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BEGIN:VEVENT
SUMMARY:William Ballinger (Princeton)
DTSTART:20201002T220000Z
DTEND:20201002T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/1
DESCRIPTION:Title: Concordance invariants from the E(-1) spectral sequence\nby W
illiam Ballinger (Princeton) as part of Caltech geometry/topology seminar\
n\n\nAbstract\nMany recent concordance invariants of knots come from pertu
rbing the differential on a knot homology theory to get a complex with tri
vial homology but an interesting filtration. I describe the invariant comi
ng 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://stable.researchseminars.org/talk/caltechGT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ahmad Issa (UBC)
DTSTART:20201009T220000Z
DTEND:20201009T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/2
DESCRIPTION:Title: Symmetric knots and the equivariant 4-ball genus\nby Ahmad Is
sa (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 or
ientable surface embedded in the 4-ball with boundary K. If the knot K has
a symmetry (e.g. K is periodic or strongly invertible)\, one can define t
he equivariant 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 ongo
ing work with Keegan Boyle on trying to understanding the equivariant 4-ge
nus.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harold Williams (USC)
DTSTART:20201016T220000Z
DTEND:20201016T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/3
DESCRIPTION:Title: Kasteleyn operators from mirror symmetry\nby Harold Williams
(USC) as part of Caltech geometry/topology seminar\n\n\nAbstract\nIn this
talk we explain an interpretation of the Kasteleyn operator of a doubly-pe
riodic bipartite graph from the perspective of homological mirror symmetry
. Specifically\, given a consistent bipartite graph G in T^2 with a comple
x-valued edge weighting E we show the following two constructions are the
same. The first is to form the Kasteleyn operator of (G\,E) and pass to it
s spectral 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 can
onically associated to G\, equip it with a brane structure prescribed by E
\, and pass to its homologically mirror coherent sheaf. This lives on a to
ric compactification of (C*)^2 determined by the Legendrian link which lif
ts the zig-zag paths of G (and to which the noncompact Lagrangian L is asy
mptotic). As a corollary\, we obtain a complementary geometric perspective
on certain features of algebraic integrable systems associated to lattice
polygons\, studied for example by Goncharov-Kenyon and Fock-Marshakov. Th
is is joint work with David Treumann and Eric Zaslow.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boyu Zhang (Princeton)
DTSTART:20201023T220000Z
DTEND:20201023T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/4
DESCRIPTION:Title: Several detection results of Khovanov homology on links\nby B
oyu Zhang (Princeton) as part of Caltech geometry/topology seminar\n\n\nAb
stract\nThe Khovanov homology is a combinatorially defined invariant for k
nots and links. I will present several new detection results of Khovanov h
omology on links. In particular\, we show that if L is an n-component link
with Khovanov homology of rank 2^n\, then it is given by the connected su
ms and disjoint unions of unknots and Hopf links. This result gives a posi
tive answer to a question asked by Batson-Seed\, and it generalizes the un
link detection theorem by Hedden-Ni and Batson-Seed. The proof relies on a
new excision formula for the singular instanton Floer homology. This is j
oint work with Yi Xie.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (Princeton)
DTSTART:20201030T220000Z
DTEND:20201030T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/5
DESCRIPTION:Title: Generalized soap bubbles and the topology of manifolds with posit
ive scalar curvature\nby Chao Li (Princeton) as part of Caltech geomet
ry/topology seminar\n\n\nAbstract\nIt has been a classical question which
manifolds admit Riemannian metrics with positive scalar curvature. I will
present some recent progress on this question\, ruling out positive scalar
curvature on closed aspherical manifolds of dimensions 4 and 5 (as conjec
tured by Schoen-Yau and by Gromov)\, as well as complete metrics of positi
ve scalar curvature on an arbitrary manifold connect sum with a torus. App
lications include a Schoen-Yau Liouville theorem for all locally conformal
ly flat manifolds. The proofs of these results are based on analyzing gene
ralized soap bubbles - surfaces that are stable solutions to the prescribe
d mean curvature problem. This talk is based on joint work with O. Chodosh
.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Samperton (UIUC)
DTSTART:20201106T230000Z
DTEND:20201107T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/6
DESCRIPTION:Title: 3-manifold invariants\, G-equivariant TQFT\, and complexity\n
by Eric Samperton (UIUC) as part of Caltech geometry/topology seminar\n\n\
nAbstract\nLet G be a finite group. G-equivariant TQFTs have received att
ention from both mathematicians and physicists\, motivated in part by the
search for new topological phases that can be used as the hardware for a u
niversal quantum computer. Our goal will be to convey two complexity-theo
retic lessons. First\, when G is sufficiently complicated (nonabelian sim
ple)\, 3-manifold invariants derived from G-equivariant TQFTs are very dif
ficult to compute (#P-hard)\, even on a quantum computer. Second\, no mat
ter what finite group G one uses\, a 3-dimensional G-equivariant TQFT can
not be used for universal topological quantum computation if the underlyin
g non-equivariant theory is not already universal. This talk is based on
joint works with Greg Kuperberg and Colleen Delaney.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Bamler (UC Berkeley)
DTSTART:20201113T230000Z
DTEND:20201114T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/7
DESCRIPTION:Title: Compactness and partial regularity theory of Ricci flows in highe
r dimensions\nby Richard Bamler (UC Berkeley) as part of Caltech geome
try/topology 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 sm
ooth on the complement of a singular set of parabolic codimension at least
4. We furthermore obtain a stratification of the singular set with optima
l dimensional bounds depending on the symmetries of the tangent flows. Our
methods also imply the corresponding quantitative stratification result a
nd the expected $L^p$-curvature bounds.\n\nAs an application we obtain a d
escription of the singularity formation at the first singular time and a l
ong-time characterization of immortal flows\, which generalizes the thick-
thin decomposition in dimension 3. We also obtain a backwards pseudolocali
ty theorem and discuss several other applications.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Takeda (IHES)
DTSTART:20201120T230000Z
DTEND:20201121T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/8
DESCRIPTION:Title: Pre-Calabi-Yau categories and dualizability in 2d\nby Alex Ta
keda (IHES) as part of Caltech geometry/topology seminar\n\n\nAbstract\nIn
this talk I will describe some joint work with Maxim Kontsevich on the st
udy of pre-Calabi Yau categories. I will discuss the action of a PROP on t
he Hochschild invariants of such a category and explain how this notion an
d more familiar notions of Calabi-Yau objects relate to different dualizab
ility conditions of 2d TQFTs. Time allowing I will present some motivating
examples from symplectic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oguz Savk (Bogazici University)
DTSTART:20201204T230000Z
DTEND:20201205T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/9
DESCRIPTION:Title: Brieskorn spheres\, homology cobordism and homology balls\nby
Oguz Savk (Bogazici University) as part of Caltech geometry/topology semi
nar\n\n\nAbstract\nA classical question in low-dimensional topology asks w
hich homology 3-spheres bound homology 4-balls. This question is fairly ad
dressed to Brieskorn spheres Σ(p\,q\,r)\, which are defined to be links o
f singularities x^p+y^q+z^r=0. Over the years\, Brieskorn spheres also hav
e been the main objects for the understanding of the algebraic structure o
f the integral homology cobordism group.\n\nIn this talk\, we will present
several families of Brieskorn spheres which do or do not bound integral a
nd rational homology balls via Ozsváth-Szabó d-invariant\, involutive He
egaard Floer homology\, and Kirby calculus. Also\, we will investigate the
ir positions in both integral and\nrational homology cobordism groups.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christine Breiner (Fordham University)
DTSTART:20210205T230000Z
DTEND:20210206T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/10
DESCRIPTION:Title: Harmonic branched coverings and uniformization of CAT($k$) spher
es\nby Christine Breiner (Fordham University) as part of Caltech geome
try/topology seminar\n\n\nAbstract\nConsider a metric space $(S\,d)$ with
an upper curvature bound in the sense of Alexandrov (i.e. via triangle com
parison). We show that if $(S\,d)$ is homeomorphically equivalent to the
2-sphere $S^2$\, then it is conformally equivalent to $S^2$. The method o
f proof is through harmonic maps\, and we show that the conformal equivale
nce is achieved by an almost conformal harmonic map. The proof relies on
the analysis of the local behavior of harmonic maps between surfaces\, an
d the key step is to show that an almost conformal harmonic map from a c
ompact surface onto a surface with an upper curvature bound is a branched
covering. This work is joint with Chikako Mese.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ayala (Montana State)
DTSTART:20210108T230000Z
DTEND:20210109T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/12
DESCRIPTION:Title: Orthogonal group and higher categorical adjoints\nby David A
yala (Montana State) as part of Caltech geometry/topology seminar\n\n\nAbs
tract\nIn this talk I will articulate and contextualize the following sequ
ence of results.\n\n* The Bruhat decomposition of the general linear group
defines a stratification of the orthogonal group.\n\n* Matrix multiplicat
ion defines an algebra structure on its exit-path category in a certain Mo
rita category of categories.\n\n* In this Morita category\, this algebra a
cts on the categeory of n-categories -- this action is given by adjoining
adjoints to n-categories.\n\nThis result is extracted from a larger progra
m -- entirely joint with John Francis\, some parts joint with Nick Rozenbl
yum -- which proves the cobordism hypothesis.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Turner (UT Austin)
DTSTART:20210115T230000Z
DTEND:20210116T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/13
DESCRIPTION:Title: Links all of whose branched cyclic covers are L-spaces\nby H
annah Turner (UT Austin) as part of Caltech geometry/topology seminar\n\n\
nAbstract\nGiven an oriented link in the three-sphere and a fixed positive
integer n\, there is a unique 3-manifold called its branched cyclic cover
of index n. It is not well understood when these manifolds are L-spaces -
that is\, when their Heegaard Floer homology is as simple as possible. In
this talk I'll describe new examples of links whose cyclic branched cover
s are L-spaces for any index n. The proof uses a symmetry argument and a g
eneralization of alternating links due to Scaduto-Stoffregen. This is join
t work with Ahmad Issa.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Lai (UC Berkeley)
DTSTART:20210122T230000Z
DTEND:20210123T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/14
DESCRIPTION:Title: A family of 3d steady gradient solitons that are flying wings\nby Yi Lai (UC Berkeley) as part of Caltech geometry/topology seminar\n\
n\nAbstract\nWe find a family of 3d steady gradient Ricci solitons that ar
e flying wings. This verifies a conjecture by Hamilton. For a 3d flying wi
ng\, 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 Z
2 × O(n − 1)-symmetric but non-rotationally symmetric n-dimensional ste
ady gradient solitons with positive curvature operator. We show that these
solitons are non-collapsed.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weiyan Chen (Tsinghua)
DTSTART:20210129T230000Z
DTEND:20210130T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/15
DESCRIPTION:Title: Choosing points on cubic plane curves\nby Weiyan Chen (Tsing
hua) as part of Caltech geometry/topology seminar\n\n\nAbstract\nIt is a c
lassical topic to study structures of certain special points on complex sm
ooth cubic plane curves\, for example\, the 9 flex points and the 27 sexta
ctic points. We consider the following topological question asked by Farb:
Is it true that the known algebraic structures give all the possible ways
to continuously choose n distinct points on every smooth cubic plane curv
e\, for each given positive integer n? This work is joint with Ishan Baner
jee.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Stern (UChicago)
DTSTART:20210212T230000Z
DTEND:20210213T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/16
DESCRIPTION:Title: Constructing minimal submanifolds via gauge theory\nby Danie
l Stern (UChicago) as part of Caltech geometry/topology seminar\n\n\nAbstr
act\nThe self-dual Yang-Mills-Higgs (or Ginzburg-Landau) functionals are a
natural family of energies associated to sections and metric connections
of Hermitian line bundles\, whose critical points (particularly those sati
sfying 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 character
izing the behavior of critical points over manifolds of arbitrary dimensio
n. We show in particular that critical points give rise to minimal submani
folds of codimension two in certain natural scaling limits\, and use this
information to provide new constructions of codimension-two minimal variet
ies in arbitrary Riemannian manifolds. We will also discuss recent work wi
th Davide Parise and Alessandro Pigati developing the associated Gamma-con
vergence machinery\, and describe some geometric applications.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaolong Hans Han (UIUC)
DTSTART:20210226T230000Z
DTEND:20210227T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/17
DESCRIPTION:Title: Harmonic forms and norms on cohomology of non-compact hyperbolic
3-manifolds\nby Xiaolong Hans Han (UIUC) as part of Caltech geometry/
topology seminar\n\n\nAbstract\nWe will talk about generalizations of an i
nequality of Brock-Dunfield to the non-compact case\, with tools from Hodg
e theory for non-compact hyperbolic manifolds and recent developments in t
he theory 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 de
scribe a partial generalization to the infinite volume case.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katherine Raoux (Michigan State)
DTSTART:20210219T230000Z
DTEND:20210220T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/18
DESCRIPTION:Title: Knot Floer homology and relative adjunction inequalities\nby
Katherine Raoux (Michigan State) as part of Caltech geometry/topology sem
inar\n\n\nAbstract\nIn this talk\, we present a relative adjunction inequa
lity for 4-manifolds with boundary. We begin by constructing generalized H
eegaard Floer tau-invariants associated to a knot in a 3-manifold and a no
ntrivial Floer class. Given a 4-manifold with boundary\, the tau-invariant
associated to a Floer class provides a lower bound for the genus of a pro
perly embedded surface\, provided that the Floer class is in the image of
the cobordism map induced by the 4-manifold. We will also discuss some app
lications to links and contact manifolds.\n\nThis is joint work with Matth
ew Hedden.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Knudsen (Northeastern)
DTSTART:20210305T230000Z
DTEND:20210306T000000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/19
DESCRIPTION:Title: Stable and unstable homology of graph braid groups\nby Ben K
nudsen (Northeastern) as part of Caltech geometry/topology seminar\n\n\nAb
stract\nThe homology of the configuration spaces of a graph forms a finite
ly generated module over the polynomial ring generated by its edges\; in p
articular\, each Betti number is eventually equal to a polynomial in the n
umber of particles\, an analogue of classical homological stability. The d
egree of this polynomial is captured by a connectivity invariant of the gr
aph\, and its leading coefficient may be computed explicitly in terms of c
ut counts and vertex valences. This "stable" (asymptotic) homology is gene
rated entirely by the fundamental classes of certain tori of geometric ori
gin\, but exotic non-toric classes abound unstably. These mysterious class
es are intimately tied to questions about generation and torsion whose ans
wers remain elusive except in a few special cases. This talk represents jo
int work with Byung Hee An and Gabriel Drummond-Cole.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ikshu Neithalath (UCLA)
DTSTART:20210402T220000Z
DTEND:20210402T230000Z
DTSTAMP:20260404T110913Z
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\nMorris
on\, Walker and Wedrich recently defined a generalization of Khovanov-Roza
nsky homology to links in the boundary of a 4-manifold. We will discuss re
cent joint work with Ciprian Manolescu on computing the "skein lasagna mod
ule\," a basic part of MWW's invariant\, for a certain class of 4-manifold
s.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Miller (Rice)
DTSTART:20210409T220000Z
DTEND:20210409T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/21
DESCRIPTION:Title: Amphichiral knots with large 4-genera\nby Allison Miller (Ri
ce) as part of Caltech geometry/topology seminar\n\n\nAbstract\nAn oriente
d knot is called negative amphichiral if it is isotopic to the reverse of
its mirror image. Such knots have order at most two in the concordance gro
up\, and many modern concordance invariants vanish on them. Nevertheless\,
we will see that there are negative amphichiral knots with arbitrarily la
rge 4-genera (i.e. which are highly 4-dimensionally complex)\, using Casso
n-Gordon signature invariants as a primary tool.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Kotelskiy (Indiana)
DTSTART:20210514T220000Z
DTEND:20210514T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/23
DESCRIPTION:Title: Khovanov homology via Floer theory of the 4-punctured sphere
\nby Artem Kotelskiy (Indiana) as part of Caltech geometry/topology semina
r\n\n\nAbstract\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 h
omology of a pair of specifically constructed immersed curves C(T) and C'(
T’) on the dividing 4-punctured sphere S. Next\, motivated by several ta
ngle-replacement questions in knot theory\, we will describe a recently ob
tained structural result concerning the curve invariant C(T)\, which sever
ely restricts the types of curves that may appear as tangle invariants. Th
e proof relies on the matrix factorization framework of Khovanov-Rozansky\
, as well as the homological mirror symmetry statement for the 3-punctured
sphere. This is joint work with Liam Watson and Claudius Zibrowius.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Caudell (BC)
DTSTART:20210528T220000Z
DTEND:20210528T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/24
DESCRIPTION:Title: Lens space surgeries\, lattices\, and the Poincaré homology sph
ere\nby Jacob Caudell (BC) as part of Caltech geometry/topology semina
r\n\n\nAbstract\nMoser's classification of Dehn surgeries on torus knots (
1971) inspired a now fifty-years-old project to classify "exceptional" Deh
n surgeries on knots in the three-sphere. A prominent component of this pr
oject seeks to classify which knots admit surgeries to the "simplest" non-
trivial 3-manifolds--lens spaces. By combining data from Floer homology an
d the theory of integer lattices into the notion of a changemaker lattice\
, Greene (2010) solved the lens space realization problem: every lens spac
e which may be realized as surgery on a knot in the three-sphere may be re
alized 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 surgery and their applications\, introduce a generalization of Green
e's changemaker lattices\, and discuss applications to surgeries on knots
in the Poincaré homology sphere.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lan-Hsuan Huang (UConn)
DTSTART:20210416T220000Z
DTEND:20210416T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/25
DESCRIPTION:Title: Existence of static vacuum extensions\nby Lan-Hsuan Huang (U
Conn) as part of Caltech geometry/topology seminar\n\n\nAbstract\nThe stud
y of static vacuum Riemannian metrics arises naturally in general relativi
ty and differential geometry. A static vacuum metric produces a static spa
cetime by a warped product\, and it is related to scalar curvature deforma
tion and gluing. The well-known Uniqueness Theorem of Static Black Holes s
ays that an asymptotically flat\, static vacuum metric with black hole bou
ndary must belong to the Schwarzschild family. In contrast to the rigidity
phenomenon\, R. Bartnik conjectured that there are asymptotically flat\,
static vacuum metric realizing certain arbitrarily specified boundary data
. I will discuss recent progress toward this conjecture. It is based on jo
int work with Zhongshan An.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Schwartz (Princeton)
DTSTART:20210423T220000Z
DTEND:20210423T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/26
DESCRIPTION:Title: The failure of the 4D light bulb theorem with dual spheres of no
n-zero square\nby Hannah Schwartz (Princeton) as part of Caltech geome
try/topology seminar\n\n\nAbstract\nExamples of surfaces embedded in a 4-m
anifold that are homotopic but not isotopic are neither rare nor surprisin
g. It is then quite amazing that\, in settings such as the recent 4D light
bulb theorems of both Gabai and Schneiderman-Teichner\, the existence of
an embedded sphere of square zero intersecting a surface transversally in
a single point has the power to "upgrade" a homotopy of that surface into
a smooth isotopy. We will discuss the limitations of this phenonemon\, usi
ng contractible 4-manifolds called corks to produce homotopic spheres in a
4-manifold with a common dual of non-zero square that are not smoothly is
otopic.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Vidussi (UC Riverside)
DTSTART:20210430T220000Z
DTEND:20210430T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/27
DESCRIPTION:Title: Algebraic fibrations of surface-by-surface groups\nby Stefan
o Vidussi (UC Riverside) as part of Caltech geometry/topology seminar\n\n\
nAbstract\nAn algebraic fibration of a group G is an epimorphism to the in
tegers with a finitely generated kernel. This notion has been studied at l
east since the '60s\, and has recently attracted renewed attention. Among
other things\, we will study it in the context of fundamental groups of su
rface bundles over a surface\, where it has some interesting relations wit
h some classical problems about the mapping class group. This is based on
joint work with S. Friedl\, and with R. Kropholler and G. Walsh.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Kindred (UN Lincoln)
DTSTART:20210507T220000Z
DTEND:20210507T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/28
DESCRIPTION:Title: Definite surfaces\, plumbing\, and Tait's conjectures\nby Th
omas Kindred (UN Lincoln) as part of Caltech geometry/topology seminar\n\n
\nAbstract\nIn 1898\, P.G. Tait asserted several properties of alternating
link diagrams\, which remained unproven until the discovery of the Jones
polynomial in 1985. By 1993\, the Jones polynomial had led to proofs of al
l of Tait’s conjectures\, but the geometric content of these new results
remained 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 conj
ectures. Recently\, I used these characterizations and "replumbing" moves\
, among other techniques\, to give the first entirely geometric proof of T
ait’s flyping conjecture\, first proven in 1993 by Menasco and Thistleth
waite.\n\nI will describe these recent developments\, focusing in particul
ar on the fundamentals of plumbing (also called Murasugi sum)\, and defini
te surfaces (which characterize alternating links a la Greene). As an asid
e\, I will also sketch a (partly new\, simplified) proof of the classical
result of Murasugi and Crowell that the genus of an alternating knot equal
s half the degree of its Alexander polynomial. The talk will be broadly a
ccessible. Expect lots of pictures!\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodora Bourni (UT Knoxville)
DTSTART:20210521T220000Z
DTEND:20210521T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/29
DESCRIPTION:Title: Ancient solutions to mean curvature flow\nby Theodora Bourni
(UT Knoxville) as part of Caltech geometry/topology seminar\n\n\nAbstract
\nMean curvature flow (MCF) is the gradient flow of the area functional\;
it moves the surface in the direction of steepest decrease of area. An im
portant motivation for the study of MCF comes from its potential geometric
applications\, such as classification theorems and geometric inequalities
. MCF develops “singularities” (curvature blow-up)\, which obstruct th
e flow from existing for all times and therefore understanding these high
curvature regions is of great interest. This is done by studying ancient
solutions\, solutions that have existed for all times in the past\, and wh
ich model singularities. In this talk we will discuss their importance and
ways of constructing and classifying such solutions. In particular\, we w
ill focus on “collapsed” solutions and construct\, in all dimensions n
>=2\, a large family of new examples\, including both symmetric and asymme
tric examples\, as well as many eternal examples that do not evolve by tra
nslation. Moreover\, we will show that collapsed solutions decompose “b
ackwards in time” into a canonical configuration of Grim hyperplanes whi
ch satisfies certain necessary conditions. This is joint work with Mat Lan
gford and Giuseppe Tinaglia.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasa Sesum (Rutgers)
DTSTART:20210604T220000Z
DTEND:20210604T230000Z
DTSTAMP:20260404T110913Z
UID:caltechGT/30
DESCRIPTION:Title: Ancient solutions in geometric flows\nby Natasa Sesum (Rutge
rs) as part of Caltech geometry/topology seminar\n\n\nAbstract\nWe will ta
lk about classification of ancient solutions in geometric flows. In partic
ular\, we will show the only closed ancient noncollapsed Ricci flow soluti
ons are the shrinking spheres and Perelman's solution. We will talk about
the higher dimensional analogue of this result under suitable curvature as
sumptions as well. These are joint works with Brendle\, Daskalopoulos and
Naff.\n
LOCATION:https://stable.researchseminars.org/talk/caltechGT/30/
END:VEVENT
END:VCALENDAR