.g., the collection of random variables on some probability space). Instead, I prefer to say that "so far, I've been exposed to/am working on [this or that field of math]."

The fields of math that I've been most exposed to so far are:

1. Probability Theory

2. Stochastic Analysis and SDE

3. Elliptic/Parabolic PDE (& ties to Probability theory)

4. Fluids PDE & Harmonic Analysis (I very much enjoyed a topics class at UMD proving local-well-posedness for the Euler and Navier Stokes equations).

5. Signal Processing & Harmonic Analysis (wavelets, discrete harmonic analysis and such). My one (not-yet-published) paper together with UMD Professor Wojtek Czaja and UMD Ph.D. student Brandon Kolstoe is in this field.
   
   

The fields of math that I've not been exposed to prior to this academic year, but am currently studying are:

1.  Malliavin Calculus (slowly moving through Nualart's book with fellow graduate student Bryan Castillo)

2. SPDE (in general) and Rough Paths and Regularity Structures (in particular). (I occasionally interrogate Professor Alex Dunlap about the content of his minicourse on this topic whenever I'm confused about something in his notes.)

3. Under the mentorship of Professor Jim Nolen, I spent some time reading, understanding all the arguments, and trying to make some slight generalizations of the results in this paper.