My most recent project (joint work with Maurice Duits and Seung-Yeop Lee) is on the 2-matrix model, and its relation to the Ising model on random graphs. In what will probably be a series of 3-4 papers, we make rigorous the results of physicists, which may be found in the following works (among others):

1. V. A. Kazakov, Ising Model on a Dynamical Planar Random Lattice: Exact Solution. Phys. Lett. A. 119 (3), 1986.

2. V. A. Kazakov and D. V. Boulatov, The Ising Model on a Random Planar Lattice: The Structure of the Phase Transition and the Exact Critical Exponents. Phys. Lett. B. 186 (3), 1986.

3. E. Brézin and V. A. Kazakov, Exactly solvable field theories of closed strings. Phys. Lett. B. 236 (2), 1990.

4. M. R. Douglas, Strings in less than one dimension and generalized KdV hierarchies. Phys. Lett B. 238 (2-4), 1990.

5. D.J. Gross and A. A. Migdal, A non-perturbative treatment of two-dimensional quantum gravity. Nucl. Phys. B. 340 (2-3), 1990.

The first two references pertain to the calculation of the planar free energy of the quartic 2-matrix model; the last three references pertain to the critical partition function for the same matrix model. Using Riemann-Hilbert methods, we are able to compute the planar free energy, and provide a more explicit characterization of the phase portrait of this model. We are also able to show that the critical partition function is a tau function for a certain integrable equation. 

• Helsinki-Stockholm Probability and Mathematical Physics Days 2025, November 13th-14th, 2025, Helsinki, Finland

• Brunel-Bielefeld Workshop on Random Matrix Theory, December 8th-12th, 2025, Bielefeld, Germany

• OPSFA 2025, August 17th-21st, 2026, Kyoto, Japan

I will also be in Paris for the month of November at Sorbonne University visiting Maurice Duits.