Discrete Geometry Courses and Certifications

Harvard CMSA

Geometric Methods for Analyzing Discrete Shapes

Explore geometric methods for analyzing discrete shapes through expert presentations on triangulations, conformal mappings, and computational geometry applications.

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

The Szemeredi-Trotter Theorem - Lecture 8

Explore the Szemeredi-Trotter theorem's sharp solution to discrete projection problems in the plane using topology-based proofs that differ from traditional approaches.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

BIMSA

Two Geometric Applications of the Linear Algebra Method

Explore geometric applications of linear algebra with János Pach, covering discrete geometry, convexity, and combinatorics in this research seminar.

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

NCCR SwissMAP

Orthogonal Ring Patterns and Discrete Surfaces

Explore orthogonal ring patterns and discrete surfaces in integrable systems, focusing on applications in condensed matter physics and quantum field theory.

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

Institute for Pure & Applied Mathematics (IPAM)

Vertex Order Shellings in Simplicial Complexes

Delve into the mathematical exploration of vertex order shellings in simplicial complexes, examining their topological properties and relationship with matroid independence complexes through Björner's theorem.

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

Institute for Pure & Applied Mathematics (IPAM)

Minkowski Bases of Type Cones in Deformation Theory

Delve into advanced geometric concepts exploring deformation cones, polytope decomposition, and barycentric subdivisions of simplicial fans, with applications to braid fans and normal fan products.

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

BIMSA

The Sphere Packing Problem

Discover the mathematical elegance of sphere packing through Maryna Viazovska's groundbreaking work on optimal arrangements in high-dimensional spaces.

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

International Centre for Theoretical Sciences

The Discrete Charm of Geometry by Alexander Bobenko

Explore the fascinating world of discrete geometry and its applications in architecture, computer graphics, and physics. Discover structure-preserving discretizations through simple examples and stunning visuals.

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Computational Interactions between Algebra, Combinatorics, and Discrete Geometry - 2025

Explore cutting-edge computational methods connecting algebra, combinatorics, and discrete geometry through expert presentations on polytopes, matroids, and algebraic structures.

• YouTube
• 15 hours 6 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Statistical Mechanics and Discrete Geometry

Explore cutting-edge connections between statistical mechanics, discrete geometry, and cluster algebras through expert presentations on bipartite graphs, dimer models, and geometric structures.

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

Fields Institute

Challenges in Discrete Geometry - Part I- Convex Polytopes

Explore convex polytopes, from Euler's formula to modern combinatorial results. Discover connections to other mathematical areas and intriguing open problems in discrete geometry.

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

Applied Algebraic Topology Network

Topological Methods in Discrete Geometry

Explore topological applications in discrete geometry, focusing on mass partitions and Helly-type theorems. Learn about classical results and recent generalizations in these areas.

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

Applied Algebraic Topology Network

Topological Methods in Discrete Geometry - New Developments

Explores recent advancements in topological methods for discrete geometry, focusing on configuration spaces in cooperative game theory and their connections to embedding problems in Euclidean spaces.

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

Institute for Pure & Applied Mathematics (IPAM)

The Multinomial Dimer Model - Statistical Mechanics and Discrete Geometry

Explore the multinomial dimer model's limit shape theory, bistochastic gauge, and 3D Aztec diamond applications in statistical mechanics and discrete geometry.

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

Institute for Pure & Applied Mathematics (IPAM)

Incidences and Dimers in Projective Geometry - Statistical Mechanics and Discrete Geometry

Explore the connection between linear incidence theorems in projective geometry and bipartite graphs on surfaces, incorporating dimer model dynamics to derive dynamic linear incidence theorems.

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