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Explore topological methods like persistent homology and mapper, and their applications in computer vision, biology, and medicine. Learn how these techniques enhance traditional machine learning approaches.
Explorez les capacités symplectiques, la conjecture isopérimétrique de Viterbo et les variétés de contact dont toutes les orbites de Reeb sont fermées dans cette présentation de géométrie symplectique.
Explore algebraic geometry theory behind metric limits of Ricci positive Kähler–Einstein manifolds and the solution to Li-Xu's Stable Degeneration Conjecture in complex algebraic varieties.
Exploración de coorientaciones en geometrÃa algebraica real, examinando intersecciones de variedades reales y complejas, y sus implicaciones para números de enlace y clases de cohomologÃa.
Explore continuous maps between spheres, their abelian group structures, and connections to key problems in topology like Hopf and Kervaire invariants and smooth structures on spheres.
Explore mathematical structures in generative linguistics, from formal languages to Hopf algebras and geometric spaces, and their applications in modeling language production, parsing, and variation.
Explore techniques for existence, regularity, and singularity formation in geometric problems, focusing on harmonic maps, Yang-Mills connections, and nematic liquid crystals. Discover new gluing methods for parabolic flows.
Explore Arnold's group-theoretic approach to ideal hydrodynamics and its applications to vortex sheets, fluids with moving boundaries, and multiphase fluids using Lie groupoid symmetries.
Explore uniform volume doubling on Lie groups and its impact on functional inequalities, focusing on SU(2) and related structures. Learn about heat kernel estimates and measure contracting property.
Explore mathematical properties of black holes, focusing on stability as solutions to Einstein's equation and recent proof of nonlinear stability for slowly rotating Kerr black holes.
Exploración de la simetrÃa especular 3D en teorÃa cuántica de campos y sus conexiones con geometrÃa algebraica, topologÃa simpléctica y teorÃa de representación geométrica. Análisis de dualidades y categorÃas 2D.
Explore exotic phenomena in 4D topology, focusing on submanifold embeddings that survive stabilizations. Discover insights into topological vs. smooth categories and their implications for 4-manifold structures.
Explore Audin's conjecture and its generalization to Liouville manifolds, examining moduli spaces of punctured holomorphic discs and their relation to string topology operations.
Explore optical properties of conics, billiard reflections, and geometric consequences. Discover classic results, Ivory's lemma, Poncelet Porism, and related theorems in this mathematical journey.
Explore the interplay between hyperbolic geometry and homology cobordism in low-dimensional topology, focusing on monopole Floer homology and its applications to hyperbolic homology spheres.
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