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SUMMARY:Karen Butt (University of Chicago)
DTSTART:20250416T160000Z
DTEND:20250416T170000Z
DTSTAMP:20260513T213026Z
UID:VSGS/111
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/111/">M
 onotonicity of Liouville entropy along the Ricci flow</a>\nby Karen Butt (
 University of Chicago) as part of Virtual seminar on geometry with symmetr
 ies\n\n\nAbstract\nWe consider the geodesic flow of a closed negatively cu
 rved surface. Its Liouville entropy is an invariant of the measurable dyna
 mics of the flow\, which roughly captures the average exponential divergen
 ce of nearby trajectories. For negatively curved surfaces of fixed total a
 rea\, Katok proved this invariant is maximized at hyperbolic metrics\, ie\
 , metrics of constant negative curvature. Our main result is that\, in thi
 s setting\, the Liouville entropy is monotonically increasing along the no
 rmalized Ricci flow on the space of metrics. This affirmatively answers a 
 question of Manning\, and gives a new proof of Katok’s aforementioned re
 sult. In addition to geometric and dynamical methods\, our proof also uses
  microlocal analysis. This is joint work with Erchenko\, Humbert\, and Mit
 sutani.\n
LOCATION:https://researchseminars.org/talk/VSGS/111/
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