Higgs Bundles Courses and Certifications

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

IMSA

Higgs Bundles, Convex Cocompact Subgroups of SU(1,n), and Slodowy Slices

Explore Higgs bundles, SU(1,n) subgroups, and Slodowy slices. Discover connections between stable Higgs bundles and holonomy groups, focusing on SU(1,n) representations and complex hyperbolic manifolds.

• YouTube
• 1 hour 8 minutes
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

IMSA

Hodge Theory, Higgs Bundles on Moduli Spaces of Manifolds and Hyperbolicity II

Explores Hodge theory, Higgs bundles, and their applications to moduli spaces and hyperbolicity, focusing on complex geometry and variation of Hodge structures.

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

IMSA

Hodge Theory, Higgs Bundles on Moduli Spaces of Manifolds and Hyperbolicity I

Explores connections between Hodge theory, Higgs bundles, and moduli spaces, focusing on geometric properties of log spaces and variations of Hodge structures in complex manifolds.

• YouTube
• 1 hour 2 minutes
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Representations of Fuchsian Groups, Parahoric Group Schemes by Vikraman Balaji

Explore advanced mathematical concepts including Fuchsian groups, parahoric schemes, and root systems. Delve into complex algebraic structures and their representations in this in-depth lecture on geometric group theory.

• YouTube
• 1 hour 32 minutes
• On-Demand
• Free Video

BIMSA

Algebraic Curves and Minimal Surfaces

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

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

Institut des Hautes Etudes Scientifiques (IHES)

Heegaard Branes and Exact Results for Non-perturbative Complex Chern-Simons Theory

Explore Heegaard branes in moduli spaces of Higgs bundles and their applications in mathematics, from geometric Langlands to low-dimensional topology and complex Chern-Simons theory.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Non Abelian Hodge Theory in Positive Characteristic

Explore non-abelian Hodge theory in positive characteristic with Siqing Zhang, delving into advanced mathematical concepts and their applications.

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