Yi Tian

I am a PhD student in mathematics at the University of Cambridge (since 2024), advised by Jason Miller. I completed my master's at Universität Bonn in 2024 with Eveliina Peltola, and my undergraduate studies at Peking University in 2022 with Zhiyu Tian.

Email CRSid@cam.ac.uk
CRSid yt425
Curriculum vitae ↗
Google Scholar ↗

Papers

Dual of stable carpets

The conformally invariant metric on CLE\(_4\) I, II, III

with E. Kammerer, K. Kavvadias, and J. Miller

arXiv:2609.04138 arXiv:2609.04139 arXiv:2609.04140

Quasisymmetric geometry of random fractals

Quasisymmetric rigidity of the Brownian sphere

with J. Miller

arXiv:2606.10973
The conformal dimension of the Brownian tree is one

with J. Miller

arXiv:2604.25769
The conformal dimension of the Brownian sphere is two

with J. Miller

arXiv:2603.24473

Intrinsic metric and diffusion/heat flow on simple conformal loop ensemble carpets

Existence and uniqueness of the Brownian motion on simple conformal loop ensemble carpets

with J. Miller

in preparation
Existence and uniqueness of the conformally covariant geodesic metric on simple conformal loop ensemble carpets

with J. Miller

arXiv:2511.16208

Talks

The conformally invariant metric on CLE\(_4\) (poster)

Random Explorations, IMSI Chicago
Jul 2026
Quasisymmetric geometry of the Brownian sphere

Peking Summer Program in Probability, PKU
Jun 2026
Analysis on conformally invariant random fractals

Jane Street Graduate Research Fellowship Workshop, online
Apr 2026
The conformally covariant geodesic metric on simple conformal loop ensemble carpets

Combinatorial and hyperbolic random planar geometry, CIRM Marseille
Aug 2025
The conformally covariant geodesic metric on simple conformal loop ensemble carpets

Probabilistic methods in quantum field theory, Bonn
Jul 2025

Images

Uniform exploration of CLE(4), first panel — Simulations of the uniform exploration (first two panels), a geodesic, and the geodesic tree for the conformally invariant metric on CLE\(_4\). Based on the work [KKMT26].

Uniform exploration of CLE(4), second panel — Simulations of the uniform exploration (first two panels), a geodesic, and the geodesic tree for the conformally invariant metric on CLE\(_4\). Based on the work [KKMT26].

Metric balls on a CLE carpet with kappa = 2.72 — Simulations of metric balls for the conformally covariant geodesic metric on CLE\(_\kappa\) carpets, with \(\kappa = 2.72, 2.85, 3, 10/3, 3.99\), respectively. Based on the work [MT25].

Metric balls on a CLE carpet with kappa = 2.85 — Simulations of metric balls for the conformally covariant geodesic metric on CLE\(_\kappa\) carpets, with \(\kappa = 2.72, 2.85, 3, 10/3, 3.99\), respectively. Based on the work [MT25].