### No Seminar - Spring Break

- Series
- Geometry Topology Seminar
- Time
- Monday, March 18, 2019 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- None – None

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- Series
- Geometry Topology Seminar
- Time
- Monday, March 18, 2019 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- None – None

- Series
- Geometry Topology Seminar
- Time
- Monday, March 11, 2019 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 154
- Speaker
- Hannah Schwartz – Bryn Mawr

It is well known that two knots in S^3 are ambiently isotopic if and only if there is an orientation preserving automorphism of S^3 carrying one knot to the other. In this talk, we will examine a family of smooth 4-manifolds in which the analogue of this fact does not hold, i.e. each manifold contains a pair of smoothly embedded, homotopic 2-spheres that are related by a diffeomorphism, but are not smoothly isotopic. In particular, the presence of 2-torsion in the fundamental groups of these 4-manifolds can be used to obstruct even a topological isotopy between the 2-spheres; this shows that Gabai's recent ``4D Lightbulb Theorem" does not hold without the 2-torsion hypothesis.

- Series
- Geometry Topology Seminar
- Time
- Monday, March 4, 2019 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 154
- Speaker
- Kouki Sato – University of Tokyo

The nu+ equivalence is an equivalence relation on the knot concordance group. It is known that the equivalence can be seen as a certain stable equivalence on knot Floer complexes, and many concordance invariants derived from Heegaard Floer theory are invariant under the equivalence. In this talk, we show that any genus one knot is nu+ equivalent to one of the unknot, the trefoil and its mirror.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 25, 2019 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Chris Davis – U Wisconsin Eau Claire

Any knot in $S^3$ may be reduced to a slice knot by making some crossing changes. Indeed, this slice knot can be taken to be the unknot. We show that the same is true of knots in homology spheres, at least topologically. Something more complicated is true smoothly, as not every homology sphere bounds a smooth simply connected homology ball. We prove that a knot in a homology sphere is null-homotopic in a homology ball if and only if that knot can be reduced to the unknot by a sequence of concordances and crossing changes. We will show that there exist knot in a homology sphere which cannot be reduced to the unknot by any such sequence. As a consequence, there are knots in homology spheres which are not concordant to those examples produced by Levine in 2016 and Hom-Lidman-Levine in 2018.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 25, 2019 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Lisa Piccirillo – UT Austin

Smooth simply connected 4-manifolds can admit second homology classes not representable by smoothly embedded spheres; knot traces are the prototypical example of 4-manifolds with such classes. I will show that there are knot traces where the minimal genus smooth surface generating second homology is not of the canonical type, resolving question 1.41 on the Kirby problem list. I will also use the same tools to show that Conway knot does not bound a smooth disk in the four ball, which completes the classification of slice knots under 13 crossings and gives the first example of a non-slice knot which is both topologically slice and a positive mutant of a slice knot.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 18, 2019 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Jen Hom – Georgia Tech

We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains an infinite-rank subgroup and a Z-summand. Our proof relies on the involutive Heegaard Floer package of Hendricks-Manolescu and Hendricks-Manolescu-Zemke. This is joint work with I. Dai, M. Stoffregen, and L. Truong.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 11, 2019 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Daniel Álvarez-Gavela – IAS

We will present an h-principle for the simplification of singularities of Lagrangian and Legendrian fronts. The h-principle says that if there is no homotopy theoretic obstruction to simplifying the singularities of tangency of a Lagrangian or Legendrian submanifold with respect to an ambient foliation by Lagrangian or Legendrian leaves, then the simplification can be achieved by means of a Hamiltonian isotopy. We will also discuss applications of the h-principle to symplectic and contact topology.

- Series
- Geometry Topology Seminar
- Time
- Friday, February 1, 2019 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Bin Sun – Vanderbilt

The notion of an acylindrically hyperbolic group was introduced by Osin as a generalization of non-elementary hyperbolic and relative hyperbolic groups. Ex- amples of acylindrically hyperbolic groups can be found in mapping class groups, outer automorphism groups of free groups, 3-manifold groups, etc. Interesting properties of acylindrically hyperbolic groups can be proved by applying techniques such as Monod-Shalom rigidity theory, group theoretic Dehn filling, and small cancellation theory. We have recently shown that non-elementary convergence groups are acylindrically hyperbolic. This result opens the door for applications of the theory of acylindrically hyperbolic groups to non-elementary convergence groups. In addition, we recovered a result of Yang which says a finitely generated group whose Floyd boundary has at least 3 points is acylindrically hyperbolic.

- Series
- Geometry Topology Seminar
- Time
- Monday, January 28, 2019 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Boyd
- Speaker
- Ian Zemke – Princeton University

In this talk, we describe some applications of link Floer homology to the topology of surfaces in 4-space. If K is a knot in S^3, we will consider the set of surfaces in B^4 which bound K. This space is naturally endowed with a plethora of non-Euclidean metrics and pseudo-metrics. The simplest such metric is the stabilization distance, which is the minimum k such that there is a stabilization sequence connecting two surfaces such that no surface in the sequence has genus greater than k. We will talk about how link Floer homology can be used to give lower bounds, as well as some techniques for computing non-trivial examples. This is joint work with Andras Juhasz.

- Series
- Geometry Topology Seminar
- Time
- Monday, January 28, 2019 - 14:30 for 1 hour (actually 50 minutes)
- Location
- Boyd
- Speaker
- Eylem Yildiz – Michigan State University

I will discuss knot concordances in 3-manifolds. In particular I will talk about knot concordances of knots in the free homotopy class of S^1 x {pt} in S^1 x S^2. It turns out, we can use some of these concordances to construct Akbulut-Ruberman type exotic 4-manifolds. As a consequence, at the end of the talk we will see absolutely exotic Stein pair of 4-manifolds. This is joint work with Selman Akbulut.

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