David Koralov

My studies

I'm a second-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.

The fields of math that I've been spending most of my time studying and working on are:

Stochastic Analysis and SDE
Elliptic/Parabolic PDE (& ties to Probability theory)
Fluids PDE & Harmonic Analysis (I very much enjoyed a topics class at UMD proving local-well-posedness for the Euler and Navier Stokes equations).
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.
SPDE (Currently reading through Professor Davar Khoshnevisan's Analysis Of Stochastic Partial Differential Equations under the guidance of Professor Alex Dunlap as well as the following papers: #1, #2.)
Together with 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.

Teaching style

When I teach, I always try my best to present a clear sequence of specific claims. When possible, I tend to err on the side of not skipping intermediate steps and being as detailed as possible, even if that sometimes means covering a little bit less material.

Example: An introductory lecture on Hamilton Jacobi Equations, given to real students, not all of whom were apriori assumed to have a background in PDEs.
The camera is pointed in the wrong direction for the first approx. 8 minutes. I didn't erase anything that was on the board during this time.

Silly facts

I've had 3 hamsters.

Caramelitio, my first hamster. (Passed away from old age in 2022)

Frijolito, my second hamster. (Passed away from old age in 2024)

Gaius Julius Caesar. (Alive and well)

Hamster Poetry

A Eulogy for Caramelito

(Written in Russian by Leonid Koralov)

A Eulogy for Frijolito

(Written in English by Leonid Koralov)

Some images where I'm with my friends and loved ones

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