Yizheng Yuan

Research Associate at University of Cambridge

Ph.D. obtained at TU Berlin (title of dissertation: Schramm-Loewner evolution and path regularity)

Research interests: probability and complex analysis, more specifically random conformal geometry, Löwner chains, Schramm-Löwner evolution and conformal loop ensembles, Gaussian multiplicative chaos, Liouville Brownian motion.


N. Holden and Y. Yuan (2022+): Regularity of the Schramm-Loewner evolution: Up-to-constant variation and modulus of continuity. ArXiv e-prints, arXiv:2211.15609 [math.PR].

V. Margarint, A. Shekhar, and Y. Yuan (2022+): On Loewner chains driven by semimartingales and complex Bessel-type SDEs. ArXiv e-prints, arXiv:2106.15429 [math.PR].

O. Butkovsky, V. Margarint, and Y. Yuan (2023): Law of the SLE tip. Electron. J. Probab. 28: 1–25.

Y. Yuan (2023): Refined regularity of SLE. Ann. Inst. Henri Poincaré Probab. Stat., to appear.

Y. Yuan (2022): Topological characterisations of Loewner traces. Indiana Univ. Math. J. 71 No. 3, 1027–1046.

P. K. Friz, H. Tran, and Y. Yuan (2021): Regularity of SLE in $(t,\kappa)$ and refined GRR estimates. Probab. Theory Related Fields, 180(1-2):71–112.

H. Tran and Y. Yuan (2020): A support theorem for SLE curves. Electron. J. Probab., 25:1–18.


Lent 2024: Schramm-Loewner Evolutions

Summer 2021: Wahrscheinlichkeitstheorie III (TA)

Winter 2020/21: Analysis III (TA)

Summer 2020: Rough Stochastic Analysis I (TA)

Summer 2020: Analysis III (TA)

Winter 2019/20: Analysis II (TA)

Summer 2019: Maß- und Integrationstheorie (TA)

Winter 2018/19: Analysis I und Lineare Algebra (TA)

Conferences, Summer Schools, Seminar Talks (selection)

Statistical Physics and Random Surfaces, Oberwolfach, 12–17 May 2024.

Probability and Geometry in, on and of non-Euclidian spaces, CIRM, Marseille, 02–06 Oct. 2023.

Quasiworld workshop, Helsinki, 14–18 Aug. 2023.

Random Conformal Geometry and Related Fields in Jeju, Jeju Island, Korea, 05–09 June 2023.
Talk: Regularity of SLE trace.

Schramm-Loewner evolution and related topics, University of Pennsylvania, Philadelphia, 18–19 Feb. 2023.
Talk: Regularity of SLE: Up-to-constant variation and modulus of continuity.

Probability and Mathematical Physics, Helsinki, 28 June–07 July 2022.

The Analysis and Geometry of Random Spaces, MSRI, Berkeley, 28 Mar.–01 Apr. 2022.

14th Oxford-Berlin Meeting, 10–12 Feb. 2021.
Talk: SLE with random time-dependent parameter.

Rainwater Seminar, University of Washington, Seattle, 10 Mar. 2020.
Talk: Topological characterisations of Loewner traces.

49th Saint-Flour Probability Summer School, Saint-Flour (France), 07–19 July 2019.
Talk: Regularity of Schramm-Loewner evolution.

Analysis and Geometry of Random Shapes, Los Angeles, 07–11 Jan. 2019.

10th Oxford-Berlin Meeting, Oxford, 29 Nov.–01 Dec. 2018.
Talk: A multiparameter Garsia-Rodemich-Rumsey inequality and application to SLE.

Pathwise SLE, Berlin, 24–26 April 2018.



Department of Pure Mathematics and Mathematical Statistics

University of Cambridge
Centre for Mathematical Sciences
Wilberforce Road
Cambridge CB3 0WB

Tel.: +44 (0)1223 766925
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Last updated 16 Nov 2023