The Sharp Threshold for Making Squares
Explores the threshold for finding perfect square products in random integer sequences, combining number theory and probabilistic combinatorics to prove a conjecture on this sharp threshold.
Langevin Monte Carlo: Randomized Midpoint Method Revisited
Explore advanced Langevin Monte Carlo techniques, focusing on the Randomized Midpoint method's superior sampling error guarantees and recent improvements for high-dimensional target distributions.
Causal Effect Identification from Multiple Incomplete Data Sources
Explore causal effect identification using do-calculus search algorithms, addressing complex data scenarios like missing data and context-specific independence in causal inference.
What's the Point of Mathematics? - Mathematical Modeling Applications
Explore the real-world applications and significance of mathematics with Dr. Nira Chamberlain, a renowned expert in mathematical modeling across various industries.
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.
Building the Universe with Mathematics
Explore how mathematics can design our universe, from numbers to multidimensional concepts. Discover the progression of ideas that shape existence, including geometry, algebra, infinity, and relativity.
Mysterious Numbers - Unlocking the Secrets of the Universe
Explore extraordinary numbers in physics with Tony Padilla, uncovering fundamental truths about black holes, holographic reality, and the cosmological constant through unusually big, small, and infinite numbers.
How to Make the World Add Up - Navigating Disinformation with Data Analysis
Explore the world of data analysis and disinformation with economist Tim Harford, learning to critically evaluate statistics and uncover truth in a world of misleading numbers.
Pushing the Limits of Human Mobility
Explore biomechanics and cutting-edge technology for enhancing human movement. Learn how computer simulations and smart sensors are revolutionizing mobility and athletic performance.
How to Think Like a Mathematician - Applying Logic to Real-World Situations
Discover how mathematical thinking can enhance clarity in everyday situations, from fake news to privilege, using logic and precise reasoning to navigate complex issues.
Rendering a Sphere Using Ray Tracing - Ray Tracing Series
Learn to render a sphere using ray tracing techniques in C++. Covers creating a Renderer class, structuring code like a pixel shader, and implementing sphere rendering with optimized performance.
What We Cannot Know - Exploring the Limits of Human Knowledge
Explore the limits of human knowledge with mathematician Marcus du Sautoy as he investigates whether we can ever know everything or if some fields will always remain beyond our comprehension.
How Science is Taking the Luck out of Gambling
Explore the scientific strategies behind successful gambling, from sports forecasting to AI poker players. Learn how betting has influenced mathematics, economics, and artificial intelligence.
Cohomological Donaldson-Thomas Invariants of 3-Manifolds
Explore Morse homology of complex Chern-Simons functional, its connections to 4D supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.
Ernesto Lupercio, CINVESTAV - Stringy Motives
Explore the localization principle for orbifolds in this advanced mathematical survey, featuring joint research on stringy motives and their applications.
On Mapping Class Groups of Non-Orientable Surfaces
Exploración de la estructura y cohomología de grupos de clases de mapeo en superficies no orientables, incluyendo resultados recientes sobre el plano proyectivo y la botella de Klein.
Eduardo Gonzalez- Quantum Cohomology, Seidel Elements, Shift Operators & Coulomb Branches
Explore advanced mathematical concepts in quantum cohomology, Seidel elements, and Coulomb branches. Discover the interplay between equivariant cohomology and symplectic homology in Lie group manifolds.
String Diagrams for Structural Causal Modeling and Inference
Explore structural causal modelling and inference using string diagrams, a powerful visual tool for understanding complex causal relationships in data analysis.
Scaling and Fractals After Mandelbrot - On the Frontiers of the Geosciences - Part 1
Explore scaling and fractals in geosciences, building on Mandelbrot's work. Discover cutting-edge applications and insights at the frontiers of Earth and space sciences.
Fractals and Multifractals in Geophysics - Lorenz Lecture
Explore fractals and their applications in geophysics with renowned mathematician Benoit Mandelbrot in this historic AGU Fall Meeting lecture from 2001.