Robert C. Trosten

Hello! I'm Robert; I'm currently in my final year of a joint BS/MS in Mathematics at Carnegie Mellon, and will be pursuing a PhD in mathematics at the Courant Institute at NYU starting this fall!

My main research interest is all things mathematical fluid mechanics – these are the questions I love asking, as I find fluids to be at the perfect intersection of mathematically and physically fascinating and relevant – the wind whipping against our skin in the winter cold, the water washing over us at the beach, the coffee we drink with breakfast, the shampoo we use to wash our hair are all fluids! 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, as well as gaining a better understanding of PDE from both geometric and stochastic points of view. I love PDE and analysis in all its forms, but am especially interested in problems related to hydrodynamic stability, nonlinear wave propagation, and enhanced/anomalous dissipation. 

I do love math for its own sake, and can also be motivated to work on all sorts of problems in analysis-flavored fields as well, such as dynamical systems, ergodic theory, probability, differential geometry, and topology. I particularly love applying "soft" arguments to "hard" analysis, as I find that often a bit of extra abstraction helps clear away the distractions in your problem, leaving several visible paths of attack once you know what really matters. 

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. I'm also 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 interested, here's my CV as well. :^)