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SUMMARY:Why Should You Symp. for Dehn Twists? (Spoiler: Their Symplectic C
 harm Is Infinite) - Jose Luis Narbona Valiente\, University of Cambridge
DTSTART:20250214T160000Z
DTEND:20250214T170000Z
UID:TALK225625@talks.cam.ac.uk
CONTACT:Adrian Dawid
DESCRIPTION:On this Valentine’s day\, let's talk about a love triangle: 
 smooth automorphisms\, symplectic geometry\, and Dehn twists - a special k
 ind of transformation that "twist" spaces in interesting ways. \n \nIn the
  world of orientable surfaces\, Dehn twists are infinite order generators 
 of the mapping class group. Surprisingly\, in 4 dimensions Dehn twists hav
 e finite order (just 2!). \nWhat it is more striking is a result of Seidel
 \, who showed using Floer cohomology that these transformations\, which pr
 eserve the symplectic structure\, when viewed inside the symplectic mappin
 g class group\, retain their infinite order in any dimension. \nIn a way t
 his tells us that the symplectic generalization of Dehn twists is the natu
 ral one. \n \nIn this talk we’ll start from the beginning\, introducing 
 Dehn twists from the ground up and exploring how their behaviour splits be
 tween the smooth and symplectic worlds. By the end\, it will be clear why 
 symplectic geometers can’t stop talking about Floer theory (from which n
 o prior knowledge is required)—it’s not just a tool\, it’s a window 
 into the soul of symplectic manifolds. 
LOCATION:MR13
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