Centre International de Rencontres Mathématiques Courses

Vertical Coincidences of an Elliptic Curve Defined Over a Number Field

Explore vertical coincidences in elliptic curves over number fields, extending Daniels-Lozano-Robledo's work beyond rational numbers to general number field cases.

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

Reducing Models for Branched Covers of the Projective Line

Explore methods for computing small affine plane models from curves over number fields with finite degree maps to the projective line.

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

Plabic Tangles and Cluster Promotion Maps

Explore plabic tangles and their connection to cluster promotion maps on Grassmannians through planar bipartite graphs and rational mappings.

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

Switching Identities for Loop-Soups and Consequences

Discover new identities in law for loop-soups and Gaussian Free Fields on cable graphs, exploring configurations conditioned on connections and consequences inspired by Rick Kenyon's ideas.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

The Infinite Bin Model - Old and New

Explore the infinite bin model - a family of ranked-biased branching random walks on integers, examining special cases, long memory properties, and hydrodynamic limits with wall-crossing phenomena.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Coulomb Gas Approach to Conformal Field Theory and Lattice Models

Explore Coulomb gas techniques connecting statistical mechanics lattice models to Conformal Field Theory, including recent progress on general domains and Riemann surfaces.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

The Multinomial Dimer Model

Explore the multinomial dimer model's exact solvability in large N limits, covering limit shapes, free energy formulas, and applications to Aztec diamonds and 3D cuboids.

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

Holomorphic Symplectic Geometry of Elliptic Surfaces

Explore the intricate relationship between holomorphic symplectic structures and elliptic fibrations on complex surfaces through advanced geometric analysis.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Conformal Measures and Currents in Holomorphic Dynamics

Explore conformal measures and currents in holomorphic dynamics, covering 1D rational maps, complex Henon maps, and Kleinian groups using Patterson-Sullivan construction methods.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Starting with the Gauss-Bonnet Formula - Rigidity Phenomena on Bounded Symmetric Domains

Explore rigidity phenomena on bounded symmetric domains through the Gauss-Bonnet formula, covering Hermitian metric rigidity, holomorphic maps, and applications to complex geometry.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Perturbations of Parabolic Endomorphisms in Dimension 2

Explore perturbations of holomorphic endomorphisms in C² that are tangent to the identity, focusing on how dynamics change under perturbation and generalizing results from one-dimensional cases.

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

On K3 Surfaces with Non-Elementary Hyperbolic Automorphism Group

Explore advanced research on K3 surfaces with non-elementary hyperbolic automorphism groups, focusing on finiteness of Néron-Severi lattices under optimal conditions.

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

Sums of Odd-ly Many Fractions and Distribution of Primes

Discover new bounds on constrained sets of fractions and their applications to prime distribution, exploring mysterious odd k-tuple solutions and near-optimal upper bounds.

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

Recent Progress on Some Irrationality Questions of Erdős

Explore recent advances on Erdős' irrationality problems using prime number theory tools and conditional/unconditional results in mathematical analysis.

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

A Two Dimensional Delta Symbol Method and Applications

Discover a two-dimensional delta symbol method for studying rational points on hypersurfaces and its application to establishing quantitative Hasse principles for quadratic forms.

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