Classical Spherical Trigonometry - Universal Hyperbolic Geometry
Comprehensive overview of classical spherical trigonometry, covering key concepts, laws, and theorems. Introduces a new algebraic approach to simplify and enhance the traditional framework.
Non-escape of Mass for Arithmetic Quantum Limits on Hyperbolic 4-Manifolds
Explore the intricacies of the Arithmetic Quantum Unique Ergodicity (AQUE) conjecture in this advanced mathematics seminar. Delve into the groundbreaking research on non-escape of mass for Hecke-Maass cusp forms on congruence quotients of hyperbolic 4-sp…
Non-escape of Mass for Arithmetic Quantum Limits on Hyperbolic 4-Manifolds
Explore non-escape of mass for Hecke-Maass cusp forms on hyperbolic 4-manifolds, addressing challenges in unbounded Hecke relations and utilizing quaternionic matrices for unique factorization.
MetaHKG: Meta Hyperbolic Learning for Few-shot Temporal Reasoning - M1.2
Explore meta hyperbolic learning for few-shot temporal reasoning in knowledge graphs, enhancing reasoning capabilities with limited data.
Floating Bodies and Duality in Spaces of Constant Curvature
Explores p-affine surface area and floating bodies in curved spaces, extending Meyer & Werner's Euclidean results to spherical and hyperbolic geometries. Examines limiting behavior as curvature approaches zero.
Anti de Sitter - Class 2
Explore Anti de Sitter space in theoretical physics with Pedro Vieira, delving into advanced concepts and applications in this comprehensive lecture.
Plongements du Disque de Poincaré dans l'Espace Ambiant - Partie III
Découvrez la construction explicite d'un plongement isométrique C^1 du disque de Poincaré, explorant ses propriétés surprenantes et son importance en géométrie hyperbolique.
Plongements du Disque de Poincaré dans l'Espace Ambiant - Partie I
Découvrez la construction explicite d'un plongement isométrique C^1 du disque de Poincaré, explorant ses propriétés surprenantes et son importance en géométrie hyperbolique.
Plongements du Disque de Poincaré dans l'Espace Ambiant - Partie II
Explorez la construction explicite d'un plongement isométrique C^1 du disque de Poincaré, découvrant ses propriétés surprenantes et son importance en géométrie hyperbolique.
Les mondes mathématiques de Maryam Mirzakhani - Espaces de formes
Explorez les contributions révolutionnaires de Maryam Mirzakhani aux espaces de formes et à la géométrie, présentées par Pascal Hubert.
From Hyperbolic Geometry to Data Clustering
Explore how hyperbolic geometry and knot theory inspire innovative data clustering algorithms, bridging abstract mathematics with practical data science applications.
Anti-holomorphic Dynamical Systems on a Torus - Applications to Weierstrass Functions
Explore complex dynamics through anti-holomorphic systems on a torus, examining Weierstrass zeta-functions and their applications to Green functions and constant curvature metrics.
Ergodicity and Horocycle Ergodic Averages on Compact Spaces - Lecture 2
Delve into ergodic and mixing properties of horocycle flows, exploring their time-changes, asymptotics, and fundamental mathematical concepts in dynamical systems theory.
On the Dani Correspondence and Its Applications - Lecture 2
Delve into Diophantine approximation through ergodic theory, exploring the Dani correspondence and its dynamic interpretation of rational number density in the real line.
Ergodic and Mixing Properties of Horocycle Flows - Lecture 1
Delve into the mathematical foundations of horocycle flows and their time-changes, exploring ergodic theory, mixing properties, and applications in hyperbolic geometry through advanced theoretical concepts.
Time-Changes: Definitions, Basic Facts, Ergodicity and Mixing - Lecture 4
Delve into ergodic and mixing properties of horocycle flows, exploring time-changes, their parabolic behavior, and fascinating phenomena in dynamical systems and mathematical physics.
Mixing and Equidistribution in Horocycle Flows - Lecture 3
Delve into ergodic theory and mixing properties of horocycle flows, exploring their smooth time-changes, rigidity theorems, and applications beyond SL2(R) in dynamical systems.
Beyond SL2(R): Time-Changes and Other Perturbations in Different Settings - Lecture 6
Delve into advanced mathematical concepts of horocycle flows, exploring their ergodic properties, mixing phenomena, and applications beyond SL2(R) in dynamical systems theory.
Rigidity and Ratner's Rigidity Theorem in Horocycle Flows - Lecture 5
Delve into the rigidity theory of horocycle flows, exploring Ratner's Rigidity Theorem and its implications for dynamical systems in hyperbolic geometry and ergodic theory.
The Classification of Platonic Solids I - Universal Hyperbolic Geometry
Exploring the classification of Platonic solids using modern notation and turn angles. Examines planar, spherical, and higher-dimensional cases, highlighting mathematical constructions and challenges in Euclid's proof.
Petrie Polygons of a Polyhedron - Universal Hyperbolic Geometry
Explore Petrie polygons on polyhedra, focusing on Platonic solids. Learn about tesselations, Schlafli symbols, and orthogonal projections in this geometric journey.