Higher Dimensions Courses and Certifications

Numberphile

Perfect Shapes in Higher Dimensions

Explore platonic solids and regular polytopes in higher dimensions with Carlo Sequin, delving into complex geometric concepts and their fascinating properties.

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

Simons Institute

Quantum Algorithm for Simulating Real Time Evolution of Lattice Hamiltonians

Explore quantum algorithms for simulating real-time evolution of lattice Hamiltonians, covering previous work, results, and advanced concepts in quantum computation.

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

Insights into Mathematics

History of Geometry IV - The Emergence of Higher Dimensions - Sociology and Pure Maths

Explore the emergence of higher dimensions in 19th-century geometry, including projective geometry, cyclography, and spaces of lines and curves, revolutionizing our understanding of mathematical spaces.

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

Multidimensional Analysis and Geometry - Introduction to the Derivative in Higher Dimensions - Lecture 1

Explore the derivative in higher dimensions, extending single-variable concepts to multidimensional functions and introducing the derivative as a linear map for best approximation.

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

Multidimensional Analysis and Geometry: Introduction to the Derivative in Higher Dimensions - Lecture 2

Explore the derivative in higher dimensions, focusing on linear approximations for functions in 3D space. Learn how classical definitions evolve to handle multivariable calculus concepts.

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

Dublin Institute for Advanced Studies DIAS

Fracton Gauge Fields in Curved Space From Higher Dimensions

Explore fracton quasi-particles, their restricted mobility, and gauge field interactions in curved space through a five-dimensional relativistic theory perspective.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

IPhT-TV

A dS from Higher Dimensions - Landscapia

Explore higher-dimensional de Sitter spaces and their connections to Landscapia theory in this advanced physics lecture by G. Bruno De Luca.

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

NPTEL-NOC IITM

Finite Difference Time Domain Methods: Accuracy Considerations in Higher Dimensions

Explore accuracy considerations for Finite Difference Time Domain Methods in higher dimensions, enhancing understanding of numerical simulation techniques.

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

Isaac Newton Institute for Mathematical Sciences

Hunting Through Higher Dimensions - The Kervaire Invariant Problem

Discover how mathematician Zhouli Xu solved the 126th dimension of the Kervaire invariant problem, exploring higher-dimensional shapes and the journey to this breakthrough.

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

Numberphile

Darts in Higher Dimensions - Numberphile

Explore a fascinating mathematical puzzle involving darts and shrinking bullseyes in higher dimensions, featuring insights from 3Blue1Brown's Grant Sanderson.

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

Law of Conservation of Energy in Higher Dimensions - Fundamentals of Physics

Explore conservation of energy in higher dimensions, covering calculus concepts, work in 2D, conservative forces, and applications to gravitational potential energy.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Insights into Mathematics

Higher Dimensions and the Roles of Length, Area, and Volume - Rational Geometry Math Foundations

Explore higher dimensions and the fundamental role of squared measurements in geometry. Discover how quadrance, quadrea, and quadrume offer more general and invariant alternatives to traditional length, area, and volume.

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

International Centre for Theoretical Sciences

A Chabauty-Coleman-Caro-Pasten Bound in Higher Dimensions by Netan Dogra

Explore advanced techniques in arithmetic geometry, focusing on rational points on modular curves and higher-dimensional varieties using Chabauty-Coleman-Caro-Pasten methods.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

IMSA

Homological Mirror Symmetry - Quivers & Curves in Higher Dimensions

Explore the connection between quiver mutations, Poisson X-cluster varieties, and Calabi-Yau categories, leading to a correspondence between Donaldson-Thomas invariants and rational curve counts in higher dimensions.

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

Hausdorff Center for Mathematics

Louis Theran: Rigidity of Random Graphs in Higher Dimensions

Explore rigidity properties of random graphs in higher dimensions and their connection to matrix completion, with insights on thresholds and optimal conditions.

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