Homological Mirror Symmetry Courses and Certifications

Harvard CMSA

Homological Mirror Symmetry and Hodge Theory - January 2018

Explore advanced mathematical concepts in homological mirror symmetry, Hodge theory, and algebraic geometry through expert lectures from leading researchers in the field.

• YouTube
• 20 hours 7 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Homological Mirror Symmetry for Log Calabi-Yau Surfaces - Ailsa Keating

Explore homological mirror symmetry for log Calabi-Yau surfaces, constructing mirror Landau-Ginzburg models and examining connections to SYZ fibrations and related works in algebraic geometry.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Homological Mirror Symmetry for Not-So-Simple Singularities - Yanki Lekili

Explore homological mirror symmetry for invertible polynomials' Milnor fibers, focusing on explicit conjectures and proofs for simple and not-so-simple singularities.

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

IMSA

Homological Mirror Symmetry and Higgs-Coulomb Correspondence in Abelian GLSMs

Explore Higgs-Coulomb correspondence in abelian GLSMs, examining virtual counts of Landau-Ginzburg quasimaps and Mellin-Barnes integrals. Learn about wall-crossing and stability conditions in GLSM invariants.

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

IMSA

Homological Mirror Symmetry - Floer Homotopy Theory

Explore recent developments in Floer generalized homology groups, their applications, and ongoing research on curvature in Floer homotopy theory with expert Mohammed Abouzaid.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

IMSA

Homological Mirror Symmetry - Floer Homotopy Theory

Explore recent developments in Floer generalized homology groups, their applications, and ongoing research on curvature in Floer homotopy theory with Mohammed Abouzaid.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

IMSA

Homological Mirror Symmetry - Moduli Space of Non-Archimedean Holomorphic Disks

Explore non-archimedean holomorphic disks in affine log Calabi-Yau varieties, covering boundary conditions, smoothness, dimension, and properness in the context of mirror symmetry.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

IMSA

Homological Mirror Symmetry - DT Invariants & Holomorphic Curves

Explore the correspondence between Donaldson-Thomas invariants and holomorphic curves, with applications in enumerative geometry and insights from quantum field theories.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

IMSA

Homological Mirror Symmetry - Coulomb Branches & Rozansky-Witten Theory Pt. II

Explore Rozansky-Witten theory and its connection to homological mirror symmetry, from basics to modern developments involving non-compact and infinite-dimensional target spaces.

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

IMSA

Homological Mirror Symmetry - Quivers & Curves in Higher Dimensions

Explore the connection between quiver mutations, Poisson X-cluster varieties, and Calabi-Yau categories, leading to a correspondence between Donaldson-Thomas invariants and rational curve counts in higher dimensions.

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

IMSA

Homological Mirror Symmetry - Coulomb Branches and Rozansky-Witten Theory

Explore Rozansky-Witten theory and its connection to homological mirror symmetry, from basics to modern developments involving non-compact spaces and ongoing research.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

IMSA

Homological Mirror Symmetry - Twisted Shklyarov Pairing & Applications

Explore twisted Shklyarov pairing in Hochschild homology, its applications to Lefschetz fibrations, mirror symmetry, and classical problems. Joint work with Paul Seidel presented.

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

IMSA

Homological Mirror Symmetry - Homological Link Invariants from Floer Theory

Explore a groundbreaking connection between homological mirror symmetry and representation theory, solving the knot categorification problem and generalizing Heegard-Floer theory to simple Lie superalgebras.

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

IMSA

Homological Mirror Symmetry for Theta Divisors

Explore complex moduli of theta divisors in abelian varieties and their mirror Landau-Ginzburg models, focusing on global homological mirror symmetry across the entire moduli space.

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

IMSA

Homological Mirror Symmetry - Yan Soibelman

Explore holomorphic Floer theory, wall-crossing structures, and their connections to Chern-Simons theory. Discover the interplay between complex symplectic geometry and quantum field theory in this advanced mathematics lecture.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video