Explore advanced mathematical concepts in this comprehensive lecture series covering first-passage percolation (FPP) and related stochastic models. Delve into fundamental introductory concepts through multiple lectures by leading experts, examining the mathematical foundations and key properties of FPP systems. Study geodesics in FPP through detailed analysis of their behavior, properties, and geometric characteristics across various dimensional settings. Investigate fluctuation phenomena in FPP models, exploring statistical variations and their mathematical descriptions through extensive theoretical development. Learn about solvable last-passage percolation (LPP) models and their exact solutions, providing concrete examples of tractable systems within the broader percolation framework. Examine noise sensitivity and chaos in random planar geometry, understanding how small perturbations affect large-scale geometric structures. Analyze the coalescence behavior of non-crossing geodesics in planar settings and explore empirical measures along FPP geodesics. Discover time constants and limiting shapes in high-dimensional first-passage percolation, investigating asymptotic behavior as system size grows. Study convergence properties of limit shapes in near-critical two-dimensional systems and explore limiting laws in subsequence problems. Investigate concentration phenomena for interacting diffusions in the Kardar-Parisi-Zhang (KPZ) universality class and examine dynamic polymer models with invariant measures. Learn about corner growth models on circular geometries and variational formulas for large deviations under specific tail conditions. Explore non-equilibrium multi-scale analysis in competing FPP systems and study Busemann functions in random growth and polymer models. Examine disjointness properties of geodesics in planar first-passage percolation and integration techniques for KPZ two-point functions, culminating in advanced topics including geodesic coalescence and the BKS midpoint problem.

Syllabus

Introduction to FPP (Lecture 1) by Riddhipratim Basu
Introduction to FPP (Lecture 2) by Jack Thomas Hanson,
Geodesics of FPP (Lecture 1) by Michael Damron
Fluctuations of FPP (Lecture 1) by Philippe Sosoe
Solvable LPP (Lecture 1) by Márton Balázs
Fluctuations of FPP (Lecture 2) by Philippe Sosoe
Noise Sensitivity and Chaos in Random Planar Geometry by Shirshendu Ganguly
In Planar First-Passage Percolation, Non-Crossing Geodesics Tend to Coalesce by Daniel Ahlberg
Fluctuations of FPP (Lecture 2) by Philippe Sosoe
Solvable LPP (Lecture 2) by Márton Balázs
The Time Constant and Limiting Shape in High-Dimensional First Passage Percolation by Si Tang
Empirical Measures along FPP Geodesics by Erik Bates
Fluctuations of FPP (Lecture 3) by Philippe Sosoe
Solvable LPP (Lecture 3) by Márton Balázs
Convergence of Limit Shapes for 2D Near-Critical First-Passage Percolation by Chang-Long Yao
Limiting Laws in Some Subsequences Problems by Christian Houdré
Concetration for Interacting Diffusions in the KPZ Class by Philippe Sosoe
Dynamic Polymers: Invariant Measures and ordering by Noise by Yuri Bakhtin
Corner Growth Model on the Circle by Eric Cator
A Variational Formula for Large Deviations in FPP under Tail Estimates by Shuta Nakajima
Non-Equilibrium Multi-Scale Analysis and Coexistence in Competing FPP by Alexandre Stauffer
Busemann Functions in Random Growth and Polymer Models by Timo Seppäläinen
Geoffrey Grimmett (University of Cambridge, UK) by Geoffrey Grimmett
Disjointness of Geodesics for First Passage Percolation in the Plane by Kenneth S. Alexander
Integration by Parts and KPZ Two-Point Function by Leandro P. R. Pimentel
Geodesics in First-Passage Percolation by Christopher Hoffman
Geodesics of FPP (Lecture 2) by Michael Damron
Geodesics of FPP (Lecture 3) by Michael Damron
Fluctuations of FPP (Lecture 4) by Philippe Sosoe
Coalescence of Geodesics and the BKS Midpoint Problem in First-passage percolation by Barbara Dembin