Pu Yu

Hi! I am a 5th year PhD student at MIT, my advisor is Scott Sheffield. Previously I graduated from Peking University with a B.S. degree in mathematics.

I will join New York University as a Courant Instructor starting Fall 2024.

I am interested in probability theory, especially random geometry. In particular I have been working on the Schramm-Loewner Evolution, Liouville quantum gravity, and their connection with many other objects in mathematical physics.

Office: 2-342

Email: puyu1516@mit.edu

Papers and Preprints

9. Boundary touching probability and nested-path exponent for non-simple CLE (with Morris Ang, Xin Sun, and Zijie Zhuang), arxiv2401.15904.

8. Conformal welding of quantum disks and multiple SLE: the non-simple case (with Morris Ang, Nina Holden and Xin Sun), arxiv2310.20583.

7. SLE partition functions via conformal welding of random surfaces (with Xin Sun), submitted, arxiv2309.05177.

6. Reversibility of whole plane SLE for \kappa>8 (with Morris Ang), submitted, arxiv2309.05176.

5. Wilson loop expectations as sums over surfaces on the plane (with Minjae Park, Joshua Pfeffer and Scott Sheffield), submitted, arxiv2305.02306.

4. Time-reversal of multiple-force-point chordal SLE_\kappa(\rho), Electronic Journal of Probability (2023). arxiv2211.04581.

3. Quantum triangles and imaginary geometry flow lines (with Morris Ang and Xin Sun), submitted, arxiv2211.04580.

2. Baxter permuton and Liouville quantum gravity (with Jacopo Borga, Nina Holden and Xin Sun), Probability Theory and Related Fields (2023), arxiv2203.12176.

1. On mean field limit for Brownian particles with Coulomb interaction in 3D (with Lei Li and Jian-Guo Liu), Journal of Mathematical Physics (2019), arxiv1811.07797.


  • Courant Probability and Mathematical Physics Seminar, December 8, 2023.
  • MIT Probability Seminar, October 30, 2023.
  • Columbia Probability Seminar, October 6, 2023.
  • Summer school on Probability, Peking University, July 14, 2023, [slides].
  • Random Conformal Geometry and Related Fields in Jeju, June 8, 2023, [slides].
  • Uchicago Probability and Statistical Physics Seminar, April 14, 2023.
  • Workshop on Schramm-Loewner Evolution, February 18, 2023, [slides].
  • Random Geometry and Statistics Workshop, October 28, 2022, [slides].
  • THU-PKU-BNU Joint Probability Webinar, March 29, 2022, [slides].
  • Teaching

  • 18.676 Stochastic Calculus, Grader, Spring 2023.
  • 18.642 Topics in mathematical finance, Grader, Fall 2022.
  • 18.650 Fundamental of Statistics, Grader, Spring 2022.
  • 18.655 Mathematical Statistics, Grader, Spring 2022 and Fall 2020.
  • 18.02 Multivariable Calculus, Recitation Instructor, Fall 2021.
  • 18.615 Introduction to Stochastic Processes, Grader, Spring 2021.
  • Mentorship

    Research Programs

  • During 2021, I participated the MIT PRIMES program and mentored one high school student working on the master field and free Brownian motions.
  • In Summer 2020, I mentored one undergraduate student through the UROP+ program working on extended source of Internal DLA. arxiv2009.09159, arxiv2010.08166.

    Directed Reading Program

  • In Jan 2023, I mentored two undergraduate students reading Classical and Multilinear Harmonic Analysis.
  • In Jan 2022, I mentored one undergraduate student reading Probability: Theory and Examples.
  • In Jan 2021, I mentored one undergraduate student reading Probability: Theory and Examples.
  • Some other writings

  • A brief Introduction to Imaginary Geometry I, at here.
  • Last update: 1.30.24