Duncan Dauvergne

Email: dd18@math.princeton.edu Picture not found

Office: Fine Hall, Room 509

About

I am currently an Instructor at Princeton University and an NSERC postdoctoral fellow. I am interested in probability and related areas. My main research interests include last passage percolation and the KPZ universality class, interacting particle systems, random sorting networks, and random polynomials. I completed my Ph.D. in 2019 at the University of Toronto under the supervision of Balint Virág.

Here is my CV.

Publications and preprints

Last passage percolation and the KPZ universality class

  • Dauvergne, D., Sarkar, S., and Virág, B. Three-halves variation of geodesics in the directed landscape. arXiv link.
  • Dauvergne, D. Hidden invariance of last passage percolation and directed polymers. arXiv link.
  • Dauvergne, D., Nica, M., and Virág, B. Uniform convergence to the Airy line ensemble. arXiv link.
  • Dauvergne, D., Ortmann, J., and Virág, B. The directed landscape. arXiv link.
    • Relevant talk: The Airy sheet (June 2020): The Airy sheet is the scaling limit of last passage percolation between distinct spatial locations. Its construction comprises the first half of our paper `The directed landscape'. The directed landscape itself is built from metricly composing independent Airy sheets.
  • Dauvergne, D., and Virág, B. Bulk properties of the Airy line ensemble. To appear in Ann. Probab. arXiv link.

Random sorting networks

Random polynomials

Other research

  • Dauvergne, D. Not every transitively D-space is D. Topology Appl. Link.
  • Dauvergne, D. and Edelstein-Keshet, L. Application of quasi-steady state methods to molecular motor transport on microtubules in fungal hyphae. J. Theoret. Biol. Link.

Teaching

I am currently co-course coordinator for MAT 104 (Calculus II) at Princeton. Previously I was a course instructor for MAT 202 (Linear Algebra with Applications).

At the University of Toronto, I taught calculus and linear algebra and worked as a teaching assistant for classes in probability, combinatorics, real and complex analysis, mathematical logic, ODEs, calculus, and linear algebra.

A few pictures of some objects that I've thought about

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Which is which? A directed geodesic, its weight function, and a Brownian bridge.

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A wiring diagram for the sorting network in S4 with swap sequence (2 3 1 2 1 3).

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Selected trajectories in the rescaled wiring diagram of a random 2000-element sorting network. Observe the sine curves…