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DTSTART:20221106T020000
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DTSTART:20230312T020000
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UID:calendar.25750.field_event_date_2.0@math.wustl.edu
CREATED:20230306T201655Z
DESCRIPTION:Abstract: Counting embedded curves on a surface as a function o
f their length has been much studied by Mirzakhani and others. I will disc
uss analogous questions about counting surfaces in a 3-manifold, with the
key difference that now the surfaces themselves have more intrinsic topol
ogy. As there are only finitely many essential surfaces of bounded Euler c
haracteristic up to isotopy in an atoroidal 3-manifold, it makes sense to
ask how the number of isotopy classes grows as a function of the Euler ch
aracteristic. Using Haken’s normal surface theory, we can characterize no
t just the rate of growth but show the exact count is a quasi-polynomial.
Moreover, our method allows for explicit computations in reasonably comp
licated examples. This is joint work with Stavros Garoufalidis and Hyam Ru
binstein.\n\nThe only background I will assume is the notion of a manifold
, the genus of a surface, and a little about the fundamental group; tho
se currently taking the graduate geometry/topology sequence are overqualif
ied.\n\nHost: Ali Daemi\n\nTea will be served in Cupples I, room 200 at 3
:30pm.
DTSTART;TZID=America/Chicago:20230323T160000
DTEND;TZID=America/Chicago:20230323T170000
LAST-MODIFIED:20230321T190617Z
SUMMARY:Counting essential surfaces in 3-manifolds
URL;TYPE=URI:https://math.wustl.edu/events/counting-essential-surfaces-3-ma
nifolds
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