Seminars and Colloquia by Series

Embedding closed hyperbolic 3-manifolds in small volume hyperbolic 4-manifolds

Series
Geometry Topology Seminar
Time
Monday, October 26, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michelle Chu – University of Illinois at Chicago –

The smallest volume cusped hyperbolic 3-manifolds, the figure-eight knot complement and its sister, contain many immersed but no embedded closed totally geodesic surfaces. In this talk we discuss the existence or lack thereof of codimension-1 closed embedded totally geodesic submanifolds in minimal volume cusped hyperbolic 4-manifolds. This talk is based on joint work with Alan Reid.

Ribbon homology cobordism

Series
Geometry Topology Seminar
Time
Monday, October 19, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Shea Vela Vick – Louisiana State University –

A cobordism between 3-manifolds is ribbon if it is built from handles of index no greater than 2. Such cobordisms arise naturally from several different topological and geometric contexts. In this talk, we discuss these objects and present a few obstructions to their existence, from Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. This is joint work with Aliakbar Daemi, Tye Lidman, and Mike Wong.

A contact invariant from bordered Heegaard Floer homology

Series
Geometry Topology Seminar
Time
Monday, October 12, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://dartmouth.zoom.us/j/98031035804?pwd=NnBpTlhVS2lzVzFWTkYyTlloeWVuQT09
Speaker
Ina Petkova – Dartmouth

Given a contact structure on a bordered 3-manifold, we describe an invariant which takes values in the bordered sutured Floer homology of the manifold. This invariant satisfies a nice gluing formula, and recovers the Oszvath-Szabo contact class in Heegaard Floer homology. This is joint work with Alishahi, Foldvari, Hendricks, Licata, and Vertesi.

Zoom info:

Meeting ID: 980 3103 5804

Passcode: 196398

SL3 Skein Algebras of Surfaces by Vijay Higgins

Series
Geometry Topology Seminar
Time
Monday, September 28, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Virtual
Speaker
Vijay Higgins – UC Santa Barbara –

The SL2 skein algebra of a surface is built from diagrams of curves on the surface. To multiply two diagrams, we draw one diagram on top of the other and then resolve the crossings with the Kauffman bracket. If we replace SL2 with another quantum group, we replace curves by embedded graphs on the surface. Recently, Thang Le showed that the SL2 skein algebra has a nice decomposition into simpler algebras whenever the surface has an ideal triangulation. This triangular decomposition is a powerful tool and should help us to study other skein algebras if we are able to show that the necessary ingredients exist. In this talk, I will explain what these ingredients are and how to find them for the SL3 skein algebra of trivalent webs on a surface.

8.3.3

The embedded contact homology of prequantization bundles

Series
Geometry Topology Seminar
Time
Monday, September 21, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
on line
Speaker
Morgan Weiler – Rice

The 2011 PhD thesis of Farris demonstrated that the ECH of a prequantization bundle over a Riemann surface is isomorphic as a Z/2Z-graded group to the exterior algebra of the homology of its base, the only known computation of ECH to date which does not rely on toric methods. We extend this result by computing the Z-grading on the chain complex, permitting a finer understanding of this isomorphism. We fill in some technical details, including the Morse-Bott direct limit argument and some writhe bounds. The former requires the isomorphism between filtered Seiberg-Witten Floer cohomology and filtered ECH as established by Hutchings--Taubes. The latter requires the work on higher asymptotics of pseudoholomorphic curves by Cristofaro-Gardiner--Hutchings—Zhang.

L-space surgeries on 2-component L-space links

Series
Geometry Topology Seminar
Time
Monday, September 14, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/803706608
Speaker
Beibei Liu – Georgia Tech

All 3-manifolds can be described as surgery on links in the three-sphere by the celebrated theorem of Lickorish and Wallace. Motivated by the L-space conjecture, it is interesting to understand what surgery manifolds are L-spaces, which have the simplest possible Floer homology such as lens spaces. In this talk, we concentrate on surgeries on a family of links, which are called L-space links, and show possible L-space surgeries on such links. We also give some link detection results in terms of the surgeries. 

Triple linking and Heegaard Floer homology.

Series
Geometry Topology Seminar
Time
Monday, August 31, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Allison Moore – Virginia Commonwealth University –

We will describe several appearances of Milnor’s invariants in the link Floer complex. This will include a formula that expresses the Milnor triple linking number in terms of the h-function. We will also show that the triple linking number is involved in a structural property of the d-invariants of surgery on certain algebraically split links. We will apply the above properties toward new detection results for the Borromean and Whitehead links. This is joint work with Gorsky, Lidman and Liu.

Equivalence relations on 4 manifolds

Series
Geometry Topology Seminar
Time
Monday, August 24, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/766579216
Speaker
Mark Powell – Durham University –

I will compare and contrast a selection of popular equivalence relations on 4 manifolds, and explain some recent progress on classification results.

The speaker will hold online office hours from 3:00-4:00 pm for interested graduate students and postdocs.

SU(2) representations for toroidal homology spheres

Series
Geometry Topology Seminar
Time
Monday, August 17, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/803706608
Speaker
Tye Lidman – NCSU

The three-dimensional Poincare conjecture shows that any closed three-manifold other than the three-sphere has non-trivial fundamental group. A natural question is how to measure the non-triviality of such a group, and conjecturally this can be concretely realized by a non-trivial representation to SU(2). We will show that the fundamental groups of three-manifolds with incompressible tori admit non-trivial SU(2) representations. This is joint work with Juanita Pinzon-Caicedo and Raphael Zentner.

The speaker will hold online office hours from 3:15-4:15 pm for interested graduate students and postdocs.

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