About

Julien Dubedat is a Professor and the Director of Undergraduate Studies in the Department of Mathematics at Columbia University. He holds a Ph.D. from Universite Paris-Sud, obtained in 2004. His research focuses on probability theory and mathematical physics.

Research topics

• Computer Science
• Quantum mechanics
• Mathematics
• Mathematical analysis
• Physics
• Mathematical physics
• Pure mathematics
• Geometry
• Combinatorics

Selected publications

• Stochastic Ricci Flow on Compact Surfaces

  International Mathematics Research Notices · 2021 · 6 citations

  1st authorCorresponding
  • Computer Science
  • Mathematics
  • Pure mathematics

  Abstract In this paper we introduce the stochastic Ricci flow (SRF) in two spatial dimensions. The flow is symmetric with respect to a measure induced by Liouville conformal field theory. Using the theory of Dirichlet forms, we construct a weak solution to the associated equation of the area measure on a flat torus, in the full “$L^1$ regime” $\sigma < \sigma _{L^1}=2 \sqrt \pi $ where $\sigma $ is the noise strength. We also describe the main necessary modifications needed for the SRF on general compact surfaces and list some open questions.

  DOI

• Tightness of Liouville first passage percolation for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math>

  Publications mathématiques de l IHÉS · 2020 · 60 citations

  • Mathematics
  • Mathematical physics
  • Combinatorics

  We study Liouville first passage percolation metrics associated to a Gaussian free field <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>h</mml:mi> </mml:math> mollified by the two-dimensional heat kernel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> in the bulk, and related star-scale invariant metrics. For <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mi>γ</mml:mi> <mml:msub> <mml:mi>d</mml:mi> <mml:mi>γ</mml:mi> </mml:msub> </mml:mfrac> </mml:mrow> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mi>γ</mml:mi> </mml:msub> </mml:math> is the Liouville quantum gravity dimension defined in Ding and Gwynne (Commun. Math. Phys. 374:1877–1934, 2020), we show that renormalized metrics <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>*</mml:mo> <mml:mi>h</mml:mi> </mml:mrow> </mml:msup> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msub> </mml:math> are tight with respect to the uniform topology. We also show that subsequential limits are bi-Hölder with respect to the Euclidean metric, obtain tail estimates for side-to-side distances, and derive error bounds for the normalizing constants <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> .

  DOI

Recent grants

• Conformally invariant random systems

  NSF · $96k · 2008–2011

• Geometry of random Loewner chains

  NSF · $135k · 2013–2018

• Critical planar systems and conformal invariance

  NSF · $165k · 2010–2016

• Discrete models and conformally invariant limits

  NSF · $165k · 2015–2019

Frequent coauthors

• Hugo Falconet

  New York University

  12 shared

• Ewain Gwynne

  University of Chicago

  5 shared

• Jian Ding

  4 shared

• Xin Sun

  3 shared

• Joshua Pfeffer

  Columbia University

  3 shared

• Hao Shen

  University of Wisconsin–Madison

  2 shared

• Reza Gheissari

  2 shared

• Alexander Dunlap

  2 shared

Education

• Ph.D., Probability theory and mathematical physics

  Universite Paris-Sud

  2004

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