Links to papers, lecture notes and slides from recent talks are organized by area. Some articles appear in more than one list.

Please email me directly for preprints/materials related to talks if you can't find them below. I don't like to publish partial results, but I do maintain working notes on several current projects that I'm happy to share.

Most of my notes on the embedding problem are currently in the form of technical reports, though two announcements appear below as preprints. These notes cover several parts of my program and include many original results on model development, Gibbs measures for SDP, analogies with RMT, simplified PDE. Many of these ideas are under active development in the thesis work of several students. If using these results or ideas, please cite them as technical reports. The underlying model is in constant evolution, as are its implications.

Related lecture notes that include the interplay of dynamics and algorithms, and a new take on pattern theory are included below. The pattern theory class includes several Gibbs measures for applications in machine learning, as well as a discussion of fast algorithms. Two chapters on thermodynamics of learning are not included in the current version. These notes provide a quick start on information theory and Gibbs measures (should be useful if you're an analyst trying to figure out what the fuss is all about).

Publications organized by area

Dynamical systems and integrable systems.

Fluid mechanics.

Kinetic theory, phase transitions, materials.

Models of turbulence.

Random matrix theory and numerical linear algebra.


Recent preprints

Information theory and the embedding problem for Riemannian manifolds , March 2021.

The second law: information theory and self-assembly , April 2021.

Slides and texts of recent talks

Building polyhedra by self-assembly, (AMS Fall 2017). Informal description in the Notices of the AMS.

Stochastic Loewner evolution with branching and the Dyson superprocess, (PCMI July 2017). Video of the talk may be found here . The underlying SPDE and Loewner theory is described in Vivian Olsiewski Healey's thesis (May 2017). The related preprint is available on request.

Harish-Chandra's integral, the Calogero-Moser system and the complex Burgers equation. (CMSA, Harvard, Jan 2017). This talk is on the `standard' U(N) integral and contains a new Lax pair. My student Colin McSwiggen is developing a similar, but more general asymptotic description for HC integrals over compact, semisimple Lie groups.

Kinetic theory of grain boundary networks , last updated Oct. 2016.

Complete integrability of shock clustering , last updated Oct. 2015.

Conservation laws with random data and the equation free method , Dec. 2015.

How long does it take to compute the eigenvalues of a random matrix, last updated April 2016.

Lecture notes and technical reports

Dynamical systems, Fall 2020 , last updated Jan 2021.

Pattern theory, last updated Jan 2021.

Gaussian processes, the isometric embedding problem and turbulence , last updated June 2020.

The isometric embedding problem and random matrix theory last updated, Aug. 2020.

Gibbs measures for semidefinite programming , Sept. 2020.

Mathematics and Materials. Edited with Mark Bowick, David Kinderlehrer and Charles Radin. Vol. 23, IAS/Park City Mathematics Series, AMS/SIAM (2017).

A quick introduction to kinetic theory. Lectures at Hebrew University, University of Chicago and TIFR, 2016-2017.

Statistical theories of turbulence. Graduate course Spring 2016, last updated April 2016).

Random matrix theory. Book in progress (Random matrix theory and numerical algorithms). Anticipated completion, May 2021.

Partial differential equations graduate sequence in 2005-2006.
2005 notes.
Conservation laws.
Translation of Hopf's paper on Navier-Stokes