Painlevé Equations Courses and Certifications

Bogolyubov Institute for Theoretical Physics

Painlevé I Equation and Modular Forms

Explore the deep connections between Painlevé I differential equations and modular forms through advanced mathematical analysis and theoretical insights.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Foliations, Complex Geometry, and Painlevé Equations - PT

Explore advanced mathematical connections between foliations, complex geometry, and Painlevé equations in this specialized lecture celebrating Frank Loray's contributions to the field.

• YouTube
• 41 minutes
• On-Demand
• Free Video

BIMSA

Mean Field Equations on Torus, Pre-Modular Forms and Painlevé VI Equation

Explore the intricate connections between mean field equations on torus surfaces, pre-modular forms, and the Painleve VI equation in advanced mathematical analysis.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Foliations, Complex Geometry, and Painlevé Equations - Approximation on the Circle

Explore advanced mathematical connections between foliations, complex geometry, and Painlevé equations in this specialized research presentation by Julio Rebelo.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Foliations, Complex Geometry, and Painlevé Equations - Bruno Ideal and the Variety of Centers for Singular Germs of Vector Fields

Explore Bruno ideal and the variety of centers for singular germs of vector fields in this advanced mathematical presentation on foliations and complex geometry.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Wall-Crossing Structures, Analyticity, and Resurgence

Explore advanced mathematical concepts connecting wall-crossing structures, resurgence theory, and quantum field theory through expert lectures from leading researchers.

• YouTube
• 22 hours 47 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

The Non-Abelian p-Curvature Conjecture

Explore a generalized p-curvature conjecture for non-linear ODEs, its implications for algebraic geometry, and proof techniques inspired by Katz and Esnault-Groechenig's work.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Hamiltonian Structure of Rational Isomonodromic Deformation Systems

Explore Hamiltonian structure of rational isomonodromic deformation systems, focusing on applications in physics and integrability properties of nonlinear differential equations.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Schmid College, Chapman University

Linear Systems and Differential Equations in Random Matrix Theory

Explore linear systems and differential equations in random matrix theory, focusing on solving nonlinear equations using Hankel operators, Fredholm determinants, and tau functions.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Topological Recursion, Painlevé Equation, Exact WKB and Resurgence

Explore topological recursion's connections to WKB, Painlevé equations, and BPS structures. Delve into resurgence properties and non-linear Stokes phenomena in Painlevé transcendents.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Global Lie Theory: Wild Riemann Surfaces and Their Character Varieties

Explore the evolution of topological symplectic structures, wild Riemann surfaces, and character varieties in global Lie theory. Discover connections to quantum groups, hyperkähler geometry, and integrable systems.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Galileo Galilei Institute

Random Matrices and Statistical Physics - Lecture 2

Explore connections between random matrices and statistical physics, delving into advanced mathematical concepts and their applications in complex systems analysis.

• YouTube
• 1 hour 44 minutes
• On-Demand
• Free Video

IPhT-TV

On the Integrability of the Airy Kernel and Beyond

Explore integrability of the Airy kernel and related mathematical concepts in this advanced mathematical analysis presentation by Sofia Tarricone.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Closure of Orbits of the Pure Mapping Class Group on the Character Variety

Explore the pure mapping class group's action on character varieties, examining orbit closures and their implications for various mathematical contexts and applications.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

NCCR SwissMAP

From Liouville to Painlevé and Heun via CFT/Isomonodromy Relation

Explore conformal field theory through integrable, probabilistic, and supersymmetric perspectives, connecting Liouville theory to Painlevé and Heun equations.

• YouTube
• 1 hour 37 minutes
• On-Demand
• Free Video