Seminars and Colloquia by Series

Iterated planar contact manifolds

Series
Geometry Topology Seminar
Time
Monday, April 9, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bahar Acu – Northwestern University

Planar contact manifolds have been intensively studied to understand several aspects of 3-dimensional contact geometry. In this talk, we define "iterated planar contact manifolds", a higher-dimensional analog of planar contact manifolds, by using topological tools such as "open book decompositions" and "Lefschetz fibrations”. We provide some history on existing low-dimensional results regarding Reeb dynamics, symplectic fillings/caps of contact manifolds and explain some generalization of those results to higher dimensions via iterated planar structure. This is partly based on joint work in progress with J. Etnyre and B. Ozbagci.

Truncated Heegaard Floer homology and concordance invariants

Series
Geometry Topology Seminar
Time
Monday, April 2, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Linh Truong – Columbia University
Heegaard Floer homology has proven to be a useful tool in the study of knot concordance. Ozsvath and Szabo first constructed the tau invariant using the hat version of Heegaard Floer homology and showed it provides a lower bound on the slice genus. Later, Hom and Wu constructed a concordance invariant using the plus version of Heegaard Floer homology; this provides an even better lower-bound on the slice genus. In this talk, I discuss a sequence of concordance invariants that are derived from the truncated version of Heegaard Floer homology. These truncated Floer concordance invariants generalize the Ozsvath-Szabo and Hom-Wu invariants.

Joint GT-UGA Seminar at UGA - On Uniqueness of End Sums and TBA

Series
Geometry Topology Seminar
Time
Monday, March 26, 2018 - 14:30 for 2.5 hours
Location
Room 304
Speaker
Bob Gompf and Sergei Gukov – UT Austin and Cal Tech
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.)

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 Kuperberg – UC 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 Wong – LSU
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 Sabloff – Haverford 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 Uyanik – Vanderbilt 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.

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