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 PoincarĂ© 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)

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.

**Contact:**

Department of Pure Mathematics and Mathematical Statistics

University of Cambridge

Centre for Mathematical Sciences

Wilberforce Road

Cambridge CB3 0WB

UNITED KINGDOM

Tel.: +44 (0)1223 766925

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*Last updated 16 Nov 2023*