Centre International de Rencontres Mathématiques Courses

Primes in Arithmetic Progressions and Bounded Gaps

Explore Zhang's breakthrough on bounded gaps between primes and equidistribution estimates for primes in arithmetic progressions, highlighting key connections and recent advances.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Extreme Superposition - Rogue Waves of Infinite Order

Explore rogue waves of infinite order in the focusing nonlinear Schrödinger equation, their emergence, asymptotic properties, and connections to Painlevé equations.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Projectivity Criteria for Kähler Morphisms

Explore projectivity criteria for Kähler morphisms between compact manifolds, examining when holomorphic maps with projective fibers yield projective morphisms in MMP contexts.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Explicit K-moduli Spaces of Fano 3-folds

Explore explicit K-moduli spaces of Fano 3-folds and their connections to other modular constructions in algebraic geometry.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Rationality of Some Real Conic Bundle Threefolds

Explore rationality questions for real conic bundle threefolds, examining obstructions from intermediate Jacobian torsors and real loci in algebraic geometry.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

A Family of Fano Manifolds Obtained as Linear Sections of the Spinor Tenfold

Explore the rich geometry of Fano manifolds through linear sections of the spinor tenfold, connecting E8 Lie algebras, graded structures, and classical Kummer quartic surfaces.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Real Plane Sextic Curves Without Real Singular Points

Explore topology of real algebraic curves, focusing on degree 6 curves in the projective plane and their deformation types determined by homological structure.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Instabilities and Singularities Within Fluid Boundary Layers - Lecture 2

Explore mathematical results on fluid boundary layers, focusing on Prandtl models, singularities near separation points, and instabilities in time-dependent systems.

• YouTube
• 1 hour 30 minutes
• Self-Paced
• Free Video

Instabilities and Singularities Within Fluid Boundary Layers - Lecture 1

Explore mathematical results on fluid boundary layers, focusing on the Prandtl model, singularities near separation points, and instabilities in time-dependent systems.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Instabilities and Singularities Within Fluid Boundary Layers - Lecture 3

Explore mathematical results on fluid boundary layers, focusing on Prandtl models, singularities near separation points, and instabilities in time-dependent systems.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Whither Spontaneous Stochasticity - Lecture 3

Delve into advanced mathematical foundations of spontaneous stochasticity, exploring outstanding problems, statistical-mechanical analogies, and experimental challenges in turbulence theory.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

Eulerian Spontaneous Stochasticity - Lecture 2

Delve into Eulerian spontaneous stochasticity in turbulent flows, exploring Lorenz's predictability work and non-unique weak solutions of Euler equations with deterministic initial data.

• YouTube
• 1 hour 29 minutes
• Self-Paced
• Free Video

Lagrangian Spontaneous Stochasticity - Lecture 1

Explore the mathematical foundations of spontaneous stochasticity in turbulent flows, focusing on Lagrangian dynamics and scalar advection anomalies.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Inertia-Gravity Waves Interacting with Background Flows - Lecture 2

Explore inertia-gravity waves in ocean dynamics, focusing on near-inertial waves and their interaction with background flows using quantum physics analogies and statistical mechanics methods.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

Inertia-Gravity Waves Interacting with Background Flows - Lecture 1

Explore inertia-gravity waves in ocean dynamics, focusing on near-inertial waves induced by wind and their spatial reorganization by background flows using quantum physics analogies.

• YouTube
• 1 hour 33 minutes
• Self-Paced
• Free Video