## Seminars and Colloquia by Series

### Genuine Equivariant Operads

Series
Geometry Topology Seminar
Time
Monday, October 22, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Luis Alexandre PereiraGeorgia Tech
A fundamental result in equivariant homotopy theory due to Elmendorf states that the homotopy theory of G-spaces, with w.e.s measured on all ﬁxed points, is equivalent to the homotopy theory of G-coeﬃcient systems in spaces, with w.e.s measured at each level of the system. Furthermore, Elmendorf’s result is rather robust: analogue results can be shown to hold for, among others, the categories of (topological) categories and operads. However, it has been known for some time that in the G-operad case such a result does not capture the ”correct” notion of weak equivalence, a fact made particularly clear in work of Blumberg and Hill discussing a whole lattice of ”commutative operads with only some norms” that are not distinguished at all by the notion of w.e. suggested above. In this talk I will talk about part of a joint project which aims at providing a more diagrammatic understanding of Blumberg and Hill’s work using a notion of G-trees, which are a generalization of the trees of Cisinski-Moerdijk-Weiss. More speciﬁcally, I will describe a new algebraic structure, which we dub a ”genuine equivariant operad”, which naturally arises from the study of G-trees and which allows us to state the ”correct” analogue of Elmendorf’s theorem for G-operads.

### The transverse invariant and braid dynamics

Series
Geometry Topology Seminar
Time
Monday, October 15, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skile 006
Speaker
Lev Tovstopyat-NelipBoston College
Let K be a link braided about an open book (B,p) supporting a contact manifold (Y,x). K and B are naturally transverse links. We prove that the hat version of the transverse link invariant defined by Baldwin, Vela-Vick and Vertesi is non-zero for the union of K with B. As an application, we prove that the transverse invariant of any braid having fractional Dehn twist coefficient greater than one is non-zero. This generalizes a theorem of Plamenevskaya for classical braid closures.

### No Seminar - Fall Break

Series
Geometry Topology Seminar
Time
Monday, October 8, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skile 006
Speaker
NoneNone

### Joint GT-UGA Seminar at GT - The ribbon genus of a knotted surface

Series
Geometry Topology Seminar
Time
Monday, October 1, 2018 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jason JosephUGA
The knot group has played a central role in classical knot theory and has many nice properties, some of which fail in interesting ways for knotted surfaces. In this talk we'll introduce an invariant of knotted surfaces called ribbon genus, which measures the failure of a knot group to 'look like' a classical knot group. We will show that ribbon genus is equivalent to a property of the group called Wirtinger deficiency. Then we will investigate some examples and conclude by proving a connection with the second homology of the knot group.

### Joint GT-UGA Seminar at GT - A contact Fukaya category

Series
Geometry Topology Seminar
Time
Monday, October 1, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Lenny NgDuke University
I'll describe a way to construct an A-infinity category associated to a contact manifold, analogous to a Fukaya category for a symplectic manifold. The objects of this category are Legendrian submanifolds equipped with augmentations. Currently we're focusing on standard contact R^3 but we're hopeful that we can extend this to other contact manifolds. I'll discuss some properties of this contact Fukaya category, including generation by unknots and a potential application to proving that augmentations = sheaves''. This is joint work in progress with Tobias Ekholm and Vivek Shende.

### Link Concordance and Groups

Series
Geometry Topology Seminar
Time
Monday, September 24, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Miriam KuzbaryRice University
Since its introduction in 1966 by Fox and Milnor the knot concordance group has been an invaluable algebraic tool for examining the relationships between 3- and 4- dimensional spaces. Though knots generalize naturally to links, this group does not generalize in a natural way to a link concordance group. In this talk, I will present joint work with Matthew Hedden where we define a link concordance group based on the “knotification” construction of Peter Ozsvath and Zoltan Szabo. This group is compatible with Heegaard Floer theory and, in fact, much of the work on Heegaard Floer theory for links has implied a study of these objects. Moreover, we have constructed a generalization of Milnor’s group-theoretic higher order linking numbers in a novel context with implications for our link concordance group.

### Non-isotopic embeddings of contact manifolds.

Series
Geometry Topology Seminar
Time
Monday, September 17, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John EtnyreGeorgia Tech
The study of transverse knots in dimension 3 has been instrumental in the development of 3 dimensional contact ge- ometry. One natural generalization of transverse knots to higher dimensions is contact submanifolds. Embeddings of one contact manifold into another satisfies an h-principle for codimension greater than 2, so we will discuss the case of codimension 2 contact embeddings. We will give the first pair of non-isotopic contact embeddings in all dimensions (that are formally isotopic).

### Rational cobordisms and integral homology (JungHwan Park)

Series
Geometry Topology Seminar
Time
Monday, September 10, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rational cobordisms and integral homologySchool of Mathematics Georgia Institute of Technology
We show that for any connected sum of lens spaces L there exists a connected sum of lens spaces X such that X is rational homology cobordant to L and if Y is rational homology cobordant to X, then there is an injection from H_1(X; Z) to H_1(Y; Z). Moreover, as a connected sum of lens spaces, X is uniquely determined up to orientation preserving diffeomorphism. As an application, we show that the natural map from the Z/pZ homology cobordism group to the rational homology cobordism group has large cokernel, for each prime p. This is joint work with Paolo Aceto and Daniele Celoria.

### No Seminar - Labor Day

Series
Geometry Topology Seminar
Time
Monday, September 3, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skile 006
Speaker
NoneNone

### Joint GT-UGA Seminar at UGA - Khovanov homology via immersed curves in the 4-punctured sphere

Series
Geometry Topology Seminar
Time
Monday, August 27, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Boyd 328
Speaker
Artem KotelskiyIndiana University
We will describe a geometric interpretation of Khovanov homology as Lagrangian Floer homology of two immersed curves in the 4-punctured 2-dimensional sphere. The main ingredient is a construction which associates an immersed curve to a 4-ended tangle. This curve is a geometric way to represent Khovanov (or Bar-Natan) invariant for a tangle. We will show that for a rational tangle the curve coincides with the representation variety of the tangle complement. The construction is inspired by a result of [Hedden, Herald, Hogancamp, Kirk], which embeds 4-ended reduced Khovanov arc algebra (or, equivalently, Bar-Natan dotted cobordism algebra) into the Fukaya category of the 4-punctured sphere. The main tool we will use is a category of peculiar modules, introduced by Zibrowius, which is a model for the Fukaya category of a 2-sphere with 4 discs removed. This is joint work with Claudius Zibrowius and Liam Watson.