#Riemann Surfaces

Dive into the cohomology of moduli spaces of curves with Hannah Larson. Explore tautological rings, compactifications, and the mysteries of non-tautological cohomology groups in algebraic geometry.

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1 Lesons

1 hour 3 minutes

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Commutative Algebra and Algebraic Geometry - 15th ALGA Meeting

Explore advanced topics in algebraic geometry and commutative algebra, including differential forms, Riemann surfaces, and foliations, with expert Jorge Vitório Pereira.

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15 Lesons

38 minutes

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Quantum Geometry of Fuchsian Systems - Lecture 2

Explore quantum geometry of Fuchsian systems in-depth, focusing on advanced concepts and applications in mathematical physics.

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1 Lesons

2 hours 3 minutes

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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.

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1 Lesons

35 minutes

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Volumes of Odd Strata of Quadratic Differentials

Explore volumes of odd strata of quadratic differentials in moduli spaces. Delve into combinatorics, dynamics, and geometry with insights from Elise Goujard's mathematical research.

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1 Lesons

55 minutes

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Superfícies de Riemann - Aula 18

Explore conceitos avançados de Superfícies de Riemann em uma aula de doutorado ministrada pelo Prof. Paulo Sad, aprofundando o conhecimento em geometria complexa.

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1 Lesons

1 hour 15 minutes

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Superfícies de Riemann - Aula 17

Aprofunde-se na teoria das Superfícies de Riemann com foco em tópicos avançados de doutorado, explorando conceitos complexos e suas aplicações na matemática pura.

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1 Lesons

1 hour 25 minutes

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Superfícies de Riemann - Aula 24

Aprofunde-se na teoria das Superfícies de Riemann com o Professor Paulo Sad, explorando conceitos avançados e aplicações em geometria complexa e topologia algébrica.

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1 Lesons

1 hour 24 minutes

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Imersões Conformes e Versão Conforme da Parametrização de Gauss - Aula 22

Explore conformal immersions and the conformal version of Gauss parameterization in this advanced mathematics lecture by Luis Florit.

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1 Lesons

1 hour 46 minutes

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Superfícies de Riemann - Aula 22

Explore conceitos avançados de Superfícies de Riemann em nível de doutorado, aprofundando-se na teoria matemática complexa e suas aplicações.

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1 Lesons

1 hour 15 minutes

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Superfícies de Riemann - Aula 21

Aprofunde-se na teoria das Superfícies de Riemann com o Professor Paulo Sad, explorando conceitos avançados e aplicações em geometria complexa e topologia algébrica.

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1 Lesons

1 hour 19 minutes

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Superfícies de Riemann - Aula 20

Aprofunde-se nas complexidades das Superfícies de Riemann nesta aula avançada de doutorado, explorando conceitos fundamentais e aplicações na geometria complexa.

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1 Lesons

1 hour 21 minutes

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Complex Dynamics and Character Varieties - Lecture 1

Explore complex dynamics and character varieties in mathematics, delving into advanced concepts and their applications in this comprehensive lecture.

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1 Lesons

1 hour 13 minutes

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An Introduction to Surfaces - Differential Geometry

Explore surfaces in differential geometry, covering orientability, algebraic and parametric surfaces, and examples like quadrics and the Oloid. Gain insights into this fundamental area of mathematics.

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10 Lesons

43 minutes

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Hyperbolic Geometry, Fuchsian Groups and Moduli Spaces - Lecture 1

Introducción a la geometría hiperbólica: modelos, propiedades y trigonometría. Exploración de los modelos del semiplano superior, disco y hiperboloide, con énfasis en geodésicas, ángulos y curvatura constante.

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27 Lesons

1 hour 22 minutes

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Introduction to Higgs Bundles - Lecture 1

Explore complex geometric concepts in Higgs bundles, including Riemann surfaces, theorems, and constructions. Gain insights into advanced mathematical topics through examples, exercises, and proofs.

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21 Lesons

1 hour 18 minutes

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Harmonic Maps Between Surfaces and Teichmüller Theory - Lecture 1

Explore harmonic maps between surfaces, their applications, and connections to Teichmüller theory in this advanced lecture on geometric analysis and complex geometry.

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24 Lesons

1 hour 18 minutes

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Hyperbolic Surfaces and Their Teichmüller Spaces - Lecture 2

Explore hyperbolic surfaces, Teichmüller spaces, and surface group representations. Delve into geometric structures, developing maps, and holonomy representations in this advanced mathematics lecture.

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28 Lesons

1 hour 11 minutes

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Andras Szenes- Intersection Cohomology of the Moduli Spaces of Stable Bundle II

Exploration of intersection cohomology in moduli spaces of semistable bundles on Riemann surfaces, featuring new formulas for intersection Betti numbers and geometric insights.

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1 Lesons

1 hour 1 minute

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Intersection Cohomology of the Moduli Spaces of Stable Bundle I

Explore intersection cohomology of semistable bundle moduli spaces on Riemann surfaces, including Decomposition Theorem analysis and new formula for intersection Betti numbers.

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1 Lesons

1 hour 1 minute

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Quantum Representations and Bogomolov-Katzarkov Surfaces

Exploring quantum representations and their application to Bogomolov-Katzarkov surfaces, addressing the Shafarevich conjecture on holomorphic convexity in algebraic geometry.

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1 Lesons

1 hour 11 minutes

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Mirrors of Curves and Their Fukaya Categories II

Exploración avanzada de la simetría especular homológica para curvas, enfocándose en la geometría simpléctica de sus espejos y las categorías de Fukaya. Incluye discusiones sobre modelos de Landau-Ginzburg y geometría tropical.

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1 Lesons

1 hour 2 minutes

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Geometry of Moduli Spaces of Curves - Lecture 4

Explore geometric aspects of moduli spaces of curves with O. Tommasi. Delve into advanced mathematical concepts and their applications in this comprehensive lecture from the ICTP Summer School.

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1 Lesons

1 hour 31 minutes

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Geometry of Moduli Spaces of Curves - Lecture 1

Explore geometric aspects of moduli spaces of curves with O. Tommasi. Delve into advanced mathematical concepts and their applications in this comprehensive lecture from the Summer School.

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1 Lesons

1 hour 27 minutes

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Tautological Rings of Moduli Spaces of Curves - Lecture 3

Explore advanced concepts in algebraic geometry, focusing on tautological rings and their relation to moduli spaces of curves in this in-depth mathematical lecture.

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1 Lesons

1 hour

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More Deformations of the Cohomology Ring of the Moduli Space of Representations

Explore deformations of cohomology rings in representation spaces of Riemann surfaces, examining algebraic, geometric, and physical perspectives on this rich mathematical topic.

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1 Lesons

1 hour 5 minutes

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Hausdorff Center for Mathematics

Raf Bocklandt: Deforming Dimers

Explore deformation theory of dimer models, their relation to mirror symmetry for Riemann surfaces, and various aspects illustrated with examples.

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1 Lesons

1 hour 9 minutes

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Mathemaniac

What Do Complex Functions Look Like - Essence of Complex Analysis

Explore complex functions through vivid visualizations, covering addition, multiplication, exponentiation, power functions, and logarithms. Delve into branch cuts, Riemann surfaces, and 4D rotations with engaging animations.

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10 Lesons

29 minutes

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Sphere Geometry and Complex Analysis - Algebraic Topology Lecture 4

Explore advanced concepts in sphere geometry, including inversive geometry, Riemann sphere, complex analysis, and projective lines, enhancing understanding of algebraic topology.

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8 Lesons

41 minutes

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Complex Numbers and Curves in 19th Century Mathematics

Explore complex numbers, algebraic curves, and their intersection with projective geometry and topology. Discover how these concepts revolutionized 19th-century mathematics and laid the foundation for modern algebraic geometry.

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1 Lesons

58 minutes

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Introduction to Topology in Mathematics History

Explore topology's historical development, from Euler's polyhedron discoveries to Poincaré's insights. Learn about key concepts like Euler characteristic, Riemann surfaces, and surface classification in this mathematical journey.

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11 Lesons

56 minutes

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Dimers and M-curves: Limit Shapes from Riemann Surfaces

Explore dimer models, M-curves, and limit shapes through algebraic geometry, integrating Riemann surfaces and Schottky uniformization. Gain insights into statistical mechanics and discrete geometry.

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1 Lesons

53 minutes

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Symplectic Geometry of Teichmueller Spaces for Surfaces with Boundary - Lecture 1

Explore symplectic geometry of Teichmueller spaces for surfaces with boundary in this advanced mathematics lecture by Eckhard Meinrenken from the University of Toronto.

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1 Lesons

52 minutes

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Symplectic Geometry of Teichmueller Spaces for Surfaces with Boundary - Lecture 2

Explore symplectic geometry of Teichmueller spaces for surfaces with boundary in this advanced mathematics lecture by Eckhard Meinrenken, part of a workshop on operator algebras and non-commutative geometry.

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1 Lesons

51 minutes

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Symplectic Geometry of Teichmueller Spaces for Surfaces with Boundary - Lecture 3

Explore symplectic geometry of Teichmueller spaces for surfaces with boundary in this advanced mathematics lecture by Eckhard Meinrenken, part of a workshop on operator algebras and non-commutative geometry.

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1 Lesons

57 minutes

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Hausdorff Center for Mathematics

Constructing Polylogarithms on Higher-Genus Riemann Surfaces

Generalization of elliptic polylogarithms to higher-genus Riemann surfaces, exploring homotopy-invariant iterated integrals, modular tensors, and connections to Enriquez-Zerbini polylogarithms and Fay identities.

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1 Lesons

1 hour 3 minutes

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Hausdorff Center for Mathematics

Numerical Approach to Polylogarithms on Higher-Genus Riemann Surfaces

Explore numerical evaluation of polylogarithms on genus-two Riemann surfaces using Schottky parametrization and averaging over genus-one differential forms, advancing particle physics research.

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1 Lesons

1 hour 4 minutes

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Cohomology Rings of Character Varieties

Explore cohomology rings of character varieties, including P=W conjecture proof and zero-dimensional COHA computation. Discover connections to Hilbert scheme of C^2 for punctured sphere case.

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1 Lesons

1 hour 3 minutes

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Components of Higgs Bundle Moduli Spaces - A Legacy of Hitchin's Ideas

Explore Higgs bundle moduli spaces, their components, and the lasting impact of Hitchin's groundbreaking ideas in this mathematical lecture by Steven Bradlow.

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1 Lesons

48 minutes

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Geometry of Dimer Models

Explore the asymptotic phenomena of random dimer coverings on large planar graphs, focusing on Aztec diamonds and their connection to Riemann surface geometry in this advanced mathematics lecture.

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1 Lesons

55 minutes

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Canonical Metrics on Holomorphic Bundles

Explore canonical metrics on holomorphic bundles with renowned mathematician Shing-Tung Yau, delving into advanced geometric analysis and complex differential geometry.

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1 Lesons

48 minutes

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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Discrete Conformal Geometry of Polyhedral Surfaces - Part I

Explore discrete conformal geometry of polyhedral surfaces, focusing on curvature and rigidity concepts in non-Riemannian geometry.

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1 Lesons

51 minutes

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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Higher Rank Voronoi Decompositions and Metric Degenerations of Tori

Explore higher rank Voronoi decompositions and their applications in studying asymptotic geometry of Riemann surfaces and moduli spaces.

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1 Lesons

47 minutes

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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Schmutz-Thurston Duality in Mapping Class Group-Equivariant Cell Decompositions

Explore mapping class group-equivariant cell decompositions of Teichmueller space, focusing on Schmutz and Thurston's work for closed compact surfaces without marked points.

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1 Lesons

51 minutes

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A Summary of Methods for Solving Differential Equations Involving Automorphic Forms

Explore advanced techniques for solving differential equations with automorphic forms, enhancing mathematical problem-solving skills in complex analysis and number theory.

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1 Lesons

1 hour

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M-Seminar, Kansas State University

Skeins, Clusters and Wavefunctions in Open Gromov-Witten Theory

Explore open Gromov-Witten theory and skein-theoretic cluster theory in computing wavefunctions for Lagrangian branes, as presented by Gus Schrader from Northwestern University.

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1 Lesons

1 hour 23 minutes

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NCCR SwissMAP

Top Weight Cohomology of M_{g,n} and the Handlebody Group

Explore top weight cohomology of M_{g,n} and its connection to the handlebody group in algebraic topology and Grothendieck-Teichmüller theory.

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1 Lesons

51 minutes

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Renzo Ricca

Riemann, Topology and Physics 2 - Lecture 2

Explore advanced concepts in theoretical physics, focusing on Riemann geometry, topology, and their applications in physics.

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1 Lesons

1 hour 25 minutes

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Translation Surfaces and Dynamics on Moduli Spaces - Part 2

Explore advanced concepts in translation surfaces and dynamics on moduli spaces, building upon previous knowledge to deepen understanding of mathematical theories and applications.

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1 Lesons

1 hour 18 minutes

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Translation Surfaces and Dynamics on Moduli Spaces - Part 1

Explore translation surfaces and dynamics on moduli spaces in this advanced mathematical lecture. Delve into complex geometric concepts and their applications in surface dynamics.

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1 Lesons

1 hour 27 minutes

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Translation Surfaces and Dynamics on Moduli Spaces - Part 3

Explore advanced concepts in translation surfaces and dynamics on moduli spaces. Delve into complex mathematical theories presented by Ferrán Valdez in this comprehensive lecture.

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1 Lesons

1 hour 32 minutes

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Topology of Horocyclic Flow on Geometrically Infinite Surfaces - Part 2

Explore advanced concepts in horocyclic flow topology on geometrically infinite surfaces, building upon previous knowledge and delving into complex mathematical theories.

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1 Lesons

1 hour 34 minutes

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Introduction to Topological Recursion - Lecture 2

Explore advanced concepts in topological recursion, delving into mathematical theories and applications. Gain insights into complex mathematical structures and their relationships.

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1 Lesons

2 hours 31 minutes

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Introduction to Topological Recursion - Lecture 1

Explore fundamental concepts and applications of topological recursion in mathematics, focusing on its role in geometry, physics, and combinatorics.

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1 Lesons

2 hours 37 minutes

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Reducible Topological Recursion - Lecture 2

Explore advanced concepts in reducible topological recursion, building on previous knowledge and delving into complex mathematical theories and applications.

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1 Lesons

1 hour 56 minutes

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Moduli Space of Curves and Its Intersection Theory - Lecture 2

Explore advanced concepts in algebraic geometry, focusing on moduli spaces of curves and their intersection theory in this in-depth lecture.

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1 Lesons

1 hour 53 minutes

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Reducible Topological Recursion - Lecture 1

Explore reducible topological recursion with Reinier Kramer, delving into advanced mathematical concepts and their applications in this comprehensive lecture.

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1 Lesons

1 hour 56 minutes

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Super Topological Recursion - Lecture 1

Explore super topological recursion with Kento Osuga in this comprehensive lecture, delving into advanced mathematical concepts and their applications.

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1 Lesons

1 hour 54 minutes

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Moduli Space of Curves and Its Intersection Theory - Lecture 1

Explore the moduli space of curves and its intersection theory in this advanced mathematical lecture by Nitin Kumar Chidambaram.

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1 Lesons

1 hour 51 minutes

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Isoresidual Fibration: At the Crossroads of Complex Analysis, Flat Geometry and Combinatorics

Explore the intersection of complex analysis, flat geometry, and combinatorics through isoresidual fibration. Gain insights into moduli spaces and geometric structures on surfaces.

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1 Lesons

48 minutes

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Algebraic Curves and Minimal Surfaces

Explore algebraic curves and minimal surfaces with Prof. Sebastian Heller, delving into Riemann surfaces, harmonic maps, and experimental mathematics.

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1 Lesons

51 minutes

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Symplectic Topology, Stability Conditions and Quadratic Differentials

Explore connections between symplectic topology, stability conditions, and quadratic differentials in Fukaya categories and mapping class groups.

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1 Lesons

1 hour 42 minutes

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Symplectic Topology, Stability Conditions and Quadratic Differentials

Explore connections between symplectic topology, stability conditions, and quadratic differentials in Fukaya categories and mapping class groups.

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1 Lesons

1 hour 42 minutes

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Rigidity and Multiplicity of Singularities Associated to Ample Vector Bundles

Explore rigidity and multiplicity of singularities in ample vector bundles, focusing on irreducible desingularization and multiplicity formulas for isolated singularities.

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1 Lesons

59 minutes

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Banach Center

Boundary Behaviour of Universal Covering Maps and Applications

Explore boundary behavior of universal covering maps and their applications in mathematics, focusing on advanced topological concepts.

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1 Lesons

54 minutes

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Topology of Horocyclic Flow on Geometrically Infinite Surfaces - Part 1

Explore the topology of horocyclic flow on geometrically infinite surfaces through an in-depth mathematical analysis. Gain insights into advanced concepts in surface dynamics and geometry.

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1 Lesons

1 hour 40 minutes

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Topology of Horocyclic Flow on Geometrically Infinite Surfaces - Part 3

Explore advanced topology concepts in horocyclic flow on geometrically infinite surfaces, building on previous parts of the series. Gain insights into complex mathematical theories and applications.

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1 Lesons

1 hour 36 minutes

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Machine Learning the Landscape - Lecture 1

Explore machine learning in string theory landscape, covering Calabi-Yau manifolds, cohomology, and string phenomenology. Gain insights into complex geometries and their applications in theoretical physics.

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25 Lesons

1 hour 47 minutes

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Spinor-valued Higgs Bundles - Theory and Applications

Explore spinor-valued Higgs bundles with Nigel Hitchin, examining their unique properties and implications for Riemann surface geometry. Gain insights into Dirac equations and vector bundle theory.

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1 Lesons

1 hour 14 minutes

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Dimers on a Riemann Surface and Compactified Free Field

Explore dimer models on Riemann surfaces, height function convergence, and connections to compactified free fields. Gain insights into probabilistic methods and discrete complex analysis in statistical mechanics.

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1 Lesons

47 minutes

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Minimal Bipartite Dimers and Maximal Riemann Surfaces

Exploration of critical weights for dimer models on isoradial graphs, extending Kenyon's results using theta functions on maximal Riemann surfaces, with applications to spectral theorems and Laplacians.

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1 Lesons

52 minutes

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Modular Forms and String Theory - Lecture 3

Explore connections between modular forms and string theory, delving into advanced mathematical concepts and their applications in theoretical physics.

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1 Lesons

1 hour 39 minutes

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Modular Forms and String Theory - Lecture 2

Explore connections between modular forms and string theory, delving into advanced mathematical concepts and their applications in theoretical physics.

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1 Lesons

1 hour 45 minutes

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Modular Forms and String Theory - Lecture 1

Explore the intricate connection between modular forms and string theory in this advanced physics lecture, delving into mathematical foundations and theoretical applications.

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1 Lesons

1 hour 28 minutes

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Liouville Theory: From Segal's Axioms to Conformal Blocks - 2023

Explorez la théorie de Liouville, des axiomes de Segal aux blocs conformes, dans cette conférence approfondie sur la physique théorique et la géométrie conforme.

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1 Lesons

1 hour 15 minutes

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Quantum Geometry of Fuchsian Systems - Lecture 1

Explore quantum geometry of Fuchsian systems, delving into advanced mathematical concepts and their applications in theoretical physics.

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1 Lesons

1 hour 48 minutes

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Renzo Ricca

Riemann, Topology and Physics - Lecture 1

Explore interdisciplinary connections between Riemann geometry, topology, and physics in this doctoral-level lecture by Renzo Ricca at Beijing Institute of Technology.

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1 Lesons

1 hour 15 minutes

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Institute for Advanced Study

Plumber's Algebra Structure on Symplectic Cohomology

Delve into advanced symplectic geometry concepts, exploring Plumber's PROP structures, nodal Riemann surfaces, and their applications to cohomological field theories and curve counting methods.

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1 Lesons

1 hour 4 minutes

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Institute for Advanced Study

Gap in Critical Exponent in Teichmuller Dynamics

Delve into advanced Teichmuller dynamics, exploring SL_2(R) actions on moduli spaces and the critical exponent properties of stabilizer subgroups in relation to lattice structures.

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1 Lesons

1 hour 19 minutes

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Geometry of Dimer Models - ICBS 2024

Explore asymptotic phenomena in random dimer coverings, focusing on Aztec diamonds and their connection to Riemann surface geometry.

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1 Lesons

1 hour 3 minutes

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Geometry of Dimer Models - ICBS 2024