ζDapeng Zhan
Probability · Random conformal geometry

Dapeng
Zhan

Professor of Mathematics at Michigan State University. I work on Schramm–Loewner evolution, probability, stochastic analysis, and scaling limits of two-dimensional lattice models.

Office C327 Wells Hall Email zhan@msu.edu
Explore research → MSU profile ↗ CV
SLE-inspired curve A stylized random curve winding through a conformal domain.
SLErandom curves · conformal maps
Research

Random geometry, made analytic.

My work studies random planar curves through the interaction of probability, complex analysis, stochastic differential equations, and special functions.

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Schramm–Loewner evolution

Geometry, reversibility and duality, Green’s functions, multiple SLE, SLE with force points, loop and bubble measures.

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Probability & stochastic analysis

Diffusion processes, martingales, stochastic calculus, transition densities, and probabilistic constructions of conformally invariant objects.

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Scaling limits

Connections between SLE and two-dimensional statistical lattice models, including LERW, spanning trees, percolation, and related models.

ProbabilitySLEComplex AnalysisRandom Conformal GeometryStatistical MechanicsGreen’s FunctionsSpecial Functions
Recent work

Selected updates

Recent papers and preprints, with links to arXiv or the published version.

2026

Trivariate Hypergeometric Series Formulas for Pure Partition Functions of Multiple 3-SLEκ

Preprint · explicit trivariate hypergeometric normal forms for the rainbow and neighbor link-pattern types.

arXiv ↗
2025

SLEκ(ρ) bubble measures

Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 61(2), 1212–1248.

DOI ↗
2024

Existence and uniqueness of nonsimple multiple SLE

Journal of Statistical Physics 191, Article 101.

DOI ↗
2024

Green’s function for cut points of chordal SLE attached with boundary arcs

Stochastic Processes and their Applications 170, 104309.

DOI ↗
Notes

Lecture notes

A small collection of lecture notes retained for public use.

  • MTH 992 Brownian motion and stochastic analysis · notes
  • MTH 925 Random Variables and Stochastic Processes · notes
  • SLE lecture Introductory lecture notes · notes
Background

Career & recognition

Ph.D. in Mathematics, California Institute of Technology, 2004. Dissertation: Random Loewner Chains in Riemann Surfaces.

Academic appointments

2017–present

Professor

Michigan State University

2012–2017

Associate Professor

Michigan State University

2009–2012

Assistant Professor

Michigan State University

2007–2009

Gibbs Assistant Professor

Yale University

2004–2007

Morrey Assistant Professor

University of California, Berkeley

Awards & grants

2016

Simons Fellowship

2011

Salem Prize

Jointly with Julien Dubédat; awarded for work on SLE reversibility and duality.

2011–2015

Alfred P. Sloan Research Fellowship

2011–2018

NSF CAREER Award

DMS-1056840

2009–2013

NSF Grant

DMS-09063733

2004

Scott Russell Johnson Graduate Dissertation Prize

California Institute of Technology

Publications

Research archive

Recent publications are updated to their published status. Use the filters to move between recent and earlier work.

Department of Mathematics · Michigan State University

C327 Wells Hall · East Lansing, Michigan · zhan@msu.edu

Send emailMSU Mathematics ↗