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SUMMARY:Marla Williams (University of Nebraska-Lincoln)
DTSTART:20200606T160000Z
DTEND:20200606T170000Z
DTSTAMP:20260404T095423Z
UID:GOATS/1
DESCRIPTION:Title: Trisections and Flat Surface Bundles\nby Marla Williams (Universi
ty of Nebraska-Lincoln) as part of GOATS\n\n\nAbstract\nWe’ll start with
a look at how to trisect trivial surface bundles over surfaces and how to
draw the corresponding diagrams. We’ll then move into a discussion of w
hat changes when we shift to trisecting nontrivial surface bundles\, and w
hy flatness matters for my diagram construction.\n
LOCATION:https://stable.researchseminars.org/talk/GOATS/1/
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SUMMARY:Nicholas Cazet (UC Davis)
DTSTART:20200606T202000Z
DTEND:20200606T212000Z
DTSTAMP:20260404T095423Z
UID:GOATS/3
DESCRIPTION:Title: Vertex Distortion of Lattice Knots\nby Nicholas Cazet (UC Davis)
as part of GOATS\n\n\nAbstract\nThe vertex distortion of a lattice knot is
the supremum of the ratio of the distance between a pair of vertices alon
g the knot and their distance in the 1-norm. We show analogous results of
Gromov\, Pardon and Blair-Campisi-Taylor-Tomova about the distortion of sm
ooth 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 lattice-s
tick number knot conformations with arbitrarily high distortion.\n
LOCATION:https://stable.researchseminars.org/talk/GOATS/3/
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SUMMARY:Duncan Clark (Ohio State University)
DTSTART:20200606T181000Z
DTEND:20200606T191000Z
DTSTAMP:20260404T095423Z
UID:GOATS/4
DESCRIPTION:Title: On the Goodwillie Derivatives of the Identity in Structured Ring Spec
tra\nby Duncan Clark (Ohio State University) as part of GOATS\n\n\nAbs
tract\nFunctor calculus was introduced by Goodwillie as a means for analyz
ing homotopy functors between suitable model categories. \n One notewor
thy facet is that "nice" functors $F\\colon \\mathsf{C}\\to \\mathsf{D}$ a
re determined by a certain symmetric sequence called the derivatives of $F
$. \n\n 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. \n It
is further expected that a result of this type should hold in any suitabl
e model category\, and in particular conjectured that the derivatives of t
he identity on the category of algebras over an operad $\\mathcal{O}$ in s
pectra should be equivalent to $\\mathcal{O}$ as operads. \n\n In this
talk we produce an intrinsic "homotopy-coherent" operad structure for the
derivatives of the identity which is equivalent to that on $\\mathcal{O}$\
, thus resolving the above conjecture. \n Along the way we will discuss
the necessary background of functor calculus and algebras over operads of
spectra. \n Our method is to induce a homotopy coherent operadic pairi
ng on the derivatives by a suitable pairing on the cosimplicial resolution
offered by the stabilization adjunction for $\\mathcal{O}$-algebras. \n
\n Time permitting\, we will provide some other applications of our t
echniques such as a highly homotopy-coherent chain rule for functors of st
ructured ring spectra.\n
LOCATION:https://stable.researchseminars.org/talk/GOATS/4/
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BEGIN:VEVENT
SUMMARY:Steve Wheatley (George Mason University)
DTSTART:20200606T171000Z
DTEND:20200606T173000Z
DTSTAMP:20260404T095423Z
UID:GOATS/5
DESCRIPTION:Title: Characterizations of 2-Homeomorphic Spaces\nby Steve Wheatley (G
eorge Mason University) as part of GOATS\n\n\nAbstract\nIn a 2018 paper\,
Arhangel’skii and Maksyuta give the definition of a \n2-homeomorphism\,
a topological concept that generalizes the notion of a homeomorphism. In t
his talk\, we give some characterizations of spaces that are \n2-homeomorp
hic to spaces possessing various topological properties\, including compac
t spaces and discrete spaces. We also show that\, although many topologica
l properties are not preserved under the 2-homeomorphism relation\, the pr
operty of having finite Cantor-Bendixson height is preserved.\n
LOCATION:https://stable.researchseminars.org/talk/GOATS/5/
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SUMMARY:Rhea Palak Bakshi (The George Washington University)
DTSTART:20200606T173000Z
DTEND:20200606T175000Z
DTSTAMP:20260404T095423Z
UID:GOATS/6
DESCRIPTION:Title: Framings of Links in 3-manifolds and Torsion in Skein Modules\nby
Rhea Palak Bakshi (The George Washington University) as part of GOATS\n\n
\nAbstract\nWe show that the only way of changing the framing of a link by
ambient isotopy in an oriented \n3-manifold is when the manifold admits a
properly embedded non-separating $S^2$\n. 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 McCullough’s work on the mapping class groups of \n3-ma
nifolds. We also express our results in the language of skein modules. In
particular\, we relate our results to the framing skein module and the Kau
ffman bracket skein module.\n
LOCATION:https://stable.researchseminars.org/talk/GOATS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Perez (University of Illinois at Chicago)
DTSTART:20200606T192000Z
DTEND:20200606T194000Z
DTSTAMP:20260404T095423Z
UID:GOATS/7
DESCRIPTION:Title: Towers and Elementary Embeddings in Toral Relatively Hyperbolic Group
s\nby Christopher Perez (University of Illinois at Chicago) as part of
GOATS\n\n\nAbstract\nA 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 ge
ometric way. \n In 2011\, Chloé Perin proved that if $H$ is an element
arily embedded subgroup of a torsion-free hyperbolic group $G$ (also known
as an elementary submodel)\, then $G$ is a tower over $H$. \n\n The im
plication of this and similar results is that the geometric structures of
certain groups capture their logical structures as well. \n I will be d
iscussing towers and my recent generalization of Perin’s result to toral
relatively hyperbolic groups.\n
LOCATION:https://stable.researchseminars.org/talk/GOATS/7/
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SUMMARY:Nikolas Schonsheck (Ohio State University)
DTSTART:20200606T194000Z
DTEND:20200606T200000Z
DTSTAMP:20260404T095423Z
UID:GOATS/8
DESCRIPTION:Title: Fibration Theorems for TQ-Completion of Structured Ring Spectra\n
by Nikolas Schonsheck (Ohio State University) as part of GOATS\n\n\nAbstra
ct\nBy considering algebras over an operad $\\mathcal{O}$ in one's preferr
ed category of spectra\, we can encode various flavors of algebraic struct
ure (e.g. commutative ring spectra). \n 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 th
ese objects\, with analogies to both singular homology and stabilization o
f spaces. \n\n For a given $\\mathcal{O}$algebra $X$\, there is a canon
ical way (following Bousfield-Kan) to "glue together" iterates $\\mathbf{T
Q}^n(X)$ of the $\\mathbf{TQ}$-homology spectrum of $X$ to construct "the
part of $X$ that $\\mathbf{TQ}$-homology sees\," namely its $\\mathbf{TQ}$
-completion. \n We then ask\, "When can $X$ be 'recovered from' $\\math
bf{TQ}(X)$ in this way?" \n \n Bousfield-Kan consider the analogous
question in spaces and conclude that all nilpotent spaces are weakly equiv
alent to their homology completion. \n The key technical maneuver of th
eir proof involves showing that certain fibration sequences are preserved
by completion. \n In this talk\, we will discuss certain types of fibra
tion sequences of $\\mathcal{O}$-algebras which are preserved by $\\mathbf
{TQ}$-completion\, drawing analogies along the way to the case of pointed
spaces.\n
LOCATION:https://stable.researchseminars.org/talk/GOATS/8/
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