Higgs Bundles Courses and Certifications

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
• Self-Paced
• Free Video

M-Seminar, Kansas State University

P=W via H2 - Moduli Space of Stable Twisted Higgs Bundles

Explore the cohomology of stable twisted Higgs bundles moduli space through $H_2$ Lie algebra action, unifying weight and perverse filtrations via tautological classes and Hecke operators.

• YouTube
• 1 hour 29 minutes
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Equivariant Minimal Surfaces in Symmetric Spaces via Higgs Bundles - Lecture 1

Explore equivariant minimal surfaces in symmetric spaces using Higgs bundles. Expert-led lecture delves into advanced mathematical concepts, ideal for researchers in differential geometry.

• YouTube
• 1 hour 33 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Motivic Invariants of Moduli of Irregular Parabolic Higgs Bundles and Bundles

Explore motivic integration and its application to Donaldson-Thomas invariants in moduli stacks of semistable irregular parabolic Higgs bundles and connections on projective curves.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Centre International de Rencontres Mathématiques

Higgs Bundles for Hecke Eigensheaves in Rank 2 and Genus 2

Delve into the construction of Higgs bundles for Hecke eigensheaves in geometric Langlands program, focusing on rank 2 local systems on genus 2 curves and the geometry of the wobbly locus.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Holomorphic Higgs Bundles Over the Teichmüller Space

Explore holomorphic Higgs bundles over Teichmuller space through advanced mathematical analysis and geometric theory.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Minimal Surfaces with and without Higgs Bundles - Lecture 2

Explore advanced connections between minimal surfaces and Higgs bundles in this specialized mathematical lecture from a leading geometry program.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Minimal Surfaces with and without Higgs Bundles - Lecture 1

Explore the geometric foundations of minimal surfaces and their connections to Higgs bundles in this advanced mathematical lecture from a leading expert.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

IMSA

Parabolic Higgs Bundles in Geometric Langlands Program

Explore parabolic Higgs bundles in geometric Langlands program, focusing on rank 2 local systems on genus 2 curves and associated rank 8 local systems on moduli stacks.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

ICTP Mathematics

P=W via H_2 - Part 2

Exploration of H_2 Lie algebra action on cohomology of stable twisted Higgs bundles moduli space, connecting tautological classes and Hecke operators to filtrations P and W.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

ICTP Mathematics

P=W via H_2

Exploration of Lie algebra H_2 and its action on cohomology of moduli spaces, connecting natural filtrations and tautological operations to unify mathematical concepts.

• YouTube
• 1 hour 41 minutes
• Self-Paced
• Free Video

IMSA

Asymptotics in Hitchin's Moduli Space

Explores asymptotic behavior in Hitchin's moduli space, comparing different notions of ideal points at infinity and examining the extension of the nonabelian Hodge correspondence between partial compactifications.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

IMSA

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
• Self-Paced
• Free Video