Homological Percolation: The Formation of Giant Cycles
Applied Algebraic Topology Network via YouTube
Overview
Syllabus
Intro
PERSISTENT HOMOLOGY
THE MAXIMAL PERSISTENCE OF NOISE
TYPICAL BEHAVIOR
CROSSING PROBABILITIES
CONT. PERC. IN A BOX - SETUP
CONT. PERC. - GIANT COMPONENTS
"GIANT" K-CYCLES
HOMOLOGICAL PERCOLATION
MAIN RESULT
SIGNAL VS. NOISE
H, PERCOLATION
DUALITY - PROOF
H.- -PERCOLATION
BIG PICTURE?
EULER CHARACTERISTIC
EC & PERCOLATION?
SIMULATIONS
PERMUTAHEDRAL SITE-PERCOLATION
GAUSSIAN RANDOM FIELDS
SUMMARY & FUTURE WORK
Taught by
Applied Algebraic Topology Network