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#Painlevé Equations

Showing: 12 courses
Institute for Advanced Study

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

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Explore the pure mapping class group's action on character varieties, examining orbit closures and their implications for various mathematical contexts and applications.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Modular Forms and Differential Equations: Connections and Applications

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Explore connections between modular forms and differential equations, from historical origins to modern applications in mathematics and physics.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
IPhT-TV

On the Integrability of the Airy Kernel and Beyond

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Explore integrability of the Airy kernel and related mathematical concepts in this advanced mathematical analysis presentation by Sofia Tarricone.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Topological Recursion, Painlevé Equation, Exact WKB and Resurgence

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Explore topological recursion's connections to WKB, Painlevé equations, and BPS structures. Delve into resurgence properties and non-linear Stokes phenomena in Painlevé transcendents.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Global Lie Theory: Wild Riemann Surfaces and Their Character Varieties

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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.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Schmid College, Chapman University

Linear Systems and Differential Equations in Random Matrix Theory

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Explore linear systems and differential equations in random matrix theory, focusing on solving nonlinear equations using Hankel operators, Fredholm determinants, and tau functions.
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20 Lesons
50 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

The Non-Abelian p-Curvature Conjecture

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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.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Elliptic Orthogonal Polynomials and Their Integrability

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Explore elliptic orthogonal polynomials and their integrability through Riemann-Hilbert analysis, examining discrete and continuous integrable systems and connections to the sixth Painlevé equation.
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1 Lesons
45 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Random Matrices and Statistical Physics - Lecture 2

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Explore connections between random matrices and statistical physics, delving into advanced mathematical concepts and their applications in complex systems analysis.
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1 Lesons
1 hour 44 minutes
On-Demand
Free-Video
NCCR SwissMAP

From Liouville to Painlevé and Heun via CFT/Isomonodromy Relation

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Explore conformal field theory through integrable, probabilistic, and supersymmetric perspectives, connecting Liouville theory to Painlevé and Heun equations.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
NCCR SwissMAP

From the A2 Quiver Towards the Painlevé I T Function

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Explore quantisation of moduli spaces through the A2 quiver and Painlevé I T function, gaining insights into advanced mathematical concepts.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Hamiltonian Structure of Rational Isomonodromic Deformation Systems

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Explore Hamiltonian structure of rational isomonodromic deformation systems, focusing on applications in physics and integrability properties of nonlinear differential equations.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video