Higgs Bundles Courses and Certifications

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

BunG Seminar

BunG and Higgs Bundles - Moduli Stacks and Geometric Langlands - Talk 4

Delve into advanced mathematical concepts of moduli stacks, exploring tangent/cotangent stacks, Higgs bundles, and their role in Geometric Langlands through expert analysis of BunG framework.

• YouTube
• 1 hour 45 minutes
• On-Demand
• Free Video

M-Seminar, Kansas State University

Motivic Classes of Varieties and Stacks with Applications to Higgs Bundles and More

Explore motivic classes of varieties and stacks, from point counting over finite fields to explicit formulas for moduli of Higgs bundles and connections.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Different Faces of Higgs Bundles - A Universal Moduli Space - Lecture 2

Explore the universal moduli space of Higgs bundles and its hyperkähler metric structure, connecting differential geometry with character varieties of fundamental groups.

• YouTube
• 1 hour 26 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Different Faces of Higgs Bundles - The Integrable System - Lecture 1

Explore the evolution of Hitchin integrable systems in Higgs bundle geometry, from initial observations to their central role in moduli space structure over four decades.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Advanced Topics in Mathematical Gauge Theory - Higgs Bundles

Delve into advanced mathematical gauge theory and Higgs bundles through expert lectures covering sophisticated theoretical frameworks and their geometric applications.

• YouTube
• 4 hours 11 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

An Introduction to Spectral Data for Higgs Bundles

Explore spectral data for Higgs bundles, a key concept in algebraic geometry and mathematical physics, with insights on integrable systems and moduli spaces.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Local Systems and Higgs Bundles in p-adic Geometry

Explore the algebraic nature of local systems and Higgs bundles in p-adic geometry, drawing parallels to complex varieties and characteristic p counterparts.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

IMSA

On Coassociative ALE Fibrations and Higgs Bundles

Explores G2-manifolds fibered by ALE spaces, connecting gauge theory and Hitchin's equations to Donaldson's program on coassociative K3 surface fibrations in G2-manifolds.

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

IMSA

Higgs Bundles on Elliptic Surfaces and Logarithmic Transformations

Explore Higgs bundles on elliptic surfaces and their transformations, examining vector bundles' importance in mathematics and the impact of logarithmic transformations on these structures.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

IMSA

Wobbly Fixed Points, Equivariant Multiplicities and U(p,q)-Higgs Bundles

Explores geometry of Higgs bundle moduli spaces, focusing on nilpotent cone fixed points and their classification. Analyzes U(p,q)-Higgs bundles and compares results with equivariant multiplicities.

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

IMSA

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 Video

IMSA

Higgs Bundles and the Topology of Higher Teichmüller Spaces

Explore advanced mathematical concepts in topology, focusing on Higgs bundles and their role in understanding higher Teichmüller spaces for non-compact real Lie groups.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Equivariant Minimal Surfaces in Symmetric Spaces via Higgs Bundles - Lecture 3

Explore equivariant minimal surfaces in symmetric spaces using Higgs bundles. Advanced mathematical concepts for researchers in geometry and topology.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Equivariant Minimal Surfaces in Symmetric Spaces via Higgs Bundles - Lecture 2

Explore equivariant minimal surfaces in symmetric spaces using Higgs bundles. Advanced mathematical concepts for researchers in geometry and related fields.

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