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. Here is, an often out of date, Curriculum Vitae.
Research. I am interested in the mathematical analysis of nonlinear partial differential equations (PDE) using tools from harmonic analysis. My main focus is on equations that model “wave-type” phenomena. Such equations are called nonlinear dispersive or wave PDE. They show up in a wide range of fields of physics and applied sciences such as quantum physics, 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 sometimes 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 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.
Contact
Department of Mathematics
University of Michigan
Office: 5834 East Hall
Phone: 734-764-0325
E-mail: zhani@umich.edu