Button to scroll to the top of the page.


Campus health and safety are our top priorities. Get the latest from UT on COVID-19.

Get help with Zoom and more.


Monthly View
By Month
Weekly View
By Week
Daily View
Download as iCal file
Nathan Dunfield, : Counting incompressible surfaces in 3-manifolds
Monday, September 21, 2020, 02:00pm - 03:00pm
Counting embedded curves on a hyperbolic surface as a function of their length has been much studied by Mirzakhani and others. I will discuss analogous questions about counting incompressible surfaces in a hyperbolic 3-manifold, with the key difference that now the surfaces themselves have more intrinsic topology. As there are only finitely many incompressible surfaces of bounded Euler characteristic up to isotopy in a hyperbolic 3-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 can characterize not just the rate of growth but show it is (essentially) a quasi-polynomial. Moreover, our method allows for explicit computations in reasonably complicated examples. This is joint work with Stavros Garoufalidis and Hyam Rubinstein.

Math Calendar Login