Western Hemisphere Virtual Symplectic Seminar Courses

Kobayashi Non-Hyperbolicity of Calabi-Yau Manifolds via Mirror Symmetry

Explore Kobayashi non-hyperbolicity of Calabi-Yau manifolds through mirror symmetry. Gain insights into complex geometry, holomorphic curves, and Hodge theory in this advanced mathematical seminar.

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

Monotone Twist Maps and Dowker-Type Theorems

Explore geometric inequalities in billiard systems, connecting Dowker's theorems to Mather's β-function and deriving new insights for various billiard types.

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

A Symplectic Manifold Which Can't Be Fully Filled

Explore a unique toric domain in R^4, its symplectic properties, and packing stability failures. Discover obstructions from ECH capacities in this advanced mathematical discussion.

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

Invariance of Floer Cohomology Under Higher Mutation

Explore higher mutations in monotone toric fibers and their impact on Floer cohomology. Delve into locally mutable Lagrangians and neck-stretching techniques to understand invariance under local system changes.

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

The Dual Lagrangian Fibrations of Compact Hyper-Kähler Manifolds

Explore dual Lagrangian fibrations of compact hyper-Kähler manifolds, focusing on construction, duality, and topological mirror symmetry in higher-dimensional generalizations of K3 surfaces.

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

Introduction to Lagrangian Fillings of Legendrian Links - Part 1

Explore Lagrangian fillings of Legendrian links, their construction, and techniques to distinguish Hamiltonian isotopy classes. Delve into the connection with cluster algebras and key proof elements.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Applications of the Relation Between Cluster Algebras and Symplectic Topology - Part 2

Explore applications of cluster algebras in symplectic topology, including detection of Lagrangian fillings and holomorphic symplectic structures. Examine implications for Richardson varieties and quasi-cluster structures.

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

Cluster Algebras Associated to Bott-Samelson Braids

Explore cluster algebras associated with Bott-Samelson braids, focusing on Legendrian links and their connection to algebraic varieties and Lagrangian fillings. Discover weaves and their computational applications.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Cluster Algebras for General Braid Varieties

Explore cluster algebras on braid varieties using weaves, Lusztig cycles, and symplectic topology. Gain insights into localization processes and A=U proof through Lie-theoretic and combinatorial perspectives.

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

Composition, DG-Modules, and Cobordism Maps in Bordered Floer Homology

Explore bordered Floer homology, dg-modules, and the topological interpretation of module homomorphism composition in Heegaard Floer complexes. Gain insights into cobordism maps and their consequences.

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

Global Kuranishi Charts and Product Formula for Symplectic Gromov-Witten Invariants

Explore global Kuranishi charts for moduli spaces of stable pseudoholomorphic maps and their application in proving the product formula for symplectic Gromov-Witten invariants.

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

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

Explore open/closed correspondence in Gromov-Witten theory, examining numerical invariants, generating functions, and compatibility with mirror symmetry in toric Calabi-Yau manifolds.

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

Coherent Orientations of DGA Maps Associated to Exact Lagrangian Cobordisms

Explore coherent orientations of DGA maps in exact Lagrangian cobordisms, focusing on combinatorial formulas for mini-dipped pinch moves and applications to Heegaard Floer Homology.

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

Character Varieties of Tangles and Singular Instanton Homology

Explore character varieties of tangles and singular instanton homology. Investigate Lagrangian Floer theory for knot study, examining tangle sums and their implications for knot invariants.

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

The Z/p Gysin Sequence in Symplectic Cohomology

Explore Z/p-equivariant symplectic cohomology and its Gysin sequence, connecting S^1 and Z/p versions. Discover applications to Seidel's conjecture on localized S^1-equivariant symplectic cohomology.

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