Swap, Shift and Trim to Edge Collapse a Flag Filtration
Exploring efficient algorithms for reducing flag filtrations in persistent homology, with focus on edge collapse techniques and their applications in computational topology.
Universes as Bigdata- From Geometry, to Physics, to Machine-Learning
Explore the intersection of string theory, geometry, and machine learning in physics, examining how AI aids mathematical research across various fields.
Julien Tierny - Principal Geodesic Analysis of Merge Trees and Persistence Diagrams
Computational framework for Principal Geodesic Analysis of merge trees, adapting PCA to Wasserstein metric space. Efficient algorithm for data reduction and dimensionality reduction in topological data analysis.
Teaching Neural Networks a Sense of Geometry
Explore Topological Data Analysis (TDA) and its intersection with machine learning to enhance neural networks' geometric reasoning abilities across various applications.
Computing Minimal Persistent Cycles - Polynomial and Hard Cases
Explores computing minimal persistent cycles in algebraic topology, discussing polynomial and NP-hard cases, and presenting algorithms for weak pseudomanifolds with applications to scientific data analysis.
Vanessa Robins - The Extended Persistent Homology Transform for Manifolds with Boundary
Explore extended persistent homology transform for shape analysis, offering finite distances between shapes with different Betti numbers and applications in shape clustering.
Ulrich Bauer - Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Rips Filtrations
Explore Gromov hyperbolicity, geodesic defect, and apparent pairs in Rips filtrations, extending Rips' results on contractibility and examining computational implications for persistent homology.
Computing Optimal Homotopies
Explore curve similarity measures and homotopy-based deformations in GIS, medical imaging, and graphics. Survey geometric and topological metrics, algorithms, and open questions in optimal homotopy computation.
Alpha Magnitude
Explores alpha magnitude, a new metric space invariant, its properties, and potential for estimating fractal dimensions in real-world datasets, offering computational advantages over existing methods.
Mathematical Games - Polygon Dissections - Episode 8
Explore mathematical games and puzzles involving polygon dissections with Ed Pegg Jr. Discover fascinating geometric concepts and their applications in this engaging presentation.
Hyperbolic Voronoi Percolation
Explore hyperbolic Voronoi percolation in this mathematical conference talk. Gain insights into non-Euclidean geometry and probability theory from expert Tobias Müller.
Toric Fiber Products in Geometric Modeling
Explore toric fiber products and their applications in geometric modeling, enhancing your understanding of advanced mathematical concepts in computer graphics.
On Canonical Parameterizations of 2D Shapes
Explore canonical parameterizations of 2D shapes, delving into mathematical concepts and applications in geometry and computer graphics.
Avoiding the General Position Condition When Computing the Topology of a Real Algebraic Plane Curve
Explore advanced techniques for computing real algebraic plane curve topology without relying on general position assumptions. Gain insights into innovative mathematical approaches.
Two Geometric Applications of the Linear Algebra Method
Explore geometric applications of linear algebra with János Pach, covering discrete geometry, convexity, and combinatorics in this research seminar.
Maximum Consensus Floating Point Solutions for Infeasible Low-Dimensional Linear Programs - Lecture
Explore a novel method for solving infeasible low-dimensional linear programs efficiently, using convex hull as an intermediate representation to improve performance in creating correctly rounded math libraries.
How Physics Solves Plateau's Problem - Applications in Math and 3D Graphics
Explore how physics and mean curvature flow solve Plateau's problem, with applications in mathematics, soap films, and 3D graphics. Discover connections between minimal surfaces and active research areas.
Random Separating Hyperplane Theorem and Learning Polytopes
Delve into advanced mathematical concepts of hyperplane theorem, polytope learning, and optimization oracles with applications in machine learning's hidden variable problems.
The Midpoint Hierarchy and Dynamics on a de Casteljau Bezier Polygon - Algebraic Calculus and dCB Curves 10
Explores midpoint hierarchy and particle dynamics on de Casteljau Bezier curves, focusing on t=1/2 value and quartic curves. Introduces discrete motion concepts like velocity and acceleration for control points.
De Casteljau's Algorithm and Splitting de Casteljau-Bézier Curves - Algebraic Calculus 2
Explore de Casteljau's algorithm for computing and splitting polynomially parametrized curves, with practical applications and theoretical insights using GeoGebra visualizations.
Reconstructing Manifolds by Weighted L_1-Norm Minimization
Innovative approach to shape reconstruction using weighted l_1-norm minimization, transforming triangulation into a convex optimization problem for smooth orientable manifolds in high-dimensional spaces.