Zhenhao Li

I am a third year graduate student at MIT. I am generally interested in microlocal analysis and PDEs. My advisor is Semyon Dyatlov.

My CV can be found here. My email is zhenhao at mit dot edu.

Research

• Internal waves in aquariums with characteristic corners
  Preprint. (arXiv)

• Internal waves in 2D domains with ergodic classical dynamics
  with Yves Colin de Verdière Preprint. (arXiv)

• 2D internal waves in an ergodic setting
  Preprint. (arXiv)

• Weyl laws for open quantum maps
  to appear in Journal of Spectral Theory. (arXiv)

• Uniqueness of excited states to $-\Delta u + u - u^3 = 0$ in three dimensions
  with Alex Cohen and Wilhelm Schlag, to appear in Analysis & PDE. (arXiv, GitHub)

• Dynamic transitions of the Swift-Hohenberg equation with third-order dispersion
  Discrete and Continuous Dynamical Systems-B, 26(2021), 6069-6090. (arXiv)

• Certain hyperbolic regular polygonal tiles are isoperimetric
  with Jack Hirsch, Jackson Petty, and Christopher Xue, Geometriae Dedicata, 214(2021), 65-77. (arXiv)

• The optimal double bubble for density $r^p$
  with Jack Hirsch, Jackson Petty, and Christopher Xue, Rose-Hulman Undergraduate Mathematics Journal, 22(2021). (arXiv)

• Optimal monohedral tilings of hyperbolic surfaces
  Leonardo Di Giosia, Jahangir Habib, Jack Hirsch, Lea Kenigsberg, Dylanger Pittman, Jackson Petty, Christopher Xue, Weitao Zhu, preprint. (arXiv)