Research

My most-recent preprint is co-authored with Ewan Davies, Alex Karduna, and Holden Lee. We prove rapid mixing of Glauber dynamics (a Markov chain) on the collection of list packings of a graph. The preprint is available here.
A recent preprint is co-authored with Alain Oliviero Durmus, Pierre Monmarche, and Gabriel Stoltz. We prove explicit nonasymptotic convergence rates of generalized Hamiltonian Monte Carlo (an MCMC method). The preprint is available here.
My dissertation studied the existence-and-convergence-to equilibrium for the degenerate stochastic Lorenz 96 model, a finite-dimensional ODE analogue to the Navier-Stokes equations. The manuscript is available here.

An example of Langevin dynamics

A recent research presentation

CMO_presentation_Camrud.mp4

Research with Undergraduates

I was privileged enough to participate in mathematics research as an undergraduate at Concordia College, as well as through an NSF-funded research program at New York University. These experiences were invaluable to my future career as a mathematician, and I try to participate in leading undergraduate research whenever possible. The list of program topics I have led with undergraduates includes:

Smoothing of Markov semigroups
Fractals and iterated function systems
Sampling and interpolation theory
Markov chains and mixing times
Models for turbulent flow
Semigroup theory
Fractional operator theory

Selected Publications:

Links to my research profiles: