Robert C. Trosten

Hello! I'm Robert, and I'm a second year PhD student at NYU's Courant Institute, co-advised by Bill Cooperman and Vlad Vicol. Prior to this, in 2025, I received both my B.S. and M.S. in Mathematical Sciences at Carnegie Mellon through their honors degree program; my thesis was titled On Exponential Lower Bounds for Mixing and was advised by Gautam Iyer. 

My main research interest is all things mathematical fluid mechanics, but I'm particularly interested in using abstract methods from functional analysis, probability, and dynamical systems to understand qualitative and quantitative properties of solutions to partial differential equations arising from continuum models in fluid mechanics and kinetic theory. I am particularly interested in using probabilistic methods to understand their behavior over long timescales. I love PDE and analysis in all its forms, but I am especially interested in problems related to mixing, wave propagation, enhanced/anomalous dissipation, and hydrodynamic stability.

In general, I particularly love applying "soft" arguments to "hard" analysis, leaving several visible paths of attack once you know what really matters. On the side, I also have a soft spot for areas like descriptive set theory and mathematical logic, which seem completely orthogonal to everything I've just described but actually have some very interesting connections. 

At the top of the page, I have sections for my research work, my writing outside of research, teaching experience, and a list of awesome cross-field mathematical results which I aim to continually add to whenever I learn about something cool, if you'd like to see any of that. 

Here's my CV as well, if you'd like to see that. :^)