ICM 2026 Plenary Lecture - Jeremy Quastel

ICM 2026 Plenary Lecture - Jeremy Quastel

by Jeremy Quastel

Formal & Physical Sciences Mathematics PBMathematics
🎙 Jeremy Quastel 👥 58K 📅 August 17, 2026 ⏱ 59 min 👁 8 📄 original study 🧭 2026-08-17
Available in: English (current) Français

Keywords

KPZ fixed pointrandom interface growth1:2:3 scalingTracy-Widom distributionintegrable probability

Summary

Jeremy Quastel delivers a plenary lecture at ICM 2026 on the KPZ fixed point, a universal object describing random interface growth. He introduces the physical phenomenon of interface growth, exemplified by wildfires and lichen, and presents mathematical models such as the Eden model and ballistic aggregation. The lecture focuses on the KPZ equation, a stochastic PDE, and its scaling limits. Quastel explains the 1:2:3 scaling, which leads to the KPZ fixed point, a Markov process with Brownian motion as its invariant measure. He discusses exact formulas for special initial conditions, such as the narrow wedge, connecting to the Tracy-Widom distribution from random matrix theory. The talk highlights the role of integrable probability, including the multi-line PNG model and determinantal formulas, in deriving universal results. Quastel emphasizes the collaborative effort between mathematicians and physicists in establishing these results and mentions recent breakthroughs, including the exact formulation of the KPZ fixed point in terms of transition probabilities.

155 words

Critical Evaluation

Value of the Information & Strength of the Argument

The lecture provides a comprehensive overview of the KPZ universality class, combining physical intuition with rigorous mathematical results. Quastel’s argumentation is clear and well-structured, moving from simple models to the general theory. He effectively explains the importance of scaling and universality, and the connection to random matrix theory is compelling. The presentation is accessible to a mathematical audience while maintaining depth.

Scientific Rigor, Source Quality, Title Accuracy

Quastel is a leading expert, and the lecture is based on rigorous published work, including his own contributions. The sources cited are primarily his own and collaborators’ papers, which are highly regarded. The title accurately reflects the content, focusing on the KPZ fixed point. The lecture is well-referenced, though specific citations are not explicitly listed in the video description.

135 words

Title / Content Match

The title accurately reflects the content: a plenary lecture on the KPZ fixed point.

Quality & Reliability

9/10

Lecture by a leading expert in probability theory, presenting rigorous mathematical results with clear explanations and references to published work.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Cited Sources

  • The KPZ fixed point — Quastel's paper with Matetski and Remenik, cited as the main reference for the exact formulation.

Concurring Sources

  • KPZ equation and its universality — General references on KPZ universality.

Contribution & Novelties

The lecture presents the KPZ fixed point as a universal object, synthesizing decades of research. It highlights the exact formulation by Quastel, Matetski, and Remenik, which provides a complete description of the scaling limit. The talk also emphasizes the role of integrable probability and the connection to random matrix theory.

Pour aller plus loin :

  • KPZ equation — Overview of the KPZ equation and its universality class.
  • Tracy-Widom distribution — Distribution arising in random matrix theory and KPZ.
  • Integrable probability — Field connecting exactly solvable models to probability.

88 words

Radar Profile

The radar profile shows high scores across all dimensions, indicating a lecture with substantial information, high technical depth, and strong reliability. The balance between quantity and quality is excellent, making it a valuable resource for experts.

Reliability 9/10

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