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SUMMARY:Introduction to Symplectic Cohomology and Applications - Dahye  Ch
 o (Yonsei University)
DTSTART:20240614T124500Z
DTEND:20240614T131500Z
UID:TALK217360@talks.cam.ac.uk
DESCRIPTION:In the late 1980's\, Floer developed generalized Morse theorie
 s\, where the generators of the complex are critical points of action func
 tionals on various moduli spaces\, solutions of certain ODEs\, and the gra
 dient flow lines are solutions of certain elliptic PDEs. Floer's breakthro
 ugh construction is based on that era's other breakthrough works done by m
 any people. In this talk\, we will learn one of his theories\, called Hami
 ltonian Floer (co)homology and Symplectic (co)homology\, which is a Morse 
 (co)homology on the loop space of a symplectic manifold with Hamiltonian f
 unction on it. After reviewing definitions and some properties\, we introd
 uce criteria for affine varieties to admit uniruled subvarieties of certai
 n dimensions. The measurements are from long exact sequences of versions o
 f symplectic cohomology. We provide applications of the criteria in birati
 onal geometry of log pairs in the direction of the Minimal Model Program.
LOCATION:External
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