Functional Inequalities and Improvements: Stability - Part 1
Explore functional inequalities, their applications, and recent developments in stability theory. Learn strategies for optimizing constants and functions in various mathematical fields.
Mixed Hodge Structures Attached to Hybrid Landau–Ginzburg Models
Explores mixed Hodge structures in Landau-Ginzburg models, focusing on functorial behavior and a new spectral sequence relating decomposed functions, with applications in mirror symmetry.
Discriminants and Toric Birational Geometry
Explore Gorenstein toric singularities, B-side categories in toric homological mirror symmetry, and GKZ hypergeometric D-modules. Discover the conjectural construction of associated spherical functors.
Non-Archimedean Quantum K-Theory and Gromov-Witten Invariants
Explore non-archimedean geometry's role in Gromov-Witten invariants, focusing on derived approaches, K-theory, and motivic cohomology. Learn about geometric relations and their implications for numerical invariants.
Compactification of Moduli Spaces of Quantum Toric Stacks
Explores moduli spaces of quantum toric stacks and their compactification, extending toric varieties to stacky generalizations with finitely generated subgroups of R^d as "lattices".
The Mirror Clemens-Schmid Sequence
Explore a four-term exact sequence in cohomology, its relation to filtrations, and a proposed mirror to the Clemens-Schmid sequence, with applications in K3 surface settings.
Homotopy Path Algebras
Explore Homotopy Path Algebras and their applications in algebraic topology, sheaf theory, and toric geometry. Discover connections to homological mirror symmetry and recent developments in the field.
Calculus 1 - Lines, Angle of Inclination, and the Distance Formula
Explore fundamental concepts of lines, inclination angles, and distance calculations in this comprehensive lecture, laying the groundwork for advanced calculus topics.
Calculus 3 - TNB (Frenet-Serret) Frames, Curvature, Torsion, Encapsulation
Explore TNB Frames, curvature, and torsion in vector calculus. Learn to compute Frenet-Serret frames, find osculating circles and planes, and perform vector encapsulation for 2D functions.
Mandelbulbs - The Search for a 3D Mandelbrot Fractal
Explore the fascinating world of 3D fractals, from natural examples to complex mathematical constructs like Mandelbulbs, with insights into fractal dimensions and generation techniques.
Finding the Equation of a Line From Two Points
Learn to derive a line equation from two points without explicit slope, mastering a fundamental algebraic skill for graphing and problem-solving.
Finding Equations of Parallel and Perpendicular Lines
Learn to determine equations for lines parallel or perpendicular to a given line, enhancing your understanding of linear relationships in algebra and geometry.
Graphing Lines by Solving for Y and Plotting Points
Learn efficient techniques for graphing lines by solving for y and plotting points, building on previous concepts to develop more elegant graphing methods.
Formulas for Circles, Cylinders, and Rectangular Prisms - Boxes
Learn essential formulas for calculating area, volume, and surface area of circles, cylinders, and rectangular prisms, with clear explanations and practical applications.
Fermat's Christmas Theorem - Visualising the Hidden Circle in Pi/4 = 1-1/3+1/5-1/7+...
Uncover the hidden circle in Leibniz's pi formula through geometric visualization. Explore the surprising connection between pi and odd numbers in this engaging mathematical journey.
Toroflux Paradox - Making Things Disappear with Math
Explore geometric paradoxes and mathematical illusions, including the Toroflux paradox, Cassini's Fibonacci identity, and the Get-off-the-Earth puzzle. Learn the math behind visual tricks and disappearing acts.
The Fix-the-Wobbly-Table Theorem
Explore the fascinating wobbly table theorem, its history, and mathematical proof. Learn how rotating rectangular tables can stabilize them on uneven surfaces, with insights into the underlying principles.
Visualising Pythagoras - Ultimate Proofs and Crazy Contortions
Explore visually stunning Pythagorean proofs and related theorems, including unique variations and lesser-known facts, in this engaging mathematical journey.
Laurent Saloff-Coste - Breaking Heat Kernel Estimates Into Pieces
Breaking heat kernel estimates on Riemannian manifolds by analyzing pieces separately and reconstructing the whole. Explores Brownian motion within segments and transitions between them.
Homotopy Patterns in Group Theory
Explore homotopy patterns in group theory, delving into advanced mathematical concepts and their applications in topology and algebra.
The Horocycle Flow on the Moduli Space of Translation Surfaces
Explore the intricate dynamics of horocycle flows on translation surface moduli spaces, delving into mathematical concepts and their applications in geometry and dynamical systems.