## Seminars and Colloquia by Series

### Geometry Topology Seminar : TBA by Maggie Miller

Series
Geometry Topology Seminar
Time
Monday, April 13, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Maggie MillerPrinceton University

### CANCELLED: Joint UGA-GT Topology Seminar at GT: TBA by Allison Moore

Series
Geometry Topology Seminar
Time
Monday, April 6, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Allison MooreVirginia Commonwealth University

### Joint UGA-GT Topology Seminar at GT: TBA by Shelly Harvey

Series
Geometry Topology Seminar
Time
Monday, April 6, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shelly HarveyRice University

### TBA by Anthony Conway

Series
Geometry Topology Seminar
Time
Monday, March 30, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skile 006
Speaker
Anthony ConwayMax Planck Institut für Mathematik

### Satellite operations and knot genera

Series
Geometry Topology Seminar
Time
Monday, March 9, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Allison MillerRice University

The satellite construction, which associates to a pattern knot P in a solid torus and a companion knot K in the 3-sphere the so-called satellite knot P(K), features prominently in knot theory and low-dimensional topology.  Besides the intuition that P(K) is “more complicated” than either P or K, one can attempt to quantify how the complexity of a knot changes under the satellite operation. In this talk, I’ll discuss how several notions of complexity based on the minimal genus of an embedded surface change under satelliting. In the case of the classical Seifert genus of a knot, Schubert gives an exact formula. In the 4-dimensional context the situation is more complicated, and depends on whether we work in the smooth or topological category: the smooth category is sometimes asymptotically similar to the classical setting, but our main results show that the topological category is much weirder.  This talk is based on joint work with Peter Feller and Juanita Pinzón-Caicedo.

### Joint UGA-GT Topology Seminar at UGA: The dihedral genus of a knot

Series
Geometry Topology Seminar
Time
Monday, March 2, 2020 - 16:00 for 1 hour (actually 50 minutes)
Location
Boyd
Speaker
Patricia CahnSmith College

We consider dihedral branched covers of $S^4$, branched along an embedded surface with one non-locally flat point, modelled on the cone on a knot $K\subset S^3$. Kjuchukova proved that the signature of this cover is an invariant $\Xi_p(K)$ of the $p$-colorable knot $K$. We prove that the values of $\Xi_p(K)$ fall in a bounded range for homotopy-ribbon knots. We also construct a family of (non-slice) knots for which the values of $\Xi_p$ are unbounded. More generally, we introduce the notion of the dihedral 4-genus of a knot, and derive a lower bound on the dihedral 4-genus of $K$ in terms of $\Xi_p(K)$. This work is joint with A. Kjuchukova.

### Joint UGA-GT Topology Seminar at UGA: Stein domains in complex two space with prescribed boundary

Series
Geometry Topology Seminar
Time
Monday, March 2, 2020 - 14:30 for 1 hour (actually 50 minutes)
Location
Boyd
Speaker
Bolent TosunUniversity of Alabama

A Stein manifold is a complex manifold with particularly nice convexity properties. In real dimensions above 4, the existence of a Stein structure is essentially a homotopical question, but for 4-manifolds the situation is more subtle. In this talk we will consider the existence of such structures in the ambient settings, that is, manifolds/domains with various degree of convexity as open/compact subsets of a complex manifold, e.g. complex 2-space C^2. In particular, I will discuss the following question: Which homology spheres embed in C^2 as the boundary of a Stein domain? This question was first considered and explored in detail by Gompf. At that time, he made a fascinating conjecture that no non-trivial Brieskorn homology sphere, with either orientation, embeds in C^2 as a Stein boundary. In this talk, I will survey what we know about this conjecture, and report on some closely related recent work in progress that ties to an interesting symplectic rigidity phenomena in low dimensions.

### From veering triangulations to link spaces and back again

Series
Geometry Topology Seminar
Time
Monday, February 24, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Henry SegermanOklahoma State University
Agol introduced veering triangulations of mapping tori, whose combinatorics are canonically associated to the pseudo-Anosov monodromy. In unpublished work, Guéritaud and Agol generalise an alternative construction to any closed manifold equipped with a pseudo-Anosov flow without perfect fits. Schleimer and I build the reverse map. As a first step, we construct the link space for a given veering triangulation. This is a copy of R2, equipped with transverse stable and unstable foliations, from which the Agol-Guéritaud's construction recovers the veering triangulation. The link space is analogous to Fenley's orbit space for a pseudo-Anosov flow. Along the way, we construct a canonical circular ordering of the cusps of the universal cover of a veering triangulation. I will also talk about work with Giannopolous and Schleimer building a census of transverse veering triangulations. The current census lists all transverse veering triangulations with up to 16 tetrahedra, of which there are 87,047.

### Spaces of trees and fatgraphs for string topology and moduli spaces

Series
Geometry Topology Seminar
Time
Monday, February 17, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kate PoirierCUNY - City College of Technology

Spaces of fatgraphs have long been used to study a variety of topics in math and physics. In this talk, we introduce two spaces of fatgraphs arising in string topology—one which parameterizes operations on chains of the free loop space of a manifold and one which parametrizes operations on Hochschild cochains of a “V-infinity” algebra. We present a conjecture relating these two spaces to one another and to the moduli space of Riemann surfaces. We also introduce polyhedra called “assocoipahedra” which generalize Stasheff’s associahedra to algebras with a compatible co-inner product. Assocoipahedra are used to prove that the dioperad governing V-infinity algebras satisfies certain algebraic properties.

### The Frohman-Kania-Bartoszynska invariant is the 3D index

Series
Geometry Topology Seminar
Time
Wednesday, February 12, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
S. GaroufalidisSUSTECH and MPI Bonn
We prove that a power series invariant of suitable ideal triangulations, defined by Frohman-Kania-Bartoszynska coincides with the power series invariant of Dimofte-Gaiotto-Gukov known as the 3D index. In partucular, we deduce that the FKB invariant is topological, and that the tetrahedron weight of the 3D index is a limit of quantum 6j symbols. Joint work with Roland van der Veen.