Centre International de Rencontres Mathématiques Courses

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
• Self-Paced
• Free Video

Evaluation Codes in the Sum-Rank Metric

Explore advanced coding theory through linearized Reed-Muller and Algebraic Geometry codes in sum-rank metrics, extending classical error correction beyond traditional limitations.

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

The Point-Hyperplane Geometry - Relatively Universal Embedding and Associated Code

Explore point-hyperplane geometry in projective spaces, examining Segre embeddings, universality properties, and linear codes arising from geometric structures over finite fields.

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

Structure of Supersingular Elliptic Curve Isogeny Graphs

Explore the structural properties of supersingular elliptic curve isogeny graphs and their cryptographic implications for quantum-resistant systems.

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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Improved Bounds for the Fourier Uniformity Conjecture

Discover improved bounds for the Fourier uniformity conjecture involving the Liouville function and its pseudo-random behavior in short intervals, advancing beyond Walsh's 2023 results.

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