Robert C. Trosten

Hello! I'm Robert, and I'm a first year PhD student at NYU's Courant Institute! 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 and harmonic analysis to understand the qualitative and quantitative properties of solutions to partial differential equations arising from physical situations such as continuum models in fluid mechanics and kinetic theory. I'm also interested in geometric and stochastic aspects of PDE, and find those perspectives particularly fruitful for understanding their dynamics. I love PDE and analysis in all its forms, but am especially interested in problems related to hydrodynamic stability, nonlinear wave propagation, mixing, and enhanced/anomalous dissipation. 

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. 

Shamelessly shilling some stuff I was involved in at CMU, I was Vice President External of the CMU Math Club and a Problem Writing Head for the Carnegie Mellon Informatics and Mathematics Competition; if you're interested in learning more about either of those, feel free to check out the links. If you're a current CMU student in math or chemical engineering, I have some course reviews here.

On the side, I'm now helping the Intercollegiate Math Tournament come to fruition; this is a new maths competition at the undergraduate level for both seasoned competitors and those newer to their mathematical journeys, across colleges (as the name implies).

Finally, if you're interested, here's my CV as well. :^)