Zhenhao Li

I am a fourth 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 a 2D subcritical channel
  with Jian Wang and Jared Wunsch
  Preprint (2024). (arXiv)

• Long time quantum—classical correspondence for open systems in trace norm
  Preprint (2024). (arXiv)

• Internal waves in aquariums with characteristic corners
  Preprint (2024). (arXiv)

• Internal waves in 2D domains with ergodic classical dynamics
  with Yves Colin de Verdière
  Probability and Mathematical Physics, 5(2024), 735-751. (arXiv)

• 2D internal waves in an ergodic setting
  Preprint (2023). (arXiv)

• Weyl laws for open quantum maps
  Journal of Spectral Theory, 12(2022), 1541–1566. (arXiv)

• Uniqueness of excited states to $-\Delta u + u - u^3 = 0$ in three dimensions
  with Alex Cohen and Wilhelm Schlag,
  Analysis and PDEs, 17(2024), 1887-1906. (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, Rose-Hulman Undergraduate Mathematics Journal, 24(2023). (arXiv)

Expository

• A quick introduction to b-Calculus
  based on lectures given at SLMath with Semyon Dyatlov