Duncan Dauvergne

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I am a third year Ph.D. student at the University of Toronto in probability, working under the supervision of Professor Balint Virag. You can contact me at duncan.dauvergne@mail.utoronto.ca. Here is a link to my CV.

Research

My research is focussed on random sorting networks. A sorting network is a shortest path from the identity permutation to the reverse permutation in the Cayley graph of Sn with generators given by adjacent transpositions. Such paths are called sorting networks since they can be thought of as algorithms for sorting a list of numbers from increasing order into decreasing order.

The study of random sorting networks is concerned with the following question: what does an n-element uniform random sorting network “look like”? It turns out that in the limit as n tends to infinity, a uniform random sorting network displays many striking geometric properties. For examples, particle trajectories converge to sine curves and the half-time permutation matrix measure converges to the projected surface area measure of the 2-sphere onto the unit disk.

Publications and Preprints

Dauvergne, D. The Archimedean limit of random sorting networks. PDF.

Dauvergne, D. and Virag, B. Circular support in random sorting networks. PDF.

Bloom, T. and Dauvergne D. Asymptotic zero distribution of random orthogonal polynomials. PDF.

Angel, O., Dauvergne, D., Holroyd, A.E., and Virag, B. The local limit of random sorting networks. PDF.

Dauvergne, D. Not every transitively D-space is D. Link.

Dauvergne, D. and Edelstein-Keshet, L. Application of quasi-steady state methods to molecular motor transport on microtubules in fungal hyphae. Link.

Teaching

I am currently a course instructor and coordinator for MAT 137.

In the past, I have been a course instructor for MAT 233. I have also been a teaching assistant at U of T for MAT475, MAT 344, MAT 337, MAT 334, MAT309, MAT292, MAT 223, MAT 235, MAT 237, MAT 135, and MAT 136.

A few sorting network pictures

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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…