Donaldson-Thomas Invariants Courses and Certifications

IMSA

Donaldson-Thomas and Gromov-Witten Invariants - Part 16

Explore moduli spaces of algebraic curves and coherent sheaves, focusing on Gromov-Witten and Donaldson-Thomas invariants in complex algebraic varieties and their relevance to superstring theory.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

IMSA

Cohomological Donaldson-Thomas Invariants of 3-Manifolds - Part 2

Explore Morse homology of complex Chern-Simons functional, its connections to supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.

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

ICTP Mathematics

Moduli Spaces, Mirror Symmetry, and Enumerative Geometry

Explore advanced algebraic geometry through moduli spaces, mirror symmetry, and enumerative geometry with leading experts from top institutions worldwide.

• YouTube
• 1 day 9 hours 46 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Mathematics on the Crossroad of Centuries

Explore cutting-edge mathematics bridging algebra, geometry, topology, and physics through expert lectures honoring Maxim Kontsevich's groundbreaking contributions.

• YouTube
• 20 hours 55 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Workshop on Quantum Geometry

Explore advanced quantum geometry through expert lectures on Gromov-Witten theory, Donaldson-Thomas invariants, integrable systems, and spectral curve quantization from leading researchers.

• YouTube
• 14 hours 45 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Gauge Theories and Differential Invariants - Recent Developments in Mathematics and Physics

Explore advanced gauge theories connecting theoretical physics and mathematics through Donaldson invariants, supersymmetric quantum field theories, and differential geometry applications.

• YouTube
• 20 hours 31 minutes
• Self-Paced
• Free Video

Stony Brook Mathematics

Counting Curves in Calabi-Yau Threefolds

Explore enumerative invariants and a universal approach to counting curves in Calabi-Yau threefolds. Discover how cluster formalism aids computations and potentially simplifies conjectural identities between invariants.

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

Harvard CMSA

Tyurin Degenerations, Relative Lagrangian Foliations and DT Invariant Categorification

Delve into advanced mathematical concepts exploring Tyurin degenerations, derived Lagrangian intersection theory, and categorification of DT invariants in Calabi-Yau threefolds.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

INI Seminar Room 2

Non-perturbative Topological String on Compact Calabi-Yau 3-folds

Delve into advanced topological string theory, exploring non-perturbative solutions on Calabi-Yau 3-folds through monodromy points, gauge theory indices, and wall crossing formulas to understand holomorphic anomaly equations.

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

M-Seminar, Kansas State University

Orientations on Moduli Spaces of Coherent Sheaves on Calabi-Yau 4-folds - Part I

Delve into the mathematics of orientations on moduli spaces of coherent sheaves on Calabi-Yau 4-folds, exploring corrections to previous work and the concept of "flag structures" that determine canonical orientations.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

M-Seminar, Kansas State University

Mock Modularity of Calabi-Yau Threefolds - Part 3 of 3

Explore advanced techniques for computing polar terms in mock modular forms encoding rank 0 Donaldson-Thomas invariants using wall-crossing and topological string integration.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Higher Rank DT/PT Wall-Crossing in Bridgeland Stability

Explore higher rank DT/PT wall-crossing in Bridgeland stability conditions on smooth projective threefolds, proving separation between Gieseker and PT moduli spaces.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Stony Brook Mathematics

Counting Curves and Surfaces in Calabi-Yau Threefolds and Modular Forms

Explore the S-duality modularity conjecture from string theory, connecting D-brane counting problems in Calabi-Yau threefolds to modular forms through advanced algebraic geometry.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Harvard CMSA

Topics in the Relation of Four-Manifold Invariants and Supersymmetric Field Theory

Explore advanced connections between four-manifold topology and supersymmetric quantum field theory, covering Donaldson invariants, Seiberg-Witten theory, and higher-dimensional extensions.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

M-Seminar, Kansas State University

Mock Modularity of Calabi-Yau Threefolds - Part 2 of 3

Explore modular properties of rank 0 Donaldson-Thomas invariants and their generating functions as mock modular forms for Calabi-Yau threefolds.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video