Seminars and Colloquia by Series

Joint GT-UGA Seminar at GT - Geometric Topology Meets Computational Complexity

Series
Geometry Topology Seminar
Time
Monday, February 19, 2018 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Greg KuperbergUC Davis
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.

Joint GT-UGA Seminar at GT - Unoriented skein relations for link and tangle invariants in Heegaard Floer theory

Series
Geometry Topology Seminar
Time
Monday, February 19, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mike WongLSU
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).

Non-Orientable Lagrangian Fillings of Legendrian Knots

Series
Geometry Topology Seminar
Time
Monday, February 12, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Josh SabloffHaverford College
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. I will present some first steps in constructions of and obstructions to the existence of (decomposable exact) non-orientable Lagrangian fillings. 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.

Geometry and dynamics of free group automorphisms

Series
Geometry Topology Seminar
Time
Monday, January 29, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Caglar UyanikVanderbilt University
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.

Symplectic K-theory of the integers and Galois groups.

Series
Geometry Topology Seminar
Time
Monday, December 4, 2017 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Soren GalatiusStanford University
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.

A large abelian quotient of the level 4 braid group

Series
Geometry Topology Seminar
Time
Monday, November 20, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kevin KordekGeorgia Institute of Technology
It is generally a difficult problem to compute the Betti numbers of a given finite-index subgroup of an infinite group, even if the Betti numbers of the ambient group are known. In this talk, I will describe a procedure for obtaining new lower bounds on the first Betti numbers of certain finite-index subgroups of the braid group. The focus will be on the level 4 braid group, which is the kernel of the mod 4 reduction of the integral Burau representation. This is joint work with Dan Margalit.

Pages