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SUMMARY:Nathan Dunfield (UI Urbana-Champaign)
DTSTART:20200505T150000Z
DTEND:20200505T153000Z
DTSTAMP:20260423T003255Z
UID:GaTO/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/3/">Cou
 nting incompressible surfaces in three-manifolds</a>\nby Nathan Dunfield (
 UI Urbana-Champaign) as part of Geometry and topology online\n\nLecture he
 ld in N/A.\n\nAbstract\nCounting embedded curves on a hyperbolic surface a
 s a function of their length has been much studied by Mirzakhani and other
 s. I will discuss analogous questions about counting incompressible surfac
 es in a hyperbolic three-manifold\, with the key difference that now the s
 urfaces themselves have a more intrinsic topology. As there are only finit
 ely many incompressible surfaces of bounded Euler characteristic up to iso
 topy in a hyperbolic three-manifold\, it makes sense to ask how the number
  of isotopy classes grows as a function of the Euler characteristic. Using
  Haken’s normal surface theory and facts about branched surfaces\, we ca
 n characterize not just the rate of growth but show it is (essentially) a 
 quasi-polynomial. Moreover\, our method allows for explicit computations i
 n reasonably complicated examples.\n\nThis is joint work with Stavros Garo
 ufalidis and Hyam Rubinstein.\n
LOCATION:https://researchseminars.org/talk/GaTO/3/
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