Hitchin Systems Courses and Certifications

International Mathematical Union

Tamas Hausel - Enhanced Mirror Symmetry for Langlands Dual Hitchin Systems

Explore enhanced mirror symmetry for Langlands dual Hitchin systems, covering topics from SYZ mirror symmetry to equivariant cohomology and Kirillov algebras.

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

Galileo Galilei Institute

4D N=2 Superconformal Field Theories and Families of Hitchin Systems

Explore 4D N=2 Superconformal Field Theories and their connection to Hitchin Systems in this advanced physics lecture by Jacques Distler.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

Fields Institute

Hitchin Systems - An Introduction to Complex Geometric Structures

Explore Hitchin systems with Marina Logares, delving into their mathematical properties and applications in algebraic geometry and theoretical physics.

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

INI Seminar Room 2

Fourier Transform: From Abelian Schemes to Hitchin Systems - Part 3

Delve into advanced mathematical concepts exploring Fourier transforms and their applications in abelian schemes and Hitchin systems through an in-depth mathematical analysis led by Yale's Professor Shen.

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

INI Seminar Room 2

Fourier Transform: From Abelian Schemes to Hitchin Systems - Part 2

Delve into advanced mathematical concepts exploring Fourier transforms and their applications in abelian schemes and Hitchin systems through an in-depth mathematical analysis by Yale's Prof. Shen.

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

IMSA

Products of Matrices, Non-Abelian Hodge Theory, Integrable Systems, and Theories of Class S

Explore connections between Deligne-Simpson problem and Hitchin systems, delving into SCF Theories of Class S and 3D mirror symmetry in this advanced mathematics lecture.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

ICTP Mathematics

Mirror Symmetry and Big Algebras

Explore mirror symmetry in Hitchin systems, Kirillov algebras, and equivariant cohomology. Delve into conjectures on non-very stable flows and big commutative subalgebras in affine Schubert varieties.

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

IMSA

Towards Lefschetz Thimbles in Quantum Field Theory - Part II

Delve into the complexification of quantum field theory through Lefschetz thimbles, exploring solutions to equations of motion in systems like anharmonic oscillators and sigma models.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

IMSA

Towards Lefschetz Thimbles in Quantum Field Theory - Part I

Delve into the complexification of quantum field theory through Lefschetz thimbles, exploring solutions to equations of motion in systems like anharmonic oscillators and sigma models, based on Bethe/gauge correspondence.

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

Kyoto-U OCW - Unofficial

Vertex Operator Algebras and Integrable Systems - Lecture 2

Delve into advanced mathematical concepts of vertex operator algebras, screening methods, W-algebras, and their applications in geometric Langlands theory and integrable systems with Boris Feigin.

• YouTube
• 2 hours 38 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Motives of the Hitchin System

Delve into advanced algebraic geometry exploring the Hitchin system's topology, examining symmetries through algebraic cycles, Fourier-Mukai duality, and Springer theory applications.

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

IMSA

Mirror Symmetry and Big Algebras in the Hitchin System

Explore mirror symmetry, Hitchin systems, and algebraic structures in representation theory. Discover connections between equivariant cohomology, Kirillov algebras, and affine Schubert varieties.

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

Institut des Hautes Etudes Scientifiques (IHES)

Geometry from Donaldson-Thomas Invariants

Explore geometric structures in stability conditions using DT invariants of CY3 triangulated categories, focusing on hyperkähler structures and complexified Hitchin systems.

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

Western Hemisphere Virtual Symplectic Seminar

The Dual Lagrangian Fibrations of Compact Hyper-Kähler Manifolds

Explore dual Lagrangian fibrations of compact hyper-Kähler manifolds, focusing on construction, duality, and topological mirror symmetry in higher-dimensional generalizations of K3 surfaces.

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

IMSA

Generalized Hitchin Systems - New Geometric Structures

Explore generalized Hitchin systems with Bảo Châu Ngô, delving into new geometric structures and celebrating Hitchin's mathematical legacy in this insightful conference talk.

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