IMSA Courses

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Homological Mirror Symmetry- Non-Holomorphic Deformations of Landau-Ginzburg Models

Explore non-holomorphic deformations of Landau-Ginzburg models, examining derived moduli spaces, Frobenius manifold structures, and Gromov-Witten invariants in symplectic geometry.

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

Fundamentals of Lie Groupoids and Algebroids - Lecture Series

Introducción a la teoría de Lie de grupoides y algebroides, explorando sus definiciones, propiedades y aplicaciones en diversas estructuras geométricas.

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

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
• Self-Paced
• Free Video

Homological Mirror Symmetry - Functorial Mirror Symmetry for Very Affine Hypersurfaces

Explore functorial mirror symmetry for very affine hypersurfaces, examining Auroux's conjectures and their modifications to account for derived structures in complement mirrors.

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

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
• Self-Paced
• Free Video

Homological Mirror Symmetry - Introduction to 3D Mirror Symmetry

Explore 3d mirror symmetry's duality between holomorphic symplectic manifolds, focusing on a new 2-categorical formulation that extends homological mirror symmetry concepts.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video