Riemann Surfaces Courses and Certifications

Hausdorff Center for Mathematics

Perverse Sheaves and Schobers on Riemann Surfaces - Tobias Dyckerhoff

Explore derived constructible categories on stratified Riemann surfaces, t-structures, Verdier duality, and categorified perverse sheaves with applications in algebraic geometry and topology.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

BIMSA

Intersection Theory on Moduli Space of Super Riemann Surfaces

Explore intersection theory on super Riemann surface moduli spaces, including recursion formulas, polynomiality, and applications to JT gravity.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Global Lie Theory: Wild Riemann Surfaces and Their Character Varieties

Explore the evolution of topological symplectic structures, wild Riemann surfaces, and character varieties in global Lie theory. Discover connections to quantum groups, hyperkähler geometry, and integrable systems.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Insights into Mathematics

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.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Insights into Mathematics

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.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Insights into Mathematics

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.

• YouTube
• 41 minutes
• On-Demand
• Free Video

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.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Insights into Mathematics

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.

• YouTube
• 43 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Combinatorial Algebraic Geometry - Tropical and Real

Explore advanced tropical geometry, real algebraic geometry, and combinatorial methods through expert lectures covering polytopes, optimization, quantum field theory, and geometric applications.

• YouTube
• 1 day 14 hours 25 minutes
• On-Demand
• Free Video

Harvard CMSA

Spacetime and Quantum Mechanics Master Class Workshop

Explore advanced mathematical structures connecting spacetime geometry, quantum mechanics, and scattering amplitudes through intersection theory, cluster algebras, and the amplituhedron.

• YouTube
• 13 hours 42 minutes
• On-Demand
• Free Video

ICTP Mathematics

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.

• YouTube
• 1 hour 27 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

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.

• YouTube
• 1 hour 47 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

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.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

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.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

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.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video