mini course: Fukaya categories with support

Speaker: Umut Varolgunes (Koç University)
Time: 2pm to 4pm, Sep 2, Sep 4, Sep 9, Sep 11, Sep 16, Sep 18
Location: Room 1710, SIMIS
Zoom Meeting ID: 835 6617 9446 （Passcode:SIMIS）

Lecture 1) Floer theory background

• Hamiltonian Floer complex
• Lagrangian Floer complex
• Quantitative information
• Operadic structures

Lecture 2) Symplectic cohomology with support

• Liouville manifolds
• Geometrically bounded manifolds
• Framed E2 structure
• Computations

Lecture 3) Fukaya category with support

• Liouville manifolds
• Tautologically unobstructed Lagrangians
• Bounding cochains
• Anti-symplectic involutions
• Relative version

Lecture 4) Blueprints for HMS for symplectic CY’s

• Pomerleano models
• Symplectic cutting (toric degeneration vs. NC)
• Deformed Abouzaid generation strategy
• Decompositions adapted to an ample divisor
• Deformed Lekili-Polishcuk generation strategy

Lectures 5 and 6) Mirror symmetry for CY surfaces

• Eigenray diagrams
• Looijenga interiors
• K3 surfaces