## Seminars and Colloquia by Series

Monday, March 26, 2018 - 14:30 , Location: Room 304 , Bob Gompf and Sergei Gukov , UT Austin and Cal Tech , Organizer: Caitlin Leverson
For oriented manifolds of dimension at least 4 that are simply connected at infinity, it is known that end summing (the noncompact analogue of boundary summing) is a uniquely defined operation. Calcut and Haggerty showed that more complicated fundamental group behavior at infinity can lead to nonuniqueness. We will examine how and when uniqueness fails. There are examples in various categories (homotopy, TOP, PL and DIFF) of nonuniqueness that cannot be detected in a weaker category. In contrast, we will present a group-theoretic condition that guarantees uniqueness. As an application, the monoid of smooth manifolds homeomorphic to R^4 acts on the set of smoothings of any noncompact 4-manifold. (This work is joint with Jack Calcut.)
Monday, March 19, 2018 - 13:55 , Location: Skiles 006 , None , None , Organizer: Dan Margalit
Monday, March 12, 2018 - 14:00 , Location: Skiles 006 , Jim Belk , Bard College , Organizer: Dan Margalit
Monday, February 19, 2018 - 15:30 , Location: Skiles 005 , Greg Kuperberg , UC Davis , Organizer: Caitlin Leverson
Now that the geometrization conjecture has been proven, and the virtual Haken conjecture has been proven, what is left in 3-manifold topology? One remaining topic is the computational complexity of geometric topology problems. How difficult is it to distinguish the unknot? Or 3-manifolds from each other? The right approach to these questions is not just to consider quantitative complexity, i.e., how much work they take for a computer; but also qualitative complexity, whether there are efficient algorithms with one or another kind of help. I will discuss various results on this theme, such as that knottedness and unknottedness are both in NP; and I will discuss high-dimensional questions for context.
Monday, February 19, 2018 - 14:00 , Location: Skiles 006 , Mike Wong , LSU , Organizer: Caitlin Leverson
Although the Alexander polynomial does not satisfy an unoriented skein relation, Manolescu (2007) showed that there exists an unoriented skein exact triangle for knot Floer homology. In this talk, we will describe some developments in this direction since then, including a combinatorial proof using grid homology and extensions to the Petkova-Vertesi tangle Floer homology (joint work with Ina Petkova) and Zarev's bordered sutured Floer homology (joint work with Shea Vela-Vick).
Monday, February 12, 2018 - 14:00 , Location: Skiles 006 , Josh Sabloff , Haverford College , Organizer: John Etnyre
Lagrangian fillings of Legendrian knots are interesting objects that are related, on one hand, to the 4-genus of the underlying smooth knot and, on the other hand, to Floer-type invariants of Legendrian knots. Most work on Lagrangian fillings to date has concentrated on orientable fillings.&nbsp; I will present some first steps in constructions of and obstructions to the existence of (decomposable exact) non-orientable Lagrangian fillings.&nbsp; In addition, I will discuss links between the 4-dimensional crosscap number of a knot and the non-orientable Lagrangian fillings of its Legendrian representatives. This is joint work in progress with Linyi Chen, Grant Crider-Philips, Braeden Reinoso, and Natalie Yao.
Monday, January 29, 2018 - 14:00 , Location: Skiles 006 , Caglar Uyanik , Vanderbilt University , Organizer: Dan Margalit
I will talk about the long standing analogy between the mapping class group of a hyperbolic surface and the outer automorphism group of a free group. Particular emphasis will be on the dynamics of individual elements and applications of these results to structure theorems for subgroups of these groups.
Monday, January 22, 2018 - 14:30 , Location: UGA , TBA , TBA , Organizer: Caitlin Leverson
Monday, January 15, 2018 - 13:55 , Location: Skiles 006 , None , None , Organizer: Dan Margalit
Monday, December 4, 2017 - 14:00 , Location: Skiles 006 , Soren Galatius , Stanford University , Organizer: Kirsten Wickelgren
The general linear groups GL_n(A) can be defined for any ring A, and Quillen's definition of K-theory of A takes these groups as its starting point.  If A is commutative, one may define symplectic K-theory in a very similar fashion, but starting with the symplectic groups Sp_{2n}(A), the subgroup of GL_{2n}(A) preserving a non-degenerate skew-symmetric bilinear form.  The result is a sequence of groups denoted KSp_i(A) for i = 0, 1, ....  For the ring of integers, there is an interesting action of the absolute Galois group of Q on the groups KSp_i(Z), arising from the moduli space of polarized abelian varieties.  In joint work with T. Feng and A. Venkatesh we study this action, which turns out to be an interesting extension between a trivial representation and a cyclotomic representation.