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Lagrangian Tori at Radius Zero in Kahler Manifolds

IMSA via YouTube

Overview

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Explore a mathematical lecture that delves into novel techniques for constructing Lagrangian tori in Kahler manifold degenerations. Learn about maximally degenerate families of Calabi-Yaus and their tori's asymptotic properties in relation to the SYZ picture, including volume filling and Gromov-Haudsdorff metric collapse to the essential skeleton minus codimension 2 faces. Discover the A'Campo space's construction and its hybrid coordinates, which extend degenerations from punctured disks to annuli. Understand how these coordinates simplify boundary computations and examine the crucial role of fiberwise Kahler form, which exhibits asymptotic Ricci flatness in generic regions and enables tori movement from boundary to nearby fibers along symplectic connections.

Syllabus

Tomasz Pelka, Institute of Math of the Polish Academy of Sciences: Lagrangian tori at radius zero

Taught by

IMSA

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