Super Topological Recursion - Lecture 1
Explore super topological recursion with Kento Osuga in this comprehensive lecture, delving into advanced mathematical concepts and their applications.
Topological Recursion and Matrix Models - Lecture 2
Explore advanced concepts in topological recursion and matrix models, building on fundamental principles to deepen mathematical understanding.
Super Topological Recursion - Lecture 2
Explore advanced concepts in super topological recursion, building on previous knowledge and delving into complex mathematical theories and applications.
Topological Recursion and Matrix Models - Lecture 1
Explore topological recursion and matrix models with Bertrand Eynard in this comprehensive lecture from the TRSalento school, delving into advanced mathematical concepts.
Scalar Curvature Rigidity in Manifolds
Explore scalar curvature rigidity in manifolds, examining known solutions and current research questions using spinorial techniques.
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.
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.
Positive Mass Theorem for Asymptotically Hyperbolic Manifolds
Explore the positive mass theorem for asymptotically hyperbolic manifolds and its implications in AdS/CFT correspondence and global invariants at conformal infinity.
Blow Up for the 1D Cubic NLS and Related Systems
Explore singularity formation in 1D Schrödinger equations with cubic nonlinearity and its connections to Schrödinger map and vortex filament equation.
Solitons and Channels in Nonlinear Wave Equations
Explore non-radiative solutions in nonlinear wave equations and their connection to soliton resolution, using new energy estimate channels for radial solutions.
New Perspectives on Borel Summation - Lecture 4
Explore Airy-Lucas functions through Borel summation, focusing on thimble integrals and hypergeometric Laplace transforms. Gain insights into Stokes phenomenon reflections in the Borel plane.
New Perspectives on Borel Summation - Lecture 1
Explore new perspectives on Borel summation, focusing on linear ODEs and integrals over Lefschetz thimbles, to understand when divergent series solutions produce holomorphic solutions.
Spontaneous Stochasticity in Multi-Scale Dynamics
Explore spontaneous stochasticity in multi-scale dynamics, focusing on turbulence models and the formalization of stochastic solutions using renormalization-group operator attractors.
Enumerative Geometry Through Sheaves
Explore enumerative geometry, sheaf counting, and their applications in algebraic geometry. Discover new approaches to generalized Donaldson-Thomas invariants on Calabi-Yau threefolds.
The Formulation of the Navier-Stokes Equations on Riemannian Manifolds
Explore advanced formulations of Navier-Stokes equations on Riemannian manifolds, focusing on Ebin and Marsden's approach and recent developments in this complex field of fluid dynamics.
Global Solutions to Quadratic Systems of Stochastic Reaction-Diffusion
Explorez les solutions globales des systèmes quadratiques de réaction-diffusion stochastique en dimension deux, avec un accent sur les perturbations à quatre espèces.
Random Models on Regularity-Integrability Structures
Explore a simplified proof of the BPHZ theorem using extended regularity structures with integrability exponents, advancing the study of singular stochastic partial differential equations.
Logarithmic Sobolev Inequalities on Homogeneous Spaces
Explore logarithmic Sobolev inequalities on homogeneous spaces with sub-Riemannian structures. Discover how constants depend on Lie group geometry and remain independent of dimension in certain cases.
Topological Recursion: A Recursive Way of Counting Surfaces
Explore topological recursion for enumerating surfaces in combinatorics, geometry, and physics. Learn how this universal method links to integrable systems and random matrices.
Combinatorics and Quantum Invariant Differential Operators on Reflection Equation Algebras
Explore quantum analogs of symmetric functions and differential operators in Reflection Equation Algebras, examining their properties and combinatorial applications.
Spectra of Laplace and Dirac Operators on Noncompact Manifolds
Explore spectra of Laplace and Dirac operators on complete manifolds, including types of spectra, results for special behaviors at infinity, and effects of additional potentials.