Conferences Organized

This conference will bring together international researchers to explore the intersections of universality, nonlinearity, and integrability. These interconnected fields have provided dynamic and fertile ground for mutual development, leading to exciting new advancements. The conference will feature a diverse range of talks on random matrix theory, integrable nonlinear PDEs, KPZ theory, and more. Additionally, this event will serve as an opportunity to honor Percy Deift, whose many contributions will be reflected in several of the presentations.

This conference was held in Jeju Island with focus on recent developments in Schramm-Loewner evolution and its connections to Gaussian fields and conformal field theory, the continuum random trees, random surfaces produced by Liouville quantum gravity, and Jordan curves obtained from random conformal welding.

This conference focused on recent developments in the theory of random matrices and its connections to potential theory and statistical physics. Specific topics included recent advances in determinantal Coulomb gas, the spherical Sherrington-Kirkpatrick model, the extreme gap problems, and the limit theorems for determinantal point processes.

This conference focused on recent developments in Schramm-Loewner evolution, and its connections to random Gaussian fields, and classical conformal field theory from theoretical physics. Together, these subjects have been one of the most active areas in statistical mechanics in the last fifteen years. The mathematical theory behind random conformal geometry is rich and intimately intertwined with theoretical physics, combinatorics, operator theory, spectral theory, and many other disciplines where new connections are regularly emerging.

Over the last four decades, Peter Jones has demonstrated the power of using ideas from real and harmonic analysis to solve difficult problems in complex and functional analysis, geometric measure theory, conformal dynamics, conformal probability, and geometrically based applied mathematics. Although much of this work is highly technical, it is usually motivated by simple geometric or analytic ideas. The conference explored the areas listed above from the perspectives of both established experts and younger researchers, with an emphasis on interactions between areas and the basic themes that recur in each of them. Specific topics will include recent advances in harmonic measure, Schramm-Loewner Evolutions (SLE), Gaussian Free Fields (GFF), rectifiability, and the analysis of big data.

The last decade has seen remarkable advancement in the understanding of planar lattice models and their scaling limits. A wide range of ideas and techniques from probability, analysis, and physics, including the SLE process, discrete complex analysis, random planar maps, quantum gravity, and conformal field theory, come together in this field. The workshop brought together leading researchers in these areas to interact and to present and discuss recent advances.