Lagrangian Submanifolds Courses and Certifications

Hausdorff Center for Mathematics

Introduction to Fukaya Categories - James Pascaleff

Explore symplectic geometry fundamentals for Fukaya categories, covering symplectic manifolds, Lagrangian submanifolds, exactness conditions, and more in this comprehensive lecture.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

IMSA

Remarks on Lagrangian Submanifolds of Hyper-Kaehler Manifolds

Explore properties of Lagrangian subvarieties in hyper-Kaehler manifolds, focusing on interactions with Lagrangian fibrations and albanese dimension of Lagrangian surfaces.

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

IMSA

Basic Remarks on Lagrangian Submanifolds of Hyper-Kähler Manifolds

Explore properties of Lagrangian subvarieties in hyper-Kähler manifolds, focusing on their interaction with Lagrangian fibrations and albanese dimension of Lagrangian surfaces.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Introduction to Fukaya Categories - James Pascaleff

Explore examples of Fukaya categories, focusing on surfaces and potentially other cases, building upon previous lectures on symplectic geometry and Floer cohomology.

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

Hausdorff Center for Mathematics

Introduction to Fukaya Categories - James Pascaleff

Explore Floer cohomology and Fukaya category fundamentals, including Lagrangian intersection theory, Floer differential, A∞ operations, and Gromov compactification in symplectic geometry.

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

IMSA

Open-Relative Correspondence and Topological Recursion

Explore the connection between open Gromov-Witten invariants and relative Gromov-Witten invariants in symplectic geometry, and their relation to topological recursion.

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

IMSA

Functorial Construction of Lagrangian Floer Theory and Its Possible Applications

Explore functorial construction of Lagrangian Floer theory and its potential applications in symplectic geometry with renowned mathematician Kenji Fukaya from Stony Brook University.

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

Stony Brook Mathematics

Chain Level String Bracket and Punctured Holomorphic Discs

Explore Audin's conjecture and its generalization to Liouville manifolds, examining moduli spaces of punctured holomorphic discs and their relation to string topology operations.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Institut Henri Poincaré

Tropical Fukaya Algebras

Explore curve count-based invariants in symplectic manifolds after multiple cuts, focusing on Fukaya algebras of Lagrangian submanifolds and their tropical counterparts.

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

M-Seminar, Kansas State University

Skein Valued Open Gromov-Witten Invariants and Cluster Mutations

Exploración de invariantes de Gromov-Witten abiertos con valores de madeja y mutaciones de clústeres. Desarrollo de teoría de clústeres con valores de madeja para calcular funciones de onda de Ekholm-Shende.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

M-Seminar, Kansas State University

Arclike Lagrangians in Liouville Sectors

Exploración de lagrangianos arcoides en sectores de Liouville, analizando su comportamiento a través de límites subsectoriales y su impacto en el cálculo de categorías de Fukaya envueltas.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

M-Seminar, Kansas State University

Counting Holomorphic Disks with Boundary on the Chiang Lagrangian

Exploración de invariantes de Gromov-Witten abiertos y discos holomorfos en la lagrangiana de Chiang, utilizando teoría de Floer y ecuaciones WDVV abiertas. Patrones periódicos y estructura aritmética.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

Western Hemisphere Virtual Symplectic Seminar

Open/Closed Correspondence and Mirror Symmetry in Gromov-Witten Theory

Exploración de la correspondencia abierta/cerrada en teoría de Gromov-Witten y su relación con la simetría especular en variedades de Calabi-Yau tóricas.

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

Western Hemisphere Virtual Symplectic Seminar

Invariance of Floer Cohomology Under Higher Mutation

Explora la invariancia de la cohomología de Floer bajo mutaciones superiores, utilizando técnicas de estiramiento del cuello para Lagrangianos localmente mutables.

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

BIMSA

Skein Valued Counts of Open Curves in Calabi-Yau Threefolds

Conteo de curvas holomorfas abiertas en variedades de Calabi-Yau mediante valores de contorno en el módulo skein HOMFLYPT, eliminando el cruce de paredes y logrando recuentos invariantes por deformación.

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