Calabi-Yau Threefold Courses and Certifications

BIMSA

Mock Modularity of Calabi-Yau Threefolds - ICBS 2024

Explore modular properties of generating functions for Donaldson-Thomas invariants in Calabi-Yau threefolds, their physical origins, and applications in string theory compactifications.

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

M-Seminar, Kansas State University

Mock Modularity of Calabi-Yau Threefolds - Part 1 of 3

Explore modular forms, mock modular forms, and Jacobi forms while discovering generalized Donaldson-Thomas invariants for Calabi-Yau threefolds in advanced mathematical physics.

• YouTube
• 1 hour 9 minutes
• On-Demand
• 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
• On-Demand
• Free Video

IMSA

Homological Mirror Symmetry - Counting Curves on Calabi-Yau Threefolds

Explore advanced mathematical concepts in counting curves on Calabi-Yau threefolds, including Grothendieck groups, Gopakumar-Vafa conjecture, and MNOP conjecture implications.

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

IMSA

Homological Mirror Symmetry - Categorical Donaldson-Thomas Theory of C^3 and Beyond

Explore advanced concepts in Donaldson-Thomas theory, including categorifications, refinements, and applications to C^3 and beyond, with a focus on categorical invariants and correspondences.

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

IMSA

On the Spectral Problem of a Three Term Difference Operator

Explore the spectral problem of quantum mechanical operators in complex Planck's constant scenarios, focusing on toric Calabi-Yau threefolds and their implications.

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

BIMSA

Higher Gromov-Witten Invariants of Calabi-Yau Threefolds

Explore mixed-spin-p-fields method for Calabi-Yau quintics, its application to BCOV Feynman summation rule, and generalization to hypersurfaces in toric varieties.

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

BIMSA

Universally Counting Curves in Calabi-Yau Threefolds - ICBS 2024

Explore enumerative geometry through a new perspective on curve counting in complex threefolds, focusing on the Grothendieck group of 1-cycles and universal curve enumeration invariants.

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

BIMSA

Modularity of Donaldson-Thomas Invariants on Compact Calabi-Yau Threefolds

Explore Donaldson-Thomas invariants, their connection to BPS indices, and modular behavior in string theory. Gain insights into computational methods and applications to Gopakumar-Vafa invariants and topological string amplitudes.

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

Hausdorff Center for Mathematics

Moments of Families of Elliptic Curves

Explore new developments in higher moment sums of elliptic curve families, their connections to modular forms, and applications to rigid Calabi-Yau threefolds and intermediate Jacobians.

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

Institut des Hautes Etudes Scientifiques (IHES)

Universally Counting Curves in Calabi-Yau Threefolds

Explore a universal enumerative invariant for curves in algebraic varieties, focusing on threefolds with nef anticanonical bundle and its implications for the MNOP conjecture.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video