Centre International de Rencontres Mathématiques Courses

Claspers, Graspers, and Barbells - Diffeomorphisms of S¹ × S³

Explore how barbells can be obtained from families of dancing circles called graspers, providing quick proofs of existence of infinite subgroups of mapping class groups.

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

Equivariant Trisections for Group Actions on Four-Manifolds

Explore G-equivariant trisections for 4-dimensional manifolds with group actions, reducing complex topology to 2D shadow diagrams through invariant surface embeddings.

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

Splitting Links by Integer Homology Spheres

Explore advanced topology research on 2-sphere links in S^4 that split by integer homology 3-spheres but not by standard S^3, presented by Marco Marengon in collaboration with Marco Golla.

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

Knot Signatures and Complex Singularities - Lecture 3

Explore Rudolph's conjecture on links of irreducible complex curve singularities and their linear independence in the concordance group through advanced mathematical analysis.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Knot Signatures and Complex Singularities - Lecture 2

Explore Rudolph's conjecture on links of complex curve singularities and their linear independence in the concordance group through advanced mathematical analysis.

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

Knot Signatures and Complex Singularities - Lecture 1

Explore Rudolph's conjecture on links of irreducible complex curve singularities and their linear independence in the concordance group through knot signatures.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

From Correlated to White Transport Noise in Fluid Models

Explore stochastic dynamics in incompressible fluids through variational frameworks, examining large-scale behavior with small-scale processes and noise regularization effects.

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

The Gibbs Measure of the Renormalized Two Dimensional Stochastic Gross-Pitaevskii

Explore the construction of Gibbs measures for the renormalized 2D stochastic Gross-Pitaevskii equation, a mean-field model for Bose-Einstein condensates near critical temperature.

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

Fine Properties of Random Fields - From Fluids to Quantum Field Theory

Explore advanced regularity properties of invariant measures for singular SPDEs, including breakthrough insights on 2D Navier-Stokes equations and Gaussian measure equivalence.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Numerical Methods for SDEs with Additive Noise and Distributional Drift

Explore numerical methods for stochastic differential equations with distributional drift, covering Euler-type schemes, error analysis, and applications to various noise types.

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

Stochastic Wave Equation with Cubic Non-Linearity

Explore advanced mathematical analysis of cubic stochastic nonlinear wave equations on 2D torus with spatial noise rougher than white noise, examining solution theory limits.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Tame Geometry in Quantum Field Theory and Gravity

Explore how tame geometry principles apply to quantum field theory and quantum gravity, with a focus on finiteness questions in string theory and mathematical applications.

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

Hensel Minimality in Non-Archimedean Geometry

Explore h-minimality, a concept in non-archimedean geometry that controls definable sets on the affine line through finite points, covering well-behaved characteristic zero valued fields with strong analytic and geometric implications.

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

Definable Holomorphic Continuations in O-minimal Structures

Explore holomorphic continuations of definable functions in o-minimal structures, including applications to complex Gamma and Riemann zeta functions in this mathematical research presentation.

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

Parametrizations in Valued Fields

Delve into parametrizations in valued fields, exploring the Pila-Wilkie counting theorem and its analogues for p-adic fields, with insights on parametrizations for definable sets in Hensel minimal fields.

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