### Geometry Topology Seminar : TBA by Mark Powell

- Series
- Geometry Topology Seminar
- Time
- Friday, April 17, 2020 - 14:00 for 1 hour (actually 50 minutes)
- Location
- TBD
- Speaker
- Mark Powell – Durham University – mark.a.powell@durham.ac.uk

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- Series
- Geometry Topology Seminar
- Time
- Friday, April 17, 2020 - 14:00 for 1 hour (actually 50 minutes)
- Location
- TBD
- Speaker
- Mark Powell – Durham University – mark.a.powell@durham.ac.uk

- Series
- Geometry Topology Seminar
- Time
- Monday, April 13, 2020 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Maggie Miller – Princeton University – maggiem@math.princeton.edu

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

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

- Series
- Geometry Topology Seminar
- Time
- Monday, March 30, 2020 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skile 006
- Speaker
- Anthony Conway – Max Planck Institut für Mathematik – anthonyyconway@gmail.com

- Series
- Geometry Topology Seminar
- Time
- Monday, March 9, 2020 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Allison Miller – Rice University – allison.miller@rice.edu

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.

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

- Series
- Geometry Topology Seminar
- Time
- Monday, March 2, 2020 - 14:30 for 1 hour (actually 50 minutes)
- Location
- Boyd
- Speaker
- Bolent Tosun – University 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.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 24, 2020 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Henry Segerman – Oklahoma State University – segerman@math.okstate.edu

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.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 17, 2020 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Kate Poirier – CUNY - City College of Technology – KPoirier@citytech.cuny.edu

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.

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