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SUMMARY:Maggie Miller (Massachusetts Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210507T140000Z
DTEND;VALUE=DATE-TIME:20210507T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T110144Z
UID:LDTSGweekend/1
DESCRIPTION:Title: Diagrams of immersed surfaces\nby Maggie Miller (Massachusetts In
stitute of Technology) as part of Low dimensional topology and symplectic
geometry weekend\n\n\nAbstract\nA surface embedded in a 4-manifold can be
depicted via a banded unlink diagram\, which consists of decorated links i
n S^3 with some bands attached. In 2002\, Swenton showed that diagrams of
isotopic surfaces in S^4 are related by a short list of moves. In 2019\, H
ughes\, Kim and I extended this to isotopic surfaces in a general 4-manifo
ld. In this talk\, I will describe singular banded unlink diagrams of regu
larly immersed surfaces in 4-manifolds\, and again show that there is a co
mplete set of moves on these diagrams. These diagrams can be used to const
ruct homotopies of surfaces and study the intersection sets\, which is use
ful for computing certain surface invariants. This is joint work with Mark
Hughes and Seungwon Kim.\n
LOCATION:https://researchseminars.org/talk/LDTSGweekend/1/
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BEGIN:VEVENT
SUMMARY:Jonathan Simone (University of Massachusetts Amherst)
DTSTART;VALUE=DATE-TIME:20210507T151500Z
DTEND;VALUE=DATE-TIME:20210507T161500Z
DTSTAMP;VALUE=DATE-TIME:20240328T110144Z
UID:LDTSGweekend/2
DESCRIPTION:Title: Chi-slice 3-braid links\nby Jonathan Simone (University of Massac
husetts Amherst) as part of Low dimensional topology and symplectic geomet
ry weekend\n\n\nAbstract\nA link L in the 3-sphere is called chi-slice if
it bounds a properly embedded surface F in the 4-ball with Euler character
istic 1. If L is a knot\, then this definition coincides with the usual de
finition of sliceness. One feature of such a link L is that if the determi
nant of L is nonzero\, then the double cover of the 3-sphere branched over
L bounds a rational homology ball. In this talk\, we will explore the chi
-sliceness of quasi-alternating 3-braid links. In particular\, we will con
struct explicit families of chi-slice quasi-alternating 3-braids using ban
d moves and we will obstruct the chi-sliceness of most other quasi-alterna
ting 3-braid links by showing that their double branched covers do not bou
nd rational homology 4-balls. This is a work in progress joint with Vitaly
Brejevs.\n
LOCATION:https://researchseminars.org/talk/LDTSGweekend/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Joseph (Rice University)
DTSTART;VALUE=DATE-TIME:20210507T163000Z
DTEND;VALUE=DATE-TIME:20210507T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T110144Z
UID:LDTSGweekend/3
DESCRIPTION:Title: Unknotting numbers of 2-spheres in the 4-sphere\nby Jason Joseph
(Rice University) as part of Low dimensional topology and symplectic geome
try weekend\n\n\nAbstract\nIn this talk I'll discuss two notions of an unk
notting number for knotted 2-spheres in the 4-sphere\, with the goal of co
mparing them. One is the minimal number of stabilizations needed to produc
e an unknotted surface\, and the other is the minimal number of pairs of f
inger and Whitney moves needed during a regular homotopy to the unknotted
sphere. Most of the times that these numbers can be computed\, they are th
e same\; however\, I'll present a general inequality between them and give
a family of examples where they differ. This is joint work with Michael K
lug\, Benjamin Ruppik\, and Hannah Schwartz.\n
LOCATION:https://researchseminars.org/talk/LDTSGweekend/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Sackel (Stony Brook University / SCGP)
DTSTART;VALUE=DATE-TIME:20210508T140000Z
DTEND;VALUE=DATE-TIME:20210508T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T110144Z
UID:LDTSGweekend/4
DESCRIPTION:Title: Quantitative Refinements of Non-Squeezing in Dimension 4\nby Kevi
n Sackel (Stony Brook University / SCGP) as part of Low dimensional topolo
gy and symplectic geometry weekend\n\n\nAbstract\nGromov's celebrated Non-
Squeezing Theorem states that a ball of radius R cannot embed symplectical
ly into a cylinder of radius 1 unless R ≤ 1. Nowadays\, there is an indu
stry of understanding when symplectic embeddings exist between all sorts o
f domains. We study a slightly different question -- how much do we need t
o remove from the ball of radius R so that it squeezes into a cylinder of
radius 1? In four dimensions\, we prove that the (lower) Minkowski dimensi
on of the region removed must be at least 2\, and that this result is opti
mal for R^2 ≤ 2. Time permitting\, we discuss a few related results and
open problems. This work is joint with Antoine Song\, Umut Varolgunes\, an
d Jonathan Zhu.\n
LOCATION:https://researchseminars.org/talk/LDTSGweekend/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheuk Yu Mak (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20210508T151500Z
DTEND;VALUE=DATE-TIME:20210508T161500Z
DTSTAMP;VALUE=DATE-TIME:20240328T110144Z
UID:LDTSGweekend/5
DESCRIPTION:Title: Non-displaceable Lagrangian links in four-manifolds\nby Cheuk Yu
Mak (University of Edinburgh) as part of Low dimensional topology and symp
lectic geometry weekend\n\n\nAbstract\nOne of the earliest fundamental app
lications of Lagrangian Floer theory is detecting the non-displaceablity o
f a Lagrangian submanifold. Many progress and generalisations have been m
ade since then but little is known when the Lagrangian submanifold is disc
onnected. In this talk\, we describe a new idea to address this problem.
Subsequently\, we explain how to use Fukaya-Oh-Ohta-Ono and Cho-Poddar th
eory to show that for every S^2 \\times S^2 with a non-monotone product sy
mplectic form\, there is a continuum of disconnected\, non-displaceable La
grangian submanifolds such that each connected component is displaceable.
This is a joint work with Ivan Smith.\n
LOCATION:https://researchseminars.org/talk/LDTSGweekend/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Castro (University of Arkansas)
DTSTART;VALUE=DATE-TIME:20210508T163000Z
DTEND;VALUE=DATE-TIME:20210508T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T110144Z
UID:LDTSGweekend/6
DESCRIPTION:Title: Relative Group Trisections\nby Nick Castro (University of Arkansa
s) as part of Low dimensional topology and symplectic geometry weekend\n\n
\nAbstract\nA trisection of a smooth\, compact\, 4–manifold is a decompo
sition into three diffeomorphic pieces\, where the complexity of the 4–m
anifold lies in how these pieces are attached to one another. In the case
of a manifold with boundary\, a relative trisection induces a structure on
the boundary known as an open book decomposition. In this talk\, we will
provide a correspondence between relative trisections of 4–manifolds wit
h boundary and commutative cubes of groups\, known as relative group trise
ctions. The interesting feature of a (relative) group trisection is that i
t encodes all of the smooth topology of the 4–manifold\, including the i
nduced boundary data. This extends group trisections of closed 4–manifol
ds\, due to work of Abrams\, Gay\, and Kirby\, to the relative setting. Th
is work is joint with Jason Joseph and Patrick McFaddin.\n
LOCATION:https://researchseminars.org/talk/LDTSGweekend/6/
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BEGIN:VEVENT
SUMMARY:Anubhav Mukherjee (Georgia Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210509T140000Z
DTEND;VALUE=DATE-TIME:20210509T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T110144Z
UID:LDTSGweekend/7
DESCRIPTION:Title: Obstructions to embeddings in 4-manifolds using Bauer-Furuta type inv
ariant\nby Anubhav Mukherjee (Georgia Institute of Technology) as part
of Low dimensional topology and symplectic geometry weekend\n\n\nAbstract
\nIn this talk I will discuss some new properties of an invariant for 4-ma
nifold with boundary which was originally defined by Nobuo Iida. As one of
the applications of this new invariant I will demonstrate how one can obs
truct a knot from being h-slice (i.e bound a homologically trivial disk) i
n 4-manifolds. Also\, this invariant can be useful to detect exotic smooth
structures of 4-manifolds. This a joint work with Nobuo Iida and Masaki T
aniguchi.\n
LOCATION:https://researchseminars.org/talk/LDTSGweekend/7/
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SUMMARY:Jun Li (University of Michigan-Ann Arbor)
DTSTART;VALUE=DATE-TIME:20210509T151500Z
DTEND;VALUE=DATE-TIME:20210509T161500Z
DTSTAMP;VALUE=DATE-TIME:20240328T110144Z
UID:LDTSGweekend/8
DESCRIPTION:Title: Symplectic mapping class groups in dimension 4\nby Jun Li (Univer
sity of Michigan-Ann Arbor) as part of Low dimensional topology and symple
ctic geometry weekend\n\n\nAbstract\nSymplectic manifolds arise naturally
in abstract formulations of classical mechanics\, and symplectic geometry
is an interesting mixture of the “soft” and the “rigid.” In this
talk\, we will focus on symplectic rigidity phenomena. In particular\,
we will discuss recent developments for the Symplectic mapping class group
s of 4-dimensional symplectic manifolds\, and how these root in dynamics
and topology in dimension 2. Those are based on joint works with T-J Li\,
Weiwei Wu\, and with Olga Buse. Time permitting\, we'll outline some open
problems for the informal discussion session.\n
LOCATION:https://researchseminars.org/talk/LDTSGweekend/8/
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BEGIN:VEVENT
SUMMARY:Biji Wong (Max Planck Institute for Mathematics)
DTSTART;VALUE=DATE-TIME:20210509T163000Z
DTEND;VALUE=DATE-TIME:20210509T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T110144Z
UID:LDTSGweekend/9
DESCRIPTION:Title: d-invariants of double branched covers of links\nby Biji Wong (Ma
x Planck Institute for Mathematics) as part of Low dimensional topology an
d symplectic geometry weekend\n\n\nAbstract\nUsing Heegaard Floer homology
\, one can associate to a rational homology 3-sphere Y\, equipped with a s
pinc-structure s\, a rational number\, commonly referred to as the d-invar
iant of (Y\, s). d-invariants have been useful in answering a range of que
stions in low-dimensional topology. A nice source of rational homology 3-s
pheres comes from considering double branched covers Sigma_2(K) of knots K
. If \\Sigma_2(K) is an L-space\, then the d-invariant of \\Sigma_2(K)\, a
t the unique spin-structure s_0\, is well-understood: it's a multiple of t
he signature of K. In this talk\, we'll discuss what happens when we pass
to double branched covers of multi-component links. This is work in progre
ss with M. Marengon.\n
LOCATION:https://researchseminars.org/talk/LDTSGweekend/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Wu (University College London)
DTSTART;VALUE=DATE-TIME:20210509T171500Z
DTEND;VALUE=DATE-TIME:20210509T174500Z
DTSTAMP;VALUE=DATE-TIME:20240328T110144Z
UID:LDTSGweekend/10
DESCRIPTION:Title: Obstructing Lagrangian concordance for 3-braids\nby Angela Wu (U
niversity College London) as part of Low dimensional topology and symplect
ic geometry weekend\n\n\nAbstract\nTwo knots are said to be concordant if
they jointly form the boundary of a cylinder in four-dimensional Euclidean
space. In the symplectic setting\, we say they are Lagrangian concordant
if the knots are Legendrian and the cylinder is Lagrangian. In this talk I
'll show that no Legendrian knot which is both concordant to and from the
unstabilized Legendrian unknot can be the closure of an index 3 braid exce
pt the unknot itself.\n
LOCATION:https://researchseminars.org/talk/LDTSGweekend/10/
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