Quintessential Quandle Queries
Explore the intriguing world of quandles, a mathematical structure with applications in knot theory and group theory, in this engaging invited address by Alissa Crans.
Tropical Geometry and Shallow Water Waves
Explore the fascinating intersection of tropical geometry and shallow water waves in this engaging lecture by Harvard mathematician Lauren Kiyomi Williams.
Dendrite Fractals - Easy Technique, Great Results, Different Styles - Acrylics or India Ink
Learn to create stunning dendrite fractals using acrylic inks, India ink, and fluid acrylics. Master various sizes and styles with a step-by-step guide to achieve beautiful snowflake-like patterns in any color.
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.
Bernardo Uribe, UniNorte - Bordism and Birational Invariants of Finite Groups
Explore birational invariants of finite groups and their connection to bordism invariants of equivariant manifolds, focusing on Bogomolov's results in this advanced mathematical topic.
Scientific Notation & Significant Figures
Learn essential math skills for science: scientific notation and significant figures. Master expressing large numbers and rounding for precise calculations in chemistry, physics, and biology.
Isotropic Killing Vector Fields and Related Structures on Complex Surfaces
Exploration of isotropic Killing vector fields on complex surfaces, examining integrable structures, topology, and geometric properties in 4-dimensional manifolds with split-signature metrics.
Generalized Logarithmic Transformation in Exotic Spheres and Homotopy Hopf Manifolds
Explore generalized logarithmic transformations in topology, including $\star$-diagrams, spherical T-duality, and applications to exotic spheres and homotopy Hopf manifolds.
Spherical T-Duality Meets Exotic Spheres and Homotopy Hopf Manifolds
Explore spherical T-duality, its relation to 7-dimensional homotopy spheres, and implications for complex structures on exotic manifolds in this advanced mathematical discussion.
A Formula for the Circumference of an Ellipse
Explore the mathematical derivation of an approximate formula for calculating the circumference of an ellipse, including its historical context and practical applications.
Cohomological Donaldson-Thomas Invariants of 3-Manifolds - Part 2
Explore Morse homology of complex Chern-Simons functional, its connections to supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.
A Web of Spherical Functors in Toric Birational Geometry
Explore spherical functors in toric birational geometry, expanding on Aspinwall, Plesser and Wang's conjecture. Discover numerical and mirror symmetric evidence in this joint work with Ludmil Katzarkov.
The Langlands Program
Explore the Langlands Program, a grand unified theory of mathematics, with Professor Edward Frenkel. Discover connections between different mathematical fields and their profound implications.
Tangent Groupoid in Noncommutative Geometry - Lecture 5
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Tangent Groupoid in Noncommutative Geometry - Lecture 6
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Inverse Problems on Graphs with Geometric Deep Learning
Explores geometric deep learning for graph inverse problems, focusing on non-Euclidean geometries, physics-based approaches, and applications in particle physics and community detection.
Graduate Course on the Tangent Groupoid in Noncommutative Geometry - Lecture 4
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Koch Snowflake Fractal - Area and Perimeter Calculation
Explore the fascinating Koch Snowflake fractal, calculating its infinite perimeter and constant area. Suitable for ages 14+, with step-by-step construction instructions and in-depth mathematical analysis.
The Shape of Data
Exploring how topology can extract new insights from abundant data, focusing on innovative applications of abstract mathematics to deepen our understanding of complex datasets.
How Geometry Created Modern Physics
Explore the evolution of geometry from Euclid to Einstein, uncovering how post-Euclidean concepts revolutionized our understanding of spacetime and laid the foundation for modern physics.
The Story of Mathematical Proof - From Ancient Greece to Modern Logic
Explore the evolution of mathematical proof across number theory, geometry, topology, and logic, delving into the fascinating gap between natural and real numbers.