Riemann Surfaces Courses and Certifications

International Centre for Theoretical Sciences

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.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Online Course

Imaginary Numbers Are Real

Explore the fascinating world of imaginary numbers, from their historical origins to complex functions and Riemann surfaces, in this comprehensive mathematical journey.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Online Course

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.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Online Course

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.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Online Course

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.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Online Course

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.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Online Course

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.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Online Course

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.

• YouTube
• 48 minutes
• On-Demand
• Free Online Course

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.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Online Course

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 Online Course

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 Online Course

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 Online Course

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 Online Course

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 Online Course

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 Online Course