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.
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.
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.
Embeddings and Tverberg-Type Problems: New Algorithms and Undecidability Results
Explore computational topology: algorithmic embeddability, undecidability in higher dimensions, and polynomial-time decidability of r-Tverberg problem in metastable range.
Sobolev Regularity for Maximal Operators
Explore recent developments in regularity theory for maximal operators, focusing on Sobolev and BV data. Accessible overview of an active research area with open questions.
G-Conjecture - Numberphile
Explore h-vectors and the g-conjecture with mathematician June Huh, delving into higher-dimensional shapes, triangulation, and Euler's formula. Gain insights into complex mathematical concepts.
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.
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.
Maximally Dense Sphere Packings
Explore optimal arrangements of disks in 2D and higher dimensions, focusing on recent findings for multiple disk sizes. Survey of results accessible to a broad audience.
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.
Ergodicity in Smooth Dynamics 1
Explore ergodicity in smooth dynamics, covering introductory concepts, examples, proofs, and higher dimensions with experts Jana Rodriguez-Hertz and Amie Wilkinson.
Families
Explore hyperbolic geometry, from asteroids to higher dimensions, in this engaging lecture on mathematical families and their fascinating properties.
Symmetry, Reality's Riddle
Explore the hidden mathematical beauty of symmetry in nature, art, and science with Oxford mathematician Marcus du Sautoy in this mind-expanding TED-Ed talk.
Stable Blowup for the Higher-Dimensional Skyrme Model
Explore stable blowup mechanisms in higher-dimensional Skyrme models, focusing on finite-time blowup at self-similar rates in 5+1 dimensions compared to 3+1 dimensions.