Past Iterations
Information
Submissions for contributed talks are now closed, but will be considering submissions again for a third iteration in the near future. Details will be announced here.
This is the website for GOATS #2, the second in a series of online miniconferences for graduate students in Geometry and Topology. The speakers will be graduate students, and attendance is open to anyone. We plan to hold these on an ongoing/recurring basis, and will update this page with information about future events.
 You can follow and tweet under the #mathgoats2020 hashtag.
 For those that are interested in speaking at the next GOATS, we welcome you to reach out to any of the organizers directly!
Schedule
Saturday, June 6th, 12:00 PM to 5:30 PM EDT
11:50 AM EDT: Zoom meeting opens
12:001:00PM EDT: Marla Williams, University of NebraskaLincoln

Title: TBD

Abstract: TBD
1:001:10 PM EDT: Ten Minute Break
1:101:30 PM EDT: Contributed Talk #1, Steve Wheatley, George Mason University

Title: Characterizations of $2\dash$Homeomorphic Spaces

Abstract: In a 2018 paper, Arhangelâskii and Maksyuta give the definition of a $2\dash$homeomorphism, a topological concept that generalizes the notion of a homeomorphism. In this talk, we give some characterizations of spaces that are $2\dash$homeomorphic to spaces possessing various topological properties, including compact spaces and discrete spaces. We also show that, although many topological properties are not preserved under the $2\dash$homeomorphism relation, the property of having finite CantorBendixson height is preserved.
1:301:50 PM EDT: Contributed Talk #2, Rhea Palak Bakshi, The George Washington University

Title: Framings of Links in 3manifolds and Torsion in Skein Modules

Abstract: We show that the only way of changing the framing of a link by ambient isotopy in an oriented $3\dash$manifold is when the manifold admits a properly embedded nonseparating $S^2$. This change of framing is given by the Dirac trick, also known as the light bulb trick. The main tool we use is based on McCulloughâs work on the mapping class groups of $3\dash$manifolds. We also express our results in the language of skein modules. In particular, we relate our results to the framing skein module and the Kauffman bracket skein module.
1:502:10 PM EDT: Break / Social Event #1
2:103:10 PM EDT: Duncan Clark, Ohio State University

Title: On the Goodwillie Derivatives of the Identity in Structured Ring Spectra

Abstract: Functor calculus was introduced by Goodwillie as a means for analyzing homotopy functors between suitable model categories. One noteworthy facet is that âniceâ functors $F\colon \mathsf{C}\to \mathsf{D}$ are determined by a certain symmetric sequence called the derivatives of $F$.
This sequence of derivatives is known to posses much structure: for instance, the derivatives of the identity functor on the category of based topological spaces is an operad, as first shown by Ching. It is further expected that a result of this type should hold in any suitable model category, and in particular conjectured that the derivatives of the identity on the category of algebras over an operad $\mathcal{O}$ in spectra should be equivalent to $\mathcal{O}$ as operads.
In this talk we produce an intrinsic âhomotopycoherentâ operad structure for the derivatives of the identity which is equivalent to that on $\mathcal{O}$, thus resolving the above conjecture. Along the way we will discuss the necessary background of functor calculus and algebras over operads of spectra. Our method is to induce a homotopy coherent operadic pairing on the derivatives by a suitable pairing on the cosimplicial resolution offered by the stabilization adjunction for $\mathcal{O}$algebras.
Time permitting, we will provide some other applications of our techniques such as a highly homotopycoherent chain rule for functors of structured ring spectra.
3:103:20 PM EDT: Ten Minute Break
3:203:40 PM EDT: Contributed Talk #3, Christopher Perez, University of Illinois at Chicago

Title: Towers and Elementary Embeddings in Toral Relatively Hyperbolic Groups

Abstract: A group $G$ is a tower over a subgroup $H$ if $H$ can be obtained from $G$ via a series of retractions in a nice and very geometric way. In 2011, ChloĂ© Perin proved that if $H$ is an elementarily embedded subgroup of a torsionfree hyperbolic group $G$ (also known as an elementary submodel), then $G$ is a tower over $H$.
The implication of this and similar results is that the geometric structures of certain groups capture their logical structures as well. I will be discussing towers and my recent generalization of Perinâs result to toral relatively hyperbolic groups.
3:404:00 PM EDT: Contributed Talk #4, Nikolas Schonsheck, Ohio State University

Title: Fibration Theorems for $\mathbf{TQ}\dash$Completion of Structured Ring Spectra

Abstract: By considering algebras over an operad $\mathcal{O}$ in oneâs preferred category of spectra, we can encode various flavors of algebraic structure (e.g. commutative ring spectra). Drawing intuition from singular homology of spaces and Quillen homology of rings, topological Quillen ($\mathbf{TQ}$) homology is a naturally occurring notion of homology for these objects, with analogies to both singular homology and stabilization of spaces.
For a given $\mathcal{O}\dash$algebra $X$, there is a canonical way (following BousfieldKan) to âglue togetherâ iterates $\mathbf{TQ}^n(X)$ of the $\mathbf{TQ}\dash$homology spectrum of $X$ to construct âthe part of $X$ that $\mathbf{TQ}\dash$homology sees,â namely its $\mathbf{TQ}\dash$completion. We then ask, âWhen can $X$ be ârecovered fromâ $\mathbf{TQ}(X)$ in this way?â
BousfieldKan consider the analogous question in spaces and conclude that all nilpotent spaces are weakly equivalent to their homology completion. The key technical maneuver of their proof involves showing that certain fibration sequences are preserved by completion. In this talk, we will discuss certain types of fibration sequences of $\mathcal{O}\dash$algebras which are preserved by $\mathbf{TQ}\dash$completion, drawing analogies along the way to the case of pointed spaces.
4:004:20 PM EDT: Break / Social Event #2
4:205:20 PM EDT: Nicholas Cazet, UC Davis

Title: Vertex Distortion of Lattice Knots

Abstract: The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the 1norm. We show analogous results of Gromov, Pardon and BlairCampisiTaylorTomova about the distortion of smooth knots hold for vertex distortion, the vertex distortion of a lattice knot is 1 only if it is the unknot, and that there are minimal latticestick number knot conformations with arbitrarily high distortion.
5:205:30 PM EDT: Reception
Participant Information
Adapted from the Knot Online Seminar
To Join the Meeting

You will need to download the zoom client and join using the meeting number sent to you via email confirmation after registering.

This meeting is open from 11:45am to 3:45pm (EDT).
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