|Ian Agol, UC Berkeley||10:30-11:30 am||151 Sloan||LERF and virtual fibering|
|Steve Ferry, Rutgers||1:30-2:30 pm||151 Sloan||Higson compactifications|
|Kevin Whyte, UIC||2:45-3:45 pm||151 Sloan||Virtual Betti numbers of random complexes|
|Chris Leininger, UIUC||4-5 pm||151 Sloan||Strong Tits alternative for pure braid groups|
Ian Agol. Title: LERF and virtual fibering
Abstract: We show that a Haken hyperbolic 3-manifold with LERF fundamental group is virtually fibered.
Steve Ferry. Title: Higson compactifications
Abstract: We will show how volume growth in a manifold M can be used to detect cohomology in its Higson compactification.
Kevin Whyte. Title: Virtual Betti numbers of random complexes
Abstract: We will discuss bounds on the Betti numbers of finite covers of complexes under local geometric assumptions, with applications to various models of random complexes.
Chris Leininger. Title: Strong Tits alternative for
pure braid groups
Abstract: A group satisfies the "Tits alternative" if every subgroup is either virtually solvable or contains a nonabelian free group. This is named after J. Tits who proved that all finitely generated linear groups enjoy this property. The Tits alternative was established for braid groups by Ivanov and McCarthy, but now also follows from linearity (due to Bigelow-Krammer). I'll discuss joint work with D. Margalit, in which we prove a strong version of the Tits alternative for the pure braid groups: every two elements of the pure braid group either commute or generate a free group. The proof uses 3-manifold topology and actions on trees.