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SUMMARY:Marla Williams (University of Nebraska-Lincoln)
DTSTART:20200606T160000Z
DTEND:20200606T170000Z
DTSTAMP:20260422T212751Z
UID:GOATS/1
DESCRIPTION:Title: Tr
isections and Flat Surface Bundles\nby Marla Williams (University of N
ebraska-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 t
he corresponding diagrams. We’ll then move into a discussion of what cha
nges when we shift to trisecting nontrivial surface bundles\, and why flat
ness matters for my diagram construction.\n
LOCATION:https://researchseminars.org/talk/GOATS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Cazet (UC Davis)
DTSTART:20200606T202000Z
DTEND:20200606T212000Z
DTSTAMP:20260422T212751Z
UID:GOATS/3
DESCRIPTION:Title: Ve
rtex 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 su
premum of the ratio of the distance between a pair of vertices along the k
not and their distance in the 1-norm. We show analogous results of Gromov\
, Pardon and Blair-Campisi-Taylor-Tomova about the distortion of smooth kn
ots hold for vertex distortion\, the vertex distortion of a lattice knot i
s 1 only if it is the unknot\, and that there are minimal lattice-stick nu
mber knot conformations with arbitrarily high distortion.\n
LOCATION:https://researchseminars.org/talk/GOATS/3/
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BEGIN:VEVENT
SUMMARY:Duncan Clark (Ohio State University)
DTSTART:20200606T181000Z
DTEND:20200606T191000Z
DTSTAMP:20260422T212751Z
UID:GOATS/4
DESCRIPTION:Title: On
the Goodwillie Derivatives of the Identity in Structured Ring Spectra
\nby Duncan Clark (Ohio State University) as part of GOATS\n\n\nAbstract\n
Functor calculus was introduced by Goodwillie as a means for analyzing hom
otopy functors between suitable model categories. \n One noteworthy fac
et is that "nice" functors $F\\colon \\mathsf{C}\\to \\mathsf{D}$ are dete
rmined by a certain symmetric sequence called the derivatives of $F$. \n\n
This sequence of derivatives is known to posses much structure: for in
stance\, the derivatives of the identity functor on the category of based
topological spaces is an operad\, as first shown by Ching. \n It is fur
ther expected that a result of this type should hold in any suitable model
category\, and in particular conjectured that the derivatives of the iden
tity on the category of algebras over an operad $\\mathcal{O}$ in spectra
should be equivalent to $\\mathcal{O}$ as operads. \n\n In this talk we
produce an intrinsic "homotopy-coherent" operad structure for the derivat
ives of the identity which is equivalent to that on $\\mathcal{O}$\, thus
resolving the above conjecture. \n Along the way we will discuss the ne
cessary background of functor calculus and algebras over operads of spectr
a. \n Our method is to induce a homotopy coherent operadic pairing on t
he derivatives by a suitable pairing on the cosimplicial resolution offere
d by the stabilization adjunction for $\\mathcal{O}$-algebras. \n \n
Time permitting\, we will provide some other applications of our techniqu
es such as a highly homotopy-coherent chain rule for functors of structure
d ring spectra.\n
LOCATION:https://researchseminars.org/talk/GOATS/4/
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BEGIN:VEVENT
SUMMARY:Steve Wheatley (George Mason University)
DTSTART:20200606T171000Z
DTEND:20200606T173000Z
DTSTAMP:20260422T212751Z
UID:GOATS/5
DESCRIPTION:Title: Ch
aracterizations of 2-Homeomorphic Spaces\nby Steve Wheatley (George M
ason University) as part of GOATS\n\n\nAbstract\nIn a 2018 paper\, Arhange
l’skii and Maksyuta give the definition of a \n2-homeomorphism\, a topol
ogical concept that generalizes the notion of a homeomorphism. In this tal
k\, we give some characterizations of spaces that are \n2-homeomorphic to
spaces possessing various topological properties\, including compact space
s and discrete spaces. We also show that\, although many topological prope
rties are not preserved under the 2-homeomorphism relation\, the property
of having finite Cantor-Bendixson height is preserved.\n
LOCATION:https://researchseminars.org/talk/GOATS/5/
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BEGIN:VEVENT
SUMMARY:Rhea Palak Bakshi (The George Washington University)
DTSTART:20200606T173000Z
DTEND:20200606T175000Z
DTSTAMP:20260422T212751Z
UID:GOATS/6
DESCRIPTION:Title: Fr
amings of Links in 3-manifolds and Torsion in Skein Modules\nby Rhea P
alak Bakshi (The George Washington University) as part of GOATS\n\n\nAbstr
act\nWe show that the only way of changing the framing of a link by ambien
t isotopy in an oriented \n3-manifold is when the manifold admits a proper
ly 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-manifolds
. We also express our results in the language of skein modules. In particu
lar\, we relate our results to the framing skein module and the Kauffman b
racket skein module.\n
LOCATION:https://researchseminars.org/talk/GOATS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Perez (University of Illinois at Chicago)
DTSTART:20200606T192000Z
DTEND:20200606T194000Z
DTSTAMP:20260422T212751Z
UID:GOATS/7
DESCRIPTION:Title: To
wers and Elementary Embeddings in Toral Relatively Hyperbolic Groups\n
by 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 geometric
way. \n In 2011\, Chloé Perin proved that if $H$ is an elementarily e
mbedded subgroup of a torsion-free hyperbolic group $G$ (also known as an
elementary submodel)\, then $G$ is a tower over $H$. \n\n The implicati
on of this and similar results is that the geometric structures of certain
groups capture their logical structures as well. \n I will be discussi
ng towers and my recent generalization of Perin’s result to toral relati
vely hyperbolic groups.\n
LOCATION:https://researchseminars.org/talk/GOATS/7/
END:VEVENT
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SUMMARY:Nikolas Schonsheck (Ohio State University)
DTSTART:20200606T194000Z
DTEND:20200606T200000Z
DTSTAMP:20260422T212751Z
UID:GOATS/8
DESCRIPTION:Title: Fi
bration Theorems for TQ-Completion of Structured Ring Spectra\nby Niko
las Schonsheck (Ohio State University) as part of GOATS\n\n\nAbstract\nBy
considering algebras over an operad $\\mathcal{O}$ in one's preferred cate
gory of spectra\, we can encode various flavors of algebraic structure (e.
g. commutative ring spectra). \n Drawing intuition from singular homolo
gy of spaces and Quillen homology of rings\, topological Quillen ($\\mathb
f{TQ}$) homology is a naturally occurring notion of homology for these obj
ects\, with analogies to both singular homology and stabilization of space
s. \n\n For a given $\\mathcal{O}$algebra $X$\, there is a canonical wa
y (following Bousfield-Kan) to "glue together" iterates $\\mathbf{TQ}^n(X)
$ of the $\\mathbf{TQ}$-homology spectrum of $X$ to construct "the part of
$X$ that $\\mathbf{TQ}$-homology sees\," namely its $\\mathbf{TQ}$-comple
tion. \n We then ask\, "When can $X$ be 'recovered from' $\\mathbf{TQ}(
X)$ in this way?" \n \n Bousfield-Kan consider the analogous questio
n in spaces and conclude that all nilpotent spaces are weakly equivalent t
o their homology completion. \n The key technical maneuver of their pro
of involves showing that certain fibration sequences are preserved by comp
letion. \n In this talk\, we will discuss certain types of fibration se
quences of $\\mathcal{O}$-algebras which are preserved by $\\mathbf{TQ}$-c
ompletion\, drawing analogies along the way to the case of pointed spaces.
\n
LOCATION:https://researchseminars.org/talk/GOATS/8/
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