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#Hyperbolic Surfaces

Showing: 22 courses
Centre de recherches mathématiques - CRM

The Moduli Space of Twisted Laplacians and Random Matrix Theory

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Explore the convergence of spectral number variance for twisted Laplacians to random matrix theory ensembles, extending Rudnick's work to break time-reversal symmetry and include Dirac operators.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Goe and Gue Statistics for Random Covers of Hyperbolic Surfaces

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Explore Goe and Gue statistics for random covers of hyperbolic surfaces, delving into spectral geometry, semiclassical problems, and trace formulas.
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12 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Insights into Mathematics

Non-Euclidean Geometry - Math History - NJ Wildberger

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Explore the complex history and modern interpretations of non-Euclidean geometry, challenging traditional narratives and proposing new perspectives on this fundamental mathematical concept.
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8 Lesons
51 minutes
On-Demand
Free-Video
IMSA

Best Lipschitz Maps and Transverse Measures - Lecture 1

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Exploration of best Lipschitz maps between hyperbolic surfaces, infinity harmonic maps, and transverse measures. Discusses approximation methods, geodesic laminations, and connections to Teichmüller theory and geometric topology.
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1 Lesons
56 minutes
On-Demand
Free-Video
IMSA

Best Lipschitz Maps and Transverse Measures - Part 2

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Explores best Lipschitz maps between hyperbolic surfaces, focusing on approximation methods, transverse measures, and their connection to infinitesimal earthquakes in Teichmüller theory.
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1 Lesons
55 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Lecture 4

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Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
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1 Lesons
46 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Part II

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Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
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1 Lesons
54 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Anti-de Sitter Geometry and Applications to Hyperbolic Surfaces - Part I

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Explore Anti-de Sitter geometry and its applications to hyperbolic surfaces in this advanced mathematics lecture by Andrea Seppi.
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1 Lesons
47 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Combinatorial Maps and Hyperbolic Surfaces in High Genus

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Explore combinatorial maps and hyperbolic surfaces in high genus through Baptiste Louf's insightful conference talk, delving into advanced mathematical concepts and their applications.
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1 Lesons
48 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

The Geometry of Random Genus-0 Hyperbolic Surfaces via Trees

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Explore the geometry of random genus-0 hyperbolic surfaces through tree structures in this advanced mathematical lecture by Timothy Budd.
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1 Lesons
58 minutes
On-Demand
Free-Video
Institute for Advanced Study

Spectral Gap of the Laplacian for Random Hyperbolic Surfaces

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Explore spectral gap of Laplacian for random hyperbolic surfaces in large genus limit. Delve into Weil-Petersson measure, Mirzakhani's work, and trace method applications.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Big Ideas In Dynamics

Bowditch Representations and Dynamics on Character Varieties - Part 2

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Explore advanced concepts in geometric group theory, focusing on mapping class group actions on character varieties and domains of discontinuity for various surfaces and Lie groups.
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1 Lesons
59 minutes
On-Demand
Free-Video
Institut Henri Poincaré

On the Spectral Gap of the Laplacian for Random Hyperbolic Surfaces

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Explorez le comportement spectral du laplacien sur des surfaces hyperboliques aléatoires, en mettant l'accent sur l'écart spectral dans la limite des grands genres.
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1 Lesons
59 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Divisible Convex Sets with Properly Embedded Cones

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Explore divisible convex sets, their theory, and new examples in projective geometry. Delve into connections with dynamical systems, geometric group theory, and Riemannian geometry.
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9 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Equidistribution of Periodic Tori

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Explore equidistribution of periodic tori in higher rank Lie groups, extending Bowen and Margulis' work on closed geodesics in hyperbolic surfaces.
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1 Lesons
1 hour
On-Demand
Free-Video
Institute for Advanced Study

Spectral Gap of the Laplacian for Random Hyperbolic Surfaces - Part 2

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Explore spectral gap of Laplacian for random hyperbolic surfaces using trace method and asymptotic expansions in large genus limit. Analyze Weil-Petersson measure and Friedman-Ramanujan property.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Topological Recursion: A Recursive Way of Counting Surfaces

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Explore topological recursion for enumerating surfaces in combinatorics, geometry, and physics. Learn how this universal method links to integrable systems and random matrices.
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1 Lesons
55 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Linear Programming Bounds for Hyperbolic Surfaces

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Explore new upper bounds on geometric and spectral invariants of closed hyperbolic surfaces using the Selberg trace formula and linear programming techniques.
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1 Lesons
57 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Linear Programming Bounds for Hyperbolic Surfaces - Seminar on Spectral Geometry

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Explore linear programming bounds for hyperbolic surfaces, examining closed geodesics and Laplace eigenvalues. Gain insights into quantitative behavior and predominance in Riemannian metrics.
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1 Lesons
1 hour
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Towards an Optimal Spectral Gap Result for Random Compact Hyperbolic Surfaces

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Explore recent progress in proving near-optimal spectral gaps for hyperbolic surfaces. Delve into trace methods, challenges, and new tools developed to improve bounds in spectral geometry.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Efficiently Chopping a Hyperbolic Surface in Two - Cheeger Constants and Spectral Geometry

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Explore the Cheeger constant of hyperbolic surfaces, its relation to spectral gaps, and recent findings on its upper bound for large genus surfaces. Gain insights into cutting Riemannian manifolds efficiently.
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10 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Spectral Gap for Random Schottky Surfaces

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Delve into advanced mathematical concepts exploring spectral gaps in random Schottky surfaces, examining the behavior of Laplace eigenvalues and their relationship to hyperbolic geometry and probability theory.
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1 Lesons
1 hour
On-Demand
Free-Video