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About me. I am a professor of mathematics at the University of Michigan. Before moving to Michigan in 2018, I was an assistant professor at Georgia Tech (2014-2018), and a Courant Instructor/Simons Fellow at the Courant Institute of Mathematical Sciences, NYU (2011-2014). I defended my thesis in 2011 at UCLA under the supervision of Terence Tao. More about me can be found in my (often not up-to-date) Curriculum Vitae.

Research. I am interested in the mathematical analysis of nonlinear partial differential equations (PDE). My focus there is on equations that model “wave-type” phenomena (like waves in the ocean, atmosphere, quantum physics, light propagation, plasma theory, etc). Such equations are called nonlinear dispersive or wave PDE, and they show up in a wide range of fields of physics and applied sciences such as quantum mechanics, oceanography and atmospheric sciences, plasma theory, nonlinear optics, general relativity, to mention only a few.

Recently, I have been specifically interested in questions related to turbulence and non-equilibrium statistical mechanics for nonlinear wave systems. This goes by the name of “wave turbulence theory”.

My papers and expository notes can be found on my Research and Publications page.

Teaching. Please visit this page to know about my current and past teachings.

Editorial work: I am an editor of the newly established journal Ars Inveniendi Analytica. This is a peer-reviewed, open-access (completely free for authors and readers) journal in mathematical analysis. The founding philosophy can be found here. Please follow the following submission guidlines to submit a paper.