Department of Mathematics

University of Toronto

40 St. George St.

Toronto, Ontario, M5S2E4

**Email:** firstname.lastname@utoronto.ca

**Offices:** HU1025 (St. George campus) and DH-3062 (Mississauga)

I am an Assistant Professor in the Department of Mathematics at the University of Toronto. I am interested in probability and related areas. My main research areas include last passage percolation and the KPZ universality class, interacting particle systems, infection models built on seas of random walks, random sorting networks, and random polynomials.

Here is a recent CV (updated September 2021).

- Dauvergne, D. Non-uniqueness times for the maximizer of the KPZ fixed point. arXiv link.
- Dauvergne, D., Nica, M. and Virág, B. RSK in last passage percolation: a unified approach.
*Probab. Surv.*arXiv link. - Dauvergne, D. Last passage isometries for the directed landscape. arXiv link.
- Dauvergne, D and Virág, B. The scaling limit of the longest increasing subsequence. arXiv link.
- Dauvergne, D. and Zhang, L. Disjoint optimizers and the directed landscape. arXiv link.
- Relevant talk: Building the directed landscape (Feb 2021): The link contains two talks from the One World Probability Seminar. The first is by Bálint Virág, and is a general introduction to random planar growth models, the KPZ universality class, and the world of the directed landscape. The second talk is my own; I go into detail about the construction of the directed landscape and then discuss newer results from the above paper with Lingfu Zhang.
- Dauvergne, D., Sarkar, S., and Virág, B. Three-halves variation of geodesics in the directed landscape.
*Ann. Probab. (to appear)*arXiv link. - Dauvergne, D. Hidden invariance of last passage percolation and directed polymers.
*Ann. Probab.*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.
*Acta Math. (to appear)*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.
*Ann. Probab.*arXiv link.

- Dauvergne, D., and Sly, A. Spread of infections in a heterogeneous moving population. arXiv link.
- Relevant talk: Infection spread in a sea of random walks (May 2021): This talk is mostly focussed on a second forthcoming paper, but the ideas discussed at the end of the talk are relevant to this work as well.

- Dauvergne, D. The Archimedean limit of random sorting networks.
*J. Amer. Math. Soc.*arXiv link. - Relevant set of slides: The Archimedean limit of random sorting networks (March 2019)
- Dauvergne, D. and Virág, B. Circular support in random sorting networks.
*Trans. Amer. Math. Soc.*arXiv link. - Angel, O., Dauvergne, D., Holroyd, A.E., and Virág, B. The local limit of random sorting networks.
*Ann. Inst. H. Poincaré Probab. Statist.*arXiv link.

- Dauvergne, D. A necessary and sufficient condition for global convergence of the zeros of random polynomials.
*Adv. Math.*arXiv link. - Relevant talk: Zeros of random sums of orthogonal polynomials (August 2019)
- Bloom, T. and Dauvergne, D. Asymptotic zero distribution of random orthogonal polynomials.
*Ann. Probab.*arXiv link.

- 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.

- Winter 2022: MAT 402 (UTM) Geometry
- Fall 2021: MAT 1600 (UTSG) Graduate Probability I

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

A wiring diagram for the sorting network in S_{4} with swap sequence (2 3 1 2 1 3).

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

A 'susceptible-infected-recovered' infection model in a moving population. Particles that have recovered are not shown.