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BEGIN:VEVENT
SUMMARY:William Ballinger (Princeton)
DTSTART:20201002T220000Z
DTEND:20201002T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/1
DESCRIPTION:Title: Concordance invariants from the E(-1) spectral sequence\nby William
Ballinger (Princeton) as part of Caltech geometry/topology seminar\n\n\nAb
stract\nMany recent concordance invariants of knots come from perturbing t
he differential on a knot homology theory to get a complex with trivial ho
mology but an interesting filtration. I describe the invariant coming from
Rasmussen's E(-1) spectral sequence from Khovanov homology in this way\,
and show that it gives a bound on the nonorientable slice genus.\n
LOCATION:https://researchseminars.org/talk/caltechGT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ahmad Issa (UBC)
DTSTART:20201009T220000Z
DTEND:20201009T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/2
DESCRIPTION:Title: Symmetric knots and the equivariant 4-ball genus\nby Ahmad Issa (UBC
) as part of Caltech geometry/topology seminar\n\n\nAbstract\nGiven a knot
K in the 3-sphere\, the 4-genus of K is the minimal genus of an orientabl
e surface embedded in the 4-ball with boundary K. If the knot K has a symm
etry (e.g. K is periodic or strongly invertible)\, one can define the equi
variant 4-genus by only minimising the genus over those surfaces in the 4-
ball which respect the symmetry of the knot. I'll discuss some ongoing wor
k with Keegan Boyle on trying to understanding the equivariant 4-genus.\n
LOCATION:https://researchseminars.org/talk/caltechGT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harold Williams (USC)
DTSTART:20201016T220000Z
DTEND:20201016T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/3
DESCRIPTION:Title: Kasteleyn operators from mirror symmetry\nby Harold Williams (USC) a
s part of Caltech geometry/topology seminar\n\n\nAbstract\nIn this talk we
explain an interpretation of the Kasteleyn operator of a doubly-periodic
bipartite graph from the perspective of homological mirror symmetry. Speci
fically\, given a consistent bipartite graph G in T^2 with a complex-value
d edge weighting E we show the following two constructions are the same. T
he first is to form the Kasteleyn operator of (G\,E) and pass to its spect
ral transform\, a coherent sheaf supported on a spectral curve in (C*)^2.
The second is to take a certain Lagrangian surface L in T^* T^2 canonicall
y associated to G\, equip it with a brane structure prescribed by E\, and
pass to its homologically mirror coherent sheaf. This lives on a toric com
pactification of (C*)^2 determined by the Legendrian link which lifts the
zig-zag paths of G (and to which the noncompact Lagrangian L is asymptotic
). As a corollary\, we obtain a complementary geometric perspective on cer
tain features of algebraic integrable systems associated to lattice polygo
ns\, studied for example by Goncharov-Kenyon and Fock-Marshakov. This is j
oint work with David Treumann and Eric Zaslow.\n
LOCATION:https://researchseminars.org/talk/caltechGT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boyu Zhang (Princeton)
DTSTART:20201023T220000Z
DTEND:20201023T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/4
DESCRIPTION:Title: Several detection results of Khovanov homology on links\nby Boyu Zha
ng (Princeton) as part of Caltech geometry/topology seminar\n\n\nAbstract\
nThe Khovanov homology is a combinatorially defined invariant for knots an
d links. I will present several new detection results of Khovanov homology
on links. In particular\, we show that if L is an n-component link with K
hovanov homology of rank 2^n\, then it is given by the connected sums and
disjoint unions of unknots and Hopf links. This result gives a positive an
swer to a question asked by Batson-Seed\, and it generalizes the unlink de
tection theorem by Hedden-Ni and Batson-Seed. The proof relies on a new ex
cision formula for the singular instanton Floer homology. This is joint wo
rk with Yi Xie.\n
LOCATION:https://researchseminars.org/talk/caltechGT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (Princeton)
DTSTART:20201030T220000Z
DTEND:20201030T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/5
DESCRIPTION:Title: Generalized soap bubbles and the topology of manifolds with positive sca
lar curvature\nby Chao Li (Princeton) as part of Caltech geometry/topo
logy seminar\n\n\nAbstract\nIt has been a classical question which manifol
ds admit Riemannian metrics with positive scalar curvature. I will present
some recent progress on this question\, ruling out positive scalar curvat
ure on closed aspherical manifolds of dimensions 4 and 5 (as conjectured b
y Schoen-Yau and by Gromov)\, as well as complete metrics of positive scal
ar curvature on an arbitrary manifold connect sum with a torus. Applicatio
ns include a Schoen-Yau Liouville theorem for all locally conformally flat
manifolds. The proofs of these results are based on analyzing generalized
soap bubbles - surfaces that are stable solutions to the prescribed mean
curvature problem. This talk is based on joint work with O. Chodosh.\n
LOCATION:https://researchseminars.org/talk/caltechGT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Samperton (UIUC)
DTSTART:20201106T230000Z
DTEND:20201107T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/6
DESCRIPTION:Title: 3-manifold invariants\, G-equivariant TQFT\, and complexity\nby Eric
Samperton (UIUC) as part of Caltech geometry/topology seminar\n\n\nAbstra
ct\nLet G be a finite group. G-equivariant TQFTs have received attention
from both mathematicians and physicists\, motivated in part by the search
for new topological phases that can be used as the hardware for a universa
l quantum computer. Our goal will be to convey two complexity-theoretic l
essons. First\, when G is sufficiently complicated (nonabelian simple)\,
3-manifold invariants derived from G-equivariant TQFTs are very difficult
to compute (#P-hard)\, even on a quantum computer. Second\, no matter wha
t finite group G one uses\, a 3-dimensional G-equivariant TQFT can not be
used for universal topological quantum computation if the underlying non-e
quivariant theory is not already universal. This talk is based on joint w
orks with Greg Kuperberg and Colleen Delaney.\n
LOCATION:https://researchseminars.org/talk/caltechGT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Bamler (UC Berkeley)
DTSTART:20201113T230000Z
DTEND:20201114T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/7
DESCRIPTION:Title: Compactness and partial regularity theory of Ricci flows in higher dimen
sions\nby Richard Bamler (UC Berkeley) as part of Caltech geometry/top
ology seminar\n\n\nAbstract\nWe present a new compactness theory of Ricci
flows. This theory states that any sequence of Ricci flows that is pointed
in an appropriate sense\, subsequentially converges to a synthetic flow.
Under a natural non-collapsing condition\, this limiting flow is smooth on
the complement of a singular set of parabolic codimension at least 4. We
furthermore obtain a stratification of the singular set with optimal dimen
sional bounds depending on the symmetries of the tangent flows. Our method
s also imply the corresponding quantitative stratification result and the
expected $L^p$-curvature bounds.\n\nAs an application we obtain a descript
ion of the singularity formation at the first singular time and a long-tim
e characterization of immortal flows\, which generalizes the thick-thin de
composition in dimension 3. We also obtain a backwards pseudolocality theo
rem and discuss several other applications.\n
LOCATION:https://researchseminars.org/talk/caltechGT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Takeda (IHES)
DTSTART:20201120T230000Z
DTEND:20201121T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/8
DESCRIPTION:Title: Pre-Calabi-Yau categories and dualizability in 2d\nby Alex Takeda (I
HES) as part of Caltech geometry/topology seminar\n\n\nAbstract\nIn this t
alk I will describe some joint work with Maxim Kontsevich on the study of
pre-Calabi Yau categories. I will discuss the action of a PROP on the Hoch
schild invariants of such a category and explain how this notion and more
familiar notions of Calabi-Yau objects relate to different dualizability c
onditions of 2d TQFTs. Time allowing I will present some motivating exampl
es from symplectic geometry.\n
LOCATION:https://researchseminars.org/talk/caltechGT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oguz Savk (Bogazici University)
DTSTART:20201204T230000Z
DTEND:20201205T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/9
DESCRIPTION:Title: Brieskorn spheres\, homology cobordism and homology balls\nby Oguz S
avk (Bogazici University) as part of Caltech geometry/topology seminar\n\n
\nAbstract\nA classical question in low-dimensional topology asks which ho
mology 3-spheres bound homology 4-balls. This question is fairly addressed
to Brieskorn spheres Σ(p\,q\,r)\, which are defined to be links of singu
larities x^p+y^q+z^r=0. Over the years\, Brieskorn spheres also have been
the main objects for the understanding of the algebraic structure of the i
ntegral homology cobordism group.\n\nIn this talk\, we will present severa
l families of Brieskorn spheres which do or do not bound integral and rati
onal homology balls via Ozsváth-Szabó d-invariant\, involutive Heegaard
Floer homology\, and Kirby calculus. Also\, we will investigate their posi
tions in both integral and\nrational homology cobordism groups.\n
LOCATION:https://researchseminars.org/talk/caltechGT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christine Breiner (Fordham University)
DTSTART:20210205T230000Z
DTEND:20210206T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/10
DESCRIPTION:Title: Harmonic branched coverings and uniformization of CAT($k$) spheres\
nby Christine Breiner (Fordham University) as part of Caltech geometry/top
ology seminar\n\n\nAbstract\nConsider a metric space $(S\,d)$ with an uppe
r curvature bound in the sense of Alexandrov (i.e. via triangle comparison
). We show that if $(S\,d)$ is homeomorphically equivalent to the 2-spher
e $S^2$\, then it is conformally equivalent to $S^2$. The method of proof
is through harmonic maps\, and we show that the conformal equivalence is
achieved by an almost conformal harmonic map. The proof relies on the an
alysis of the local behavior of harmonic maps between surfaces\, and the k
ey step is to show that an almost conformal harmonic map from a compact
surface onto a surface with an upper curvature bound is a branched coveri
ng. This work is joint with Chikako Mese.\n
LOCATION:https://researchseminars.org/talk/caltechGT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ayala (Montana State)
DTSTART:20210108T230000Z
DTEND:20210109T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/12
DESCRIPTION:Title: Orthogonal group and higher categorical adjoints\nby David Ayala (M
ontana State) as part of Caltech geometry/topology seminar\n\n\nAbstract\n
In this talk I will articulate and contextualize the following sequence of
results.\n\n* The Bruhat decomposition of the general linear group define
s a stratification of the orthogonal group.\n\n* Matrix multiplication def
ines an algebra structure on its exit-path category in a certain Morita ca
tegory of categories.\n\n* In this Morita category\, this algebra acts on
the categeory of n-categories -- this action is given by adjoining adjoint
s to n-categories.\n\nThis result is extracted from a larger program -- en
tirely joint with John Francis\, some parts joint with Nick Rozenblyum --
which proves the cobordism hypothesis.\n
LOCATION:https://researchseminars.org/talk/caltechGT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Turner (UT Austin)
DTSTART:20210115T230000Z
DTEND:20210116T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/13
DESCRIPTION:Title: Links all of whose branched cyclic covers are L-spaces\nby Hannah T
urner (UT Austin) as part of Caltech geometry/topology seminar\n\n\nAbstra
ct\nGiven an oriented link in the three-sphere and a fixed positive intege
r n\, there is a unique 3-manifold called its branched cyclic cover of ind
ex n. It is not well understood when these manifolds are L-spaces - that i
s\, when their Heegaard Floer homology is as simple as possible. In this t
alk I'll describe new examples of links whose cyclic branched covers are L
-spaces for any index n. The proof uses a symmetry argument and a generali
zation of alternating links due to Scaduto-Stoffregen. This is joint work
with Ahmad Issa.\n
LOCATION:https://researchseminars.org/talk/caltechGT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Lai (UC Berkeley)
DTSTART:20210122T230000Z
DTEND:20210123T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/14
DESCRIPTION:Title: A family of 3d steady gradient solitons that are flying wings\nby Y
i Lai (UC Berkeley) as part of Caltech geometry/topology seminar\n\n\nAbst
ract\nWe find a family of 3d steady gradient Ricci solitons that are flyin
g wings. This verifies a conjecture by Hamilton. For a 3d flying wing\, we
show that the scalar curvature does not vanish at infinity. The 3d flying
wings are collapsed. For dimension n ≥ 4\, we find a family of Z2 × O(
n − 1)-symmetric but non-rotationally symmetric n-dimensional steady gra
dient solitons with positive curvature operator. We show that these solito
ns are non-collapsed.\n
LOCATION:https://researchseminars.org/talk/caltechGT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weiyan Chen (Tsinghua)
DTSTART:20210129T230000Z
DTEND:20210130T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/15
DESCRIPTION:Title: Choosing points on cubic plane curves\nby Weiyan Chen (Tsinghua) as
part of Caltech geometry/topology seminar\n\n\nAbstract\nIt is a classica
l topic to study structures of certain special points on complex smooth cu
bic plane curves\, for example\, the 9 flex points and the 27 sextactic po
ints. We consider the following topological question asked by Farb: Is it
true that the known algebraic structures give all the possible ways to con
tinuously choose n distinct points on every smooth cubic plane curve\, for
each given positive integer n? This work is joint with Ishan Banerjee.\n
LOCATION:https://researchseminars.org/talk/caltechGT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Stern (UChicago)
DTSTART:20210212T230000Z
DTEND:20210213T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/16
DESCRIPTION:Title: Constructing minimal submanifolds via gauge theory\nby Daniel Stern
(UChicago) as part of Caltech geometry/topology seminar\n\n\nAbstract\nTh
e self-dual Yang-Mills-Higgs (or Ginzburg-Landau) functionals are a natura
l family of energies associated to sections and metric connections of Herm
itian line bundles\, whose critical points (particularly those satisfying
a first-order system known as the "vortex equations" in the Kahler setting
) have long been studied as a basic model problem in gauge theory. In this
talk\, we will discuss joint work with Alessandro Pigati characterizing t
he behavior of critical points over manifolds of arbitrary dimension. We s
how in particular that critical points give rise to minimal submanifolds o
f codimension two in certain natural scaling limits\, and use this informa
tion to provide new constructions of codimension-two minimal varieties in
arbitrary Riemannian manifolds. We will also discuss recent work with Davi
de Parise and Alessandro Pigati developing the associated Gamma-convergenc
e machinery\, and describe some geometric applications.\n
LOCATION:https://researchseminars.org/talk/caltechGT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaolong Hans Han (UIUC)
DTSTART:20210226T230000Z
DTEND:20210227T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/17
DESCRIPTION:Title: Harmonic forms and norms on cohomology of non-compact hyperbolic 3-mani
folds\nby Xiaolong Hans Han (UIUC) as part of Caltech geometry/topolog
y seminar\n\n\nAbstract\nWe will talk about generalizations of an inequali
ty of Brock-Dunfield to the non-compact case\, with tools from Hodge theor
y for non-compact hyperbolic manifolds and recent developments in the theo
ry of minimal surfaces. We also prove that their inequality is not sharp\,
using holomorphic quadratic differentials and recent ideas of Wolf and Wu
on minimal geometric foliations. If time permits\, we will also describe
a partial generalization to the infinite volume case.\n
LOCATION:https://researchseminars.org/talk/caltechGT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katherine Raoux (Michigan State)
DTSTART:20210219T230000Z
DTEND:20210220T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/18
DESCRIPTION:Title: Knot Floer homology and relative adjunction inequalities\nby Kather
ine Raoux (Michigan State) as part of Caltech geometry/topology seminar\n\
n\nAbstract\nIn this talk\, we present a relative adjunction inequality fo
r 4-manifolds with boundary. We begin by constructing generalized Heegaard
Floer tau-invariants associated to a knot in a 3-manifold and a nontrivia
l Floer class. Given a 4-manifold with boundary\, the tau-invariant associ
ated to a Floer class provides a lower bound for the genus of a properly e
mbedded surface\, provided that the Floer class is in the image of the cob
ordism map induced by the 4-manifold. We will also discuss some applicatio
ns to links and contact manifolds.\n\nThis is joint work with Matthew Hedd
en.\n
LOCATION:https://researchseminars.org/talk/caltechGT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Knudsen (Northeastern)
DTSTART:20210305T230000Z
DTEND:20210306T000000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/19
DESCRIPTION:Title: Stable and unstable homology of graph braid groups\nby Ben Knudsen
(Northeastern) as part of Caltech geometry/topology seminar\n\n\nAbstract\
nThe homology of the configuration spaces of a graph forms a finitely gene
rated module over the polynomial ring generated by its edges\; in particul
ar\, each Betti number is eventually equal to a polynomial in the number o
f particles\, an analogue of classical homological stability. The degree o
f this polynomial is captured by a connectivity invariant of the graph\, a
nd its leading coefficient may be computed explicitly in terms of cut coun
ts and vertex valences. This "stable" (asymptotic) homology is generated e
ntirely by the fundamental classes of certain tori of geometric origin\, b
ut exotic non-toric classes abound unstably. These mysterious classes are
intimately tied to questions about generation and torsion whose answers re
main elusive except in a few special cases. This talk represents joint wor
k with Byung Hee An and Gabriel Drummond-Cole.\n
LOCATION:https://researchseminars.org/talk/caltechGT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ikshu Neithalath (UCLA)
DTSTART:20210402T220000Z
DTEND:20210402T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/20
DESCRIPTION:Title: Skein lasagna modules of 2-handlebodies\nby Ikshu Neithalath (UCLA)
as part of Caltech geometry/topology seminar\n\n\nAbstract\nMorrison\, Wa
lker and Wedrich recently defined a generalization of Khovanov-Rozansky ho
mology to links in the boundary of a 4-manifold. We will discuss recent jo
int work with Ciprian Manolescu on computing the "skein lasagna module\,"
a basic part of MWW's invariant\, for a certain class of 4-manifolds.\n
LOCATION:https://researchseminars.org/talk/caltechGT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Miller (Rice)
DTSTART:20210409T220000Z
DTEND:20210409T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/21
DESCRIPTION:Title: Amphichiral knots with large 4-genera\nby Allison Miller (Rice) as
part of Caltech geometry/topology seminar\n\n\nAbstract\nAn oriented knot
is called negative amphichiral if it is isotopic to the reverse of its mir
ror image. Such knots have order at most two in the concordance group\, an
d many modern concordance invariants vanish on them. Nevertheless\, we wil
l see that there are negative amphichiral knots with arbitrarily large 4-g
enera (i.e. which are highly 4-dimensionally complex)\, using Casson-Gordo
n signature invariants as a primary tool.\n
LOCATION:https://researchseminars.org/talk/caltechGT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Kotelskiy (Indiana)
DTSTART:20210514T220000Z
DTEND:20210514T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/23
DESCRIPTION:Title: Khovanov homology via Floer theory of the 4-punctured sphere\nby Ar
tem Kotelskiy (Indiana) as part of Caltech geometry/topology seminar\n\n\n
Abstract\nConsider a Conway two-sphere S intersecting a knot K in 4 points
\, and thus decomposing the knot into two 4-ended tangles\, T and T’. We
will first interpret Khovanov homology Kh(K) as Lagrangian Floer homology
of a pair of specifically constructed immersed curves C(T) and C'(T’) o
n the dividing 4-punctured sphere S. Next\, motivated by several tangle-re
placement questions in knot theory\, we will describe a recently obtained
structural result concerning the curve invariant C(T)\, which severely res
tricts the types of curves that may appear as tangle invariants. The proof
relies on the matrix factorization framework of Khovanov-Rozansky\, as we
ll as the homological mirror symmetry statement for the 3-punctured sphere
. This is joint work with Liam Watson and Claudius Zibrowius.\n
LOCATION:https://researchseminars.org/talk/caltechGT/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Caudell (BC)
DTSTART:20210528T220000Z
DTEND:20210528T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/24
DESCRIPTION:Title: Lens space surgeries\, lattices\, and the Poincaré homology sphere
\nby Jacob Caudell (BC) as part of Caltech geometry/topology seminar\n\n\n
Abstract\nMoser's classification of Dehn surgeries on torus knots (1971) i
nspired a now fifty-years-old project to classify "exceptional" Dehn surge
ries on knots in the three-sphere. A prominent component of this project s
eeks to classify which knots admit surgeries to the "simplest" non-trivial
3-manifolds--lens spaces. By combining data from Floer homology and the t
heory of integer lattices into the notion of a changemaker lattice\, Green
e (2010) solved the lens space realization problem: every lens space which
may be realized as surgery on a knot in the three-sphere may be realized
by a knot already known to surger to that lens space (i.e. a torus knot or
a Berge knot). In this talk\, we present a survey of techniques in Dehn s
urgery and their applications\, introduce a generalization of Greene's cha
ngemaker lattices\, and discuss applications to surgeries on knots in the
Poincaré homology sphere.\n
LOCATION:https://researchseminars.org/talk/caltechGT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lan-Hsuan Huang (UConn)
DTSTART:20210416T220000Z
DTEND:20210416T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/25
DESCRIPTION:Title: Existence of static vacuum extensions\nby Lan-Hsuan Huang (UConn) a
s part of Caltech geometry/topology seminar\n\n\nAbstract\nThe study of st
atic vacuum Riemannian metrics arises naturally in general relativity and
differential geometry. A static vacuum metric produces a static spacetime
by a warped product\, and it is related to scalar curvature deformation an
d gluing. The well-known Uniqueness Theorem of Static Black Holes says tha
t an asymptotically flat\, static vacuum metric with black hole boundary m
ust belong to the Schwarzschild family. In contrast to the rigidity phenom
enon\, R. Bartnik conjectured that there are asymptotically flat\, static
vacuum metric realizing certain arbitrarily specified boundary data. I wil
l discuss recent progress toward this conjecture. It is based on joint wor
k with Zhongshan An.\n
LOCATION:https://researchseminars.org/talk/caltechGT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Schwartz (Princeton)
DTSTART:20210423T220000Z
DTEND:20210423T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/26
DESCRIPTION:Title: The failure of the 4D light bulb theorem with dual spheres of non-zero
square\nby Hannah Schwartz (Princeton) as part of Caltech geometry/top
ology seminar\n\n\nAbstract\nExamples of surfaces embedded in a 4-manifold
that are homotopic but not isotopic are neither rare nor surprising. It i
s then quite amazing that\, in settings such as the recent 4D light bulb t
heorems of both Gabai and Schneiderman-Teichner\, the existence of an embe
dded sphere of square zero intersecting a surface transversally in a singl
e point has the power to "upgrade" a homotopy of that surface into a smoot
h isotopy. We will discuss the limitations of this phenonemon\, using cont
ractible 4-manifolds called corks to produce homotopic spheres in a 4-mani
fold with a common dual of non-zero square that are not smoothly isotopic.
\n
LOCATION:https://researchseminars.org/talk/caltechGT/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Vidussi (UC Riverside)
DTSTART:20210430T220000Z
DTEND:20210430T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/27
DESCRIPTION:Title: Algebraic fibrations of surface-by-surface groups\nby Stefano Vidus
si (UC Riverside) as part of Caltech geometry/topology seminar\n\n\nAbstra
ct\nAn algebraic fibration of a group G is an epimorphism to the integers
with a finitely generated kernel. This notion has been studied at least si
nce the '60s\, and has recently attracted renewed attention. Among other t
hings\, we will study it in the context of fundamental groups of surface b
undles over a surface\, where it has some interesting relations with some
classical problems about the mapping class group. This is based on joint w
ork with S. Friedl\, and with R. Kropholler and G. Walsh.\n
LOCATION:https://researchseminars.org/talk/caltechGT/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Kindred (UN Lincoln)
DTSTART:20210507T220000Z
DTEND:20210507T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/28
DESCRIPTION:Title: Definite surfaces\, plumbing\, and Tait's conjectures\nby Thomas Ki
ndred (UN Lincoln) as part of Caltech geometry/topology seminar\n\n\nAbstr
act\nIn 1898\, P.G. Tait asserted several properties of alternating link d
iagrams\, which remained unproven until the discovery of the Jones polynom
ial in 1985. By 1993\, the Jones polynomial had led to proofs of all of Ta
it’s conjectures\, but the geometric content of these new results remain
ed mysterious.\n\nIn 2017\, Howie and Greene independently gave the first
geometric characterizations of alternating links\; as a corollary\, Greene
obtained the first purely geometric proof of part of Tait’s conjectures
. Recently\, I used these characterizations and "replumbing" moves\, among
other techniques\, to give the first entirely geometric proof of Tait’s
flyping conjecture\, first proven in 1993 by Menasco and Thistlethwaite.\
n\nI will describe these recent developments\, focusing in particular on t
he fundamentals of plumbing (also called Murasugi sum)\, and definite surf
aces (which characterize alternating links a la Greene). As an aside\, I w
ill also sketch a (partly new\, simplified) proof of the classical result
of Murasugi and Crowell that the genus of an alternating knot equals half
the degree of its Alexander polynomial. The talk will be broadly accessib
le. Expect lots of pictures!\n
LOCATION:https://researchseminars.org/talk/caltechGT/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodora Bourni (UT Knoxville)
DTSTART:20210521T220000Z
DTEND:20210521T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/29
DESCRIPTION:Title: Ancient solutions to mean curvature flow\nby Theodora Bourni (UT Kn
oxville) as part of Caltech geometry/topology seminar\n\n\nAbstract\nMean
curvature flow (MCF) is the gradient flow of the area functional\; it move
s the surface in the direction of steepest decrease of area. An important
motivation for the study of MCF comes from its potential geometric applic
ations\, such as classification theorems and geometric inequalities. MCF d
evelops “singularities” (curvature blow-up)\, which obstruct the flow
from existing for all times and therefore understanding these high curvatu
re regions is of great interest. This is done by studying ancient solutio
ns\, solutions that have existed for all times in the past\, and which mod
el singularities. In this talk we will discuss their importance and ways o
f constructing and classifying such solutions. In particular\, we will foc
us on “collapsed” solutions and construct\, in all dimensions n>=2\, a
large family of new examples\, including both symmetric and asymmetric ex
amples\, as well as many eternal examples that do not evolve by translatio
n. Moreover\, we will show that collapsed solutions decompose “backward
s in time” into a canonical configuration of Grim hyperplanes which sati
sfies certain necessary conditions. This is joint work with Mat Langford a
nd Giuseppe Tinaglia.\n
LOCATION:https://researchseminars.org/talk/caltechGT/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasa Sesum (Rutgers)
DTSTART:20210604T220000Z
DTEND:20210604T230000Z
DTSTAMP:20260422T225752Z
UID:caltechGT/30
DESCRIPTION:Title: Ancient solutions in geometric flows\nby Natasa Sesum (Rutgers) as
part of Caltech geometry/topology seminar\n\n\nAbstract\nWe will talk abou
t classification of ancient solutions in geometric flows. In particular\,
we will show the only closed ancient noncollapsed Ricci flow solutions are
the shrinking spheres and Perelman's solution. We will talk about the hig
her dimensional analogue of this result under suitable curvature assumptio
ns as well. These are joint works with Brendle\, Daskalopoulos and Naff.\n
LOCATION:https://researchseminars.org/talk/caltechGT/30/
END:VEVENT
END:VCALENDAR