Donaldson-Thomas Theory Courses and Certifications

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

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

IMSA

Universally Counting Curves in Calabi-Yau Threefolds

Explore enumerative geometry through a new perspective on curve counting in complex threefolds, focusing on the Grothendieck group of 1-cycles and its implications for the MNOP conjecture.

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

M-Seminar, Kansas State University

Cohomological Hall Algebra of Cyclic Quivers and Integral Form of Affine Yangians

Explore cohomological Hall algebras of cyclic quivers and their connection to affine Yangians, using tools from Donaldson-Thomas theory and moduli spaces.

• YouTube
• 1 hour 17 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

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

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

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

Centre International de Rencontres Mathématiques

Categorified Donaldson-Thomas Invariants of Calabi-Yau 3-Folds

Explore categorified Donaldson-Thomas invariants of Calabi-Yau 3-folds in this advanced mathematical lecture by Benjamin Hennion at CIRM's thematic meeting on algebraic geometry.

• YouTube
• 1 hour
• 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

Institut des Hautes Etudes Scientifiques (IHES)

Modularity of Donaldson-Thomas Invariants on Calabi-Yau Threefolds

Explore Donaldson-Thomas invariants, their mathematical significance, and modular behavior in string theory. Gain insights into BPS indices, wall-crossing phenomena, and topological string amplitudes.

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

Institut des Hautes Etudes Scientifiques (IHES)

Donaldson-Thomas Invariants: Classical, Motivic, Quadratic and Real

Explore advanced Donaldson-Thomas invariants in algebraic geometry, including classical, motivic, quadratic, and real variants. Delve into virtual fundamental classes and refined invariants.

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

Institut des Hautes Etudes Scientifiques (IHES)

DT Invariants and Holomorphic Curves in Complex Integrable Systems

Explore the correspondence between Donaldson-Thomas invariants and holomorphic curves, focusing on mirror symmetry and applications in enumerative geometry.

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

Institut des Hautes Etudes Scientifiques (IHES)

Holomorphic Floer Theory and Resurgence - Lecture 2

Explore holomorphic Floer theory and its connection to resurgence, examining the Riemann-Hilbert correspondence and its implications for perturbative expansions in mathematics and physics.

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

M-Seminar, Kansas State University

From Gromov-Witten to Donaldson-Thomas Invariants via Resurgence

Explore the connection between Gromov-Witten and Donaldson-Thomas invariants through resurgence analysis in topological string theory for Calabi-Yau threefolds.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video