### Joint GT-UGA Seminar at UGA - TBA

- Series
- Geometry Topology Seminar
- Time
- Monday, October 29, 2018 - 14:30 for 1 hour (actually 50 minutes)
- Location
- Boyd 328
- Speaker
- JungHwan Park – Georgia Tech

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- Series
- Geometry Topology Seminar
- Time
- Monday, October 29, 2018 - 14:30 for 1 hour (actually 50 minutes)
- Location
- Boyd 328
- Speaker
- JungHwan Park – Georgia Tech

- Series
- Geometry Topology Seminar
- Time
- Monday, October 22, 2018 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Luis Alexandre Pereira – Georgia 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.

- Series
- Geometry Topology Seminar
- Time
- Monday, October 15, 2018 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skile 006
- Speaker
- Lev Tovstopyat-Nelip – Boston 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.

- Series
- Geometry Topology Seminar
- Time
- Monday, October 8, 2018 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skile 006
- Speaker
- None – None

- Series
- Geometry Topology Seminar
- Time
- Monday, October 1, 2018 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Jason Joseph – UGA

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.

- Series
- Geometry Topology Seminar
- Time
- Monday, October 1, 2018 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Lenny Ng – Duke 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.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 24, 2018 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Miriam Kuzbary – Rice 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.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 17, 2018 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- John Etnyre – Georgia 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).

- 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 homology – School of Mathematics Georgia Institute of Technology – junghwan.park@math.gatech.edu

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.

- Series
- Geometry Topology Seminar
- Time
- Monday, September 3, 2018 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skile 006
- Speaker
- None – None