## Seminars and Colloquia by Series

Monday, October 23, 2017 - 13:55 , Location: Skiles 006 , Mark Hughes , BYU , Organizer: John Etnyre
The immersed Seifert genus of a knot $K$ in $S^3$ can be defined as the minimal genus of an orientable immersed surface $F$ with $\partial F = K$.  By a result of Gabai, this value is always equal to the (embedded) Seifert genus of $K$.  In this talk I will discuss the embedded and immersed cross-cap numbers of a knot, which are the non-orientable versions of these invariants.  Unlike their orientable counterparts these values do not always coincide, and can in fact differ by an arbitrarily large amount.  In further contrast to the orientable case, there are families of knots with arbitrarily high embedded 4-ball cross-cap numbers, but which are easily seen to have immersed cross-cap number 1.  After describing these examples I will discuss a classification of knots with immersed cross-cap number 1.  This is joint work with Seungwon Kim.
Monday, October 16, 2017 - 13:55 , Location: Skiles 006 , Kyle Hayden , Boston College , Organizer: John Etnyre
Every four-dimensional Stein domain has a Morse function whoseregular level sets are contact three-manifolds. This allows us to studycomplex curves in the Stein domain via their intersection with thesecontact level sets, where we can comfortably apply three-dimensional tools.We use this perspective to understand links in Stein-fillable contactmanifolds that bound complex curves in their Stein fillings.
Monday, October 9, 2017 - 13:55 , Location: Skiles 006 , None , None , Organizer: Jennifer Hom
Monday, October 2, 2017 - 15:30 , Location: Skiles 005 , Jeff Meier , UGA , Organizer: Caitlin Leverson
I'll introduce you to one of my favorite knotted objects: fibered, homotopy-ribbon disk-knots.  After giving a thorough overview of these objects, I'll discuss joint work with Kyle Larson that brings some new techniques to bear on their study.  Then, I'll present new work with Alex Zupan that introduces connections with Dehn surgery and trisections.  I'll finish by presenting a classification result for fibered, homotopy-ribbon disk-knots bounded by square knots.
Monday, October 2, 2017 - 13:55 , Location: Skiles 006 , Matt Stoffregen , MIT , Organizer: Caitlin Leverson
We use Manolescu's Pin(2)-equivariant Floer homology to study homology cobordisms among Seifert spaces.  In particular, we will show that the subgroup of the homology cobordism group generated by Seifert spaces admits a \mathbb{Z}^\infty summand.  This is joint work with Irving Dai.
Monday, September 25, 2017 - 15:00 , Location: Skiles 005 , Hung Tran , Georgia , Organizer: Dan Margalit
We give "visual descriptions" of cut points and non-parabolic cut pairs in the Bowditch boundary of a relatively hyperbolic right-angled Coxeter group. We also prove necessary and sufficient conditions for a relatively hyperbolic right-angled Coxeter group whose defining graph has a planar flag complex with minimal peripheral structure to have the Sierpinski carpet or the 2-sphere as its Bowditch boundary. We apply these results to the problem of quasi-isometry classification of right-angled Coxeter groups. Additionally, we study right-angled Coxeter groups with isolated flats whose $\CAT(0)$ boundaries are Menger curve. This is a joint work with Matthew Haulmark and Hoang Thanh Nguyen.
Monday, September 18, 2017 - 13:55 , Location: Skiles 006 , Michael Landry , Yale , , Organizer: Balazs Strenner
Let M be a closed hyperbolic 3-manifold with a fibered face \sigma of the unit ball of the Thurston norm on H_2(M). If M satisfies a certain condition related to Agol’s veering triangulations, we construct a taut branched surface in M spanning \sigma. This partially answers a 1986 question of Oertel, and extends an earlier partial answer due to Mosher. I will not assume knowledge of the Thurston norm, branched surfaces, or veering triangulations.
Monday, September 11, 2017 - 14:30 , Location: UGA Room 304 , Jeremy Van Horn-Morris and Laura Starkston , TBA , Organizer: Caitlin Leverson
Monday, September 4, 2017 - 14:15 , Location: Skiles 006 , None , None , Organizer: Dan Margalit
Tuesday, August 22, 2017 - 11:00 , Location: Skiles 006 , Juliette Bavard , University of Chicago , Organizer: Balazs Strenner
The mapping class group of the plane minus a Cantor set naturally appears in many dynamical contexts, including group actions on surfaces, the study of groups of homeomorphisms on a Cantor set, and complex dynamics. In this talk, I will present the 'ray graph', which is a Gromov-hyperbolic graph on which this big mapping class group acts by isometries (it is an equivalent of the curve graph for this surface of infinite topological type). If time allows, I will give a description of the Gromov-boundary of the ray graph in terms of long rays in the plane minus a Cantor set. This involves joint work with Alden Walker.