Qin Deng
E-mail: qindeng@mit.edu |
Office: 239B, Building 2, Massachusetts Institute of Technology |
About me
I am currently a C.L.E. Moore Instructor at MIT under the mentorship of Tobias Colding.
I am generally interested in metric geometry, geometric analysis, and Riemannian geometry. In particular, I study nonsmooth spaces with synthetic sectional and Ricci curvature bounds. Research topics I am currently interested in include the structure theory of the boundary for RCD and Alexandrov spaces, the question of unique continuation on RCD and Alexandrov spaces, the regularity of Lagrangian flows and its applications to the structure theory of RCD spaces. I have also thought a lot about symmetrization methods in the past.
I received my PhD in 2021 at University of Toronto under the supervision of Vitali Kapovitch. Here's my thesis.
Publications and preprints
- Margulis lemma on RCD(K,N) spaces (with Jaime Santos-Rodríguez, Sergio Zamora, and Xinrui Zhao) [link]
- Sharp bounds and rigidity for volumes of boundaries of Alexandrov spaces (with Vitali Kapovitch) [link]
- Unique continuation problem on RCD Spaces. I (with Xinrui Zhao) [link]
- Failure of strong unique continuation for harmonic functions on RCD spaces (with Xinrui Zhao) [link]
- Improved regularity estimates for Lagrangian flows on RCD(K,N) spaces (with Elia Brué and Daniele Semola) [link]
- Hölder continuity of tangent cones in RCD(K,N) spaces and applications to non-branching [link]
- On the rate of convergence of random polarizations on the sphere (with Almut Burchard) [link]
Teaching
I am currently teaching 18.104 Seminar in Analysis (Spring 2024) at MIT.
Previously, I taught 18.100A Real Analysis (Fall 2023), 18.152 Introduction to PDEs (Spring 2022), 18.994 Seminar in Geometry (Fall 2022) and 18.100P Real Analysis (Spring 2022) at MIT, and MAT137 Calculus with Proofs (2017-2018 LEC0501, 2018-2019 LEC0601, 2019-2020 LEC0701, 2020-2021 LEC0501, and Summers 2018-2021 LEC0101) at University of Toronto.