I am a Ph.D. student at Department of Mathematics, Stanford University. My dissertation advisors are Rick Schoen and Brian White. Before that I was a student at Peking University, where I got my Bachelor's degree in Mathematics, mentored by Huijun Fan.

My research interests include differential geometry, partial differential equations, and geometric measure theory, with a focus on variational methods in geometric problems.

Research Statement» CV»

Research papers

• A polyhedron comparison theorem for three-manifolds with positive scalar curvature, arXiv.org
• Positive scalar curvature and skeleton singularities, joint with C. Mantoulidis, submitted. arXiv.org
• Index and topology of minimal hypersurfaces in Rⁿ, accepted by Calculus of Variation and PDE. arXiv.org

Notes

• Nachdiplom Lectures - Topics in scalar curvature, lectures by Rick Schoen (Spring 2017, FIM-ETH). We encourage the readers to wait FIM-ETH for the publication of the lecture notes.
• Lectures on mean curvature flow by Or Hershkovits. Joint with Evangelie Zachos. (Winter 2017, Stanford) PDF
• Lectures on minimal submanifolds by Rick Schoen. Joint with C. Mantoulidis and D. Cheng. (Spring 2015, Stanford) PDF
• Non-existence of metric on Tⁿ with positive scalar curvature. Notes for a talk given at Stanford and University of California, Irvine in 2014. PDF

Teaching

• Average teaching evaluation: 4.53/5. My teaching statement is here.
• Teaching Assistant
  • TA mentor (Stanford University). Helped new TAs improve the quality of their sections.
  • Minimal surfaces: old and new. Lectures by Alessandro Carlotto, as part of Summer School on Geometric Analysis, Fields Institute for Research in Mathematical Sciences.
  • Linear algebra and differential calculus of several variables (Math 51, Stanford University).
  • Calculus: ACE (Additional Calculus for Engineers) (Math 42, Stanford University). ACE program are designed to enchance diversities among engineer students.
• Course Assistant
  • Linear Algebra and Matrix Theory. (Math 113, Stanford University)
  • Integral Calculus. (Math 20, Stanford University)
  • Lebesgue Integration and Fourier Analysis. (Math 172, Stanford University)
  • Applied Matrix Theory. (Math 114, Stanford University)
  • Ph.D. qualifying exam preparation in Algebra. Stanford University