BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Sathya Rengaswami (UTK)
DTSTART:20210216T195000Z
DTEND:20210216T210500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/1
DESCRIPTION:Title: Rotationally symmetric translators of curvature flows\nb
y Sathya Rengaswami (UTK) as part of UTK Geometric Analysis Seminar\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Lynch (Tubingen University)
DTSTART:20210223T195000Z
DTEND:20210223T210500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/2
DESCRIPTION:Title: Convex ancient solutions of mean curvature flow with Type I
curvature growth\nby Stephen Lynch (Tubingen University) as part of UT
K Geometric Analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Santilli (Augsburg University)
DTSTART:20210302T195000Z
DTEND:20210302T210500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/3
DESCRIPTION:Title: Soap bubble theorems in Convex Geometry and Geometric Measur
e Theory.\nby Mario Santilli (Augsburg University) as part of UTK Geom
etric Analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Tinaglia (King’s College London)
DTSTART:20210309T195000Z
DTEND:20210309T210500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/4
DESCRIPTION:Title: The geometry of constant mean curvature surfaces in Euclidea
n space.\nby Giuseppe Tinaglia (King’s College London) as part of UT
K Geometric Analysis Seminar\n\n\nAbstract\nI will begin by reviewing clas
sical geometric properties of constant mean curvature surfaces\, H>0\, in
R^3. I will then talk about several more recent results for surfaces embed
ded in R^3 with constant mean curvature\, such as curvature and radius est
imates for simply-connected surfaces embedded in R^3 with constant mean cu
rvature. Finally I will show applications of such estimates including a ch
aracterization of the round sphere as the only simply-connected surface em
bedded in R^3 with constant mean curvature and area estimates for compact
surfaces embedded in a flat torus with constant mean curvature and finite
genus. This is joint work with Meeks.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alec Payne (Courant Institute)
DTSTART:20210316T185000Z
DTEND:20210316T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/5
DESCRIPTION:by Alec Payne (Courant Institute) as part of UTK Geometric Ana
lysis Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christos Sourdis (National and Kapodistrian University of Athens)
DTSTART:20210323T185000Z
DTEND:20210323T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/6
DESCRIPTION:by Christos Sourdis (National and Kapodistrian University of A
thens) as part of UTK Geometric Analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debora Impera (Politecnico di Torino)
DTSTART:20210330T185000Z
DTEND:20210330T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/7
DESCRIPTION:Title: Quantitative index bounds for f-minimal hypersurfaces in the
Euclidean space\nby Debora Impera (Politecnico di Torino) as part of
UTK Geometric Analysis Seminar\n\n\nAbstract\nThe recent developments in t
he existence theory for minimal immersions have motivated a renewed intere
st in studying estimates on the Morse index of these objects. One possible
way to control instability is through topological invariants (in particul
ar through the first Betti number) of the minimal hypersurface. This was f
irst investigated by A. Ros for immersed minimal surfaces in $R^3$\, or a
quotient of it by a group of translations\, and then\, in higher dimension
\, by A. Savo when then ambient manifold is a round sphere. In this talk w
e will first discuss how the method used by Savo can be generalized to stu
dy the Morse index of self-shrinkers for the mean curvature flow and\, mor
e generally\, of weighted minimal hypersurfaces in a Euclidean space endow
ed with a convex weight. In particular\, when the hypersurface is compact\
, we will show that the index is bounded from below by an affine function
of its first Betti number. In the complete non-compact case\, the lower bo
und is in terms of the dimension of the space of weighted square integrabl
e f-harmonic 1-forms. In particular\, in dimension 2\, the procedure gives
an index estimate in terms of the genus of the surface. \n\nCombining thi
s technique with an adaptation to the weighted setting of well-known resul
ts by P. Li and L. F. Tam\, we will also discuss how to obtain quantitativ
e estimates on the Morse index of translators for the mean curvature flow
with bounded norm of the second fundamental form via the number of ends of
the hypersurface.\n\nThis talk is based on joint works with Michele Rimol
di and Alessandro Savo.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Halilaj (University of Ioannina)
DTSTART:20210406T185000Z
DTEND:20210406T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/8
DESCRIPTION:Title: Minimal maps\, MCF and isotopy problems\nby Andreas Hali
laj (University of Ioannina) as part of UTK Geometric Analysis Seminar\n\n
\nAbstract\nI will discuss the mean curvature flow (MCF) of graphical subm
anifolds generated\nby smooth maps between Riemannian manifolds. I will de
monstrate applications related to\nthe homotopy type of smooth maps betwee
n compact manifolds. I will also show some rigidity\nresults concerning th
e Hopf fibrations.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Panagiotis Gianniotis (National and Kapodistrian University of Ath
ens)
DTSTART:20210413T185000Z
DTEND:20210413T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/9
DESCRIPTION:Title: An isometric flow of G2 structures\nby Panagiotis Gianni
otis (National and Kapodistrian University of Athens) as part of UTK Geome
tric Analysis Seminar\n\n\nAbstract\nA G2 structure on a 7 manifold is a t
hree form that determines\, in a nonlinear way\, a Riemannian metric. Our
interest in such structures comes from the fact that when they are paralle
l with respect to the associated Levi-Civita connection then the metric is
automatically Ricci flat with holonomy contained in the Lie group G2. Par
allel G2 structures can be considered as the optimal such structures on a
given smooth manifold\, however there may not exist since there are severa
l obstructions. Unfortunately\, despite the construction of many examples
of parallel G2 structures\, there is at the moment no conjecture regarding
which smooth 7 manifolds admit holonomy G2 metrics. On the other hand\, a
ny Riemannian metric on a manifold admitting G2 structures is induced by m
any - isometric - G2 structures\, and a natural question is to find wheth
er there exists an optimal representative in a\ngiven isometric class. In
this talk I will discuss a geometric flow approach to this problem\, initi
ally proposed by Grigorian\, and present joint work with Dwivedi and Karig
iannis in which we develop the foundational theory for this flow.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Espinar (Cadiz University)
DTSTART:20210420T185000Z
DTEND:20210420T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/10
DESCRIPTION:Title: On non-compact free boundary minimal hypersurfaces in the R
iemannian Schwarzschild spaces.\nby Jose Espinar (Cadiz University) as
part of UTK Geometric Analysis Seminar\n\n\nAbstract\nWe will show that\,
in contrast with the 3-dimensional case\, the Morse index of a free bound
ary rotationally symmetric totally geodesic hypersurface of the nnn-dimens
ional Riemannnian Schwarzschild space with respect to variations that are
tangential along the horizon is zero\, for $n\\geq 4$. Moreover\, we will
show that there exist non-compact free boundary minimal hypersurfaces whic
h are not totally geodesic\, $n\\geq 8$\, with Morse index equal to zero.
Also\, for $n\\geq 4$\, there exist infinitely many non-compact free bound
ary minimal hypersurfaces\, which are not congruent to each other\, with i
nfinite Morse index. Finally\, we will discuss the density at infinity of
a free boundary minimal hypersurface with respect to a minimal cone constr
ucted over a minimal hypersurface of the unit Euclidean sphere. We obtain
a lower bound for the density in terms of the area of the boundary of the
hypersurface and the area of the minimal hypersurface in the unit sphere.
This lower bound is optimal in the sense that only minimal cones achieve i
t.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Scharrer (University of Warwick)
DTSTART:20210427T185000Z
DTEND:20210427T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/11
DESCRIPTION:Title: Isoperimetric constrained Willmore tori\nby Christian S
charrer (University of Warwick) as part of UTK Geometric Analysis Seminar\
n\n\nAbstract\nIn order to explain the bi-concave shape of red blood cells
\, Helfrich proposed the minimisation of a bending energy amongst closed s
urfaces with given fixed area and volume. In the homogeneous case\, the He
lfrich functional reduces to the scaling invariant Willmore functional. Th
us\, for the minimisation\, the constraints on area and volume reduce to a
single constraint on the scaling invariant isoperimetric ratio. This talk
is about two strict inequalities that lead to existence of isoperimetric
constrained Willmore tori.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melanie Rupflin (University of Oxford)
DTSTART:20210921T185000Z
DTEND:20210921T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/12
DESCRIPTION:Title: Lojasiewicz inequalities near simple bubble trees\nby M
elanie Rupflin (University of Oxford) as part of UTK Geometric Analysis Se
minar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Lambert (Technische Universitaet Darmstadt)
DTSTART:20210928T185000Z
DTEND:20210928T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/13
DESCRIPTION:Title: Lagrangian Mean Curvature Flow with Boundary\nby Ben La
mbert (Technische Universitaet Darmstadt) as part of UTK Geometric Analysi
s Seminar\n\n\nAbstract\nThe foundational result of Lagrangian Mean Curvat
ure Flow (LMCF) is that in Calabi–Yau manifolds\, high codimensional mea
n curvature flow preserves the Lagrangian condition. A natural question is
then to ask if this can this be generalised to manifolds with boundary. E
quivalently\, what is a well-defined boundary condition for LMCF? In this
talk I will provide an answer to this question\, and then demonstrate that
the resulting flow exhibits good behaviour in two model situations\, name
ly with boundary on the Lawlor neck and Clifford Torus respectively. No pr
ior knowledge of geometric flows will be assumed. This work is joint with
Chris Evans and Albert Wood.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Blatt (Paris-Lodron University Salzburg)
DTSTART:20211026T185000Z
DTEND:20211026T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/14
DESCRIPTION:Title: Analyticity of solutions to fractional partial differential
equations\nby Simon Blatt (Paris-Lodron University Salzburg) as part
of UTK Geometric Analysis Seminar\n\n\nAbstract\nWe will discuss an old to
pic in the field of partial differential equations in a new context: The q
uestion of analyticity of solutions to elliptic equations. While first res
ults for classical elliptic partial differential equations were already ob
tained by Bernstein in 1904\, in the context of fractional and non-local e
quations only partial results or results for very special cases like the H
artree-Fock equations and the Boltzmann equation are known up to now.\nAft
er presenting some known results\, we will discuss our recent findings for
so-called knot energies and general semi-linear integro-differential equa
tions. The main ingredients in the proof of these results are Cauchy's met
hod of majorants and a new estimate for the long range interactions of the
se equations. Partly joint with Nicole Vorderobermeier.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Magdalena Rodriguez (Universidad de Granada)
DTSTART:20211109T195000Z
DTEND:20211109T210500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/16
DESCRIPTION:Title: Constant mean curvature surfaces in $\\mathbb{H}^2\\times\\
mathbb{R}$\nby Magdalena Rodriguez (Universidad de Granada) as part of
UTK Geometric Analysis Seminar\n\n\nAbstract\nAbstract: The theory of con
stant mean curvature $H>0$ surfaces ($H$-surfaces) in $\\mathbb{H}^2\\time
s\\mathbb{R}$ became very active after the seminal work by Abresch and Ros
enberg where they described a Hopf-type holomorphic quadratic differential
on any such surface and classified the rotational $H$-spheres. The critic
al value for $H$ in $\\mathbb{H}^2\\times\\mathbb{R}$ is $\\frac 12$\, in
the sense that there exist compact examples only when $H>\\frac 12$ and en
tire graphs (i.e. graphs defined on the whole $\\mathbb{H}^2$) if $H\\leq\
\frac 12$. When $H>\\frac 12$\, the geometric behaviour of the H-surfaces
in $\\mathbb{H}^2\\times\\mathbb{R}$ is analogous\, in some sense\, to the
surfaces of positive constant mean curvature in $\\mathbb{R}^3$. In thi
s talk we will prove that a properly embedded $H$-surface in $\\mathbb{H}^
2\\times\\mathbb{R}$ with $0The mean curvature flow in null hypersurfaces and the detec
tion of MOTS\nby Julian Scheuer (Cardiff University) as part of UTK Ge
ometric Analysis Seminar\n\n\nAbstract\nThis talk is based on joint work w
ith Henri Roesch. We discuss the mean curvature flow in 3-dimensional null
hypersurfaces. In a spacetime a hypersurface is called null\, if its indu
ced metric is degenerate. The speed of the mean curvature flow of spacelik
e surfaces in a null hypersurface is the projection of the codimension-two
mean curvature vector onto the null hypersurface. Under fairly mild condi
tions we obtain that for an outer un-trapped initial surface\, a condition
which resembles the mean-convexity of a surface in Euclidean space\, the
mean curvature flow exists for all times and converges smoothly to a margi
nally outer trapped surface (MOTS). As an application we obtain the existe
nce of a smooth local foliation of the past of an outermost MOTS.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhongshan An (University of Connecticut)
DTSTART:20210907T185000Z
DTEND:20210907T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/18
DESCRIPTION:Title: Static vacuum extensions of Bartnik boundary data near flat
domains\nby Zhongshan An (University of Connecticut) as part of UTK G
eometric Analysis Seminar\n\n\nAbstract\nThe Bartnik boundary data of a Ri
emannian manifold with nonempty boundary consists of the induced metric an
d extrinsic mean curvature of the boundary manifold. Existence of static v
acuum Riemannian metrics with prescribed Bartnik data is one of the most f
undamental problems in Riemannian geometry related to general relativity.
It is also a very interesting problem on the global solvability of a natur
al geometric boundary value problem. In this talk I will first discuss the
basic properties of static vacuum metrics and their boundary geometry. Th
en I will present some recent progress towards the existence problem based
on a joint work with Lan-Hsuan Huang.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Schulze (University of Warwick)
DTSTART:20211130T195000Z
DTEND:20211130T210500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/19
DESCRIPTION:Title: Mean curvature flow with generic initial data\nby Felix
Schulze (University of Warwick) as part of UTK Geometric Analysis Seminar
\n\n\nAbstract\nMean curvature flow is the gradient flow of the area funct
ional and constitutes a natural geometric heat equation on the space of hy
persurfaces in an ambient Riemannian manifold. It is believed\, similar to
Ricci Flow in the intrinsic setting\, to have the potential to serve as a
tool to approach several fundamental conjectures in geometry. The obstacl
e for these applications is that the flow develops singularities\, which o
ne in general might not be able to classify completely. Nevertheless\, a w
ell-known conjecture of Huisken states that a generic mean curvature flow
should have only spherical and cylindrical singularities. As a first step
in this direction Colding-Minicozzi have shown in fundamental work that sp
heres and cylinders are the only linearly stable singularity models. As a
second step toward Huisken's conjecture we show that mean curvature flow o
f generic initial closed surfaces in R^3 avoids asymptotically conical and
non-spherical compact singularities. The main technical ingredient is a l
ong-time existence and uniqueness result for ancient mean curvature flows
that lie on one side of asymptotically conical or compact self-similarly s
hrinking solutions. This is joint work with Otis Chodosh\, Kyeongsu Choi a
nd Christos Mantoulidis.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ao Sun (University of Chicago)
DTSTART:20220301T195000Z
DTEND:20220301T210500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/20
DESCRIPTION:Title: Existence of minimal hypersurfaces with arbitrarily large a
rea\nby Ao Sun (University of Chicago) as part of UTK Geometric Analys
is Seminar\n\n\nAbstract\nI will present an approach to find minimal hyper
surfaces with arbitrarily large area in a closed manifold with dimension b
etween 3 and 7. The method is based on the novel Almgren-Pitts min-max th
eory\, and its further development by Marques-Neves\, Song and Zhou. Among
the applications\, we can show that there exist minimal hypersurfaces wit
h arbitrarily large area in an analytic manifold. In the case where this a
pproach does not work\, it is surprising that the space of minimal hypersu
rfaces has a Cantor set fractal structure. This is joint work with James S
tevens (UChicago).\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Saez (Pontificia Universidad Católica de Chile)
DTSTART:20220308T195000Z
DTEND:20220308T210500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/21
DESCRIPTION:Title: Uniqueness of entire graphs evolving by mean curvature flow
\nby Mariel Saez (Pontificia Universidad Católica de Chile) as part o
f UTK Geometric Analysis Seminar\n\n\nAbstract\nIn this talk I will discus
s the uniqueness of graphical mean curvature flow. We consider as initial
conditions graphs of locally Lipschitz functions and prove that in the one
dimensional case solutions are unique without any further assumptions. Th
is result is then generalized for rotationally symmetric solutions. In the
general n- dimensional case\, we prove uniqueness under additional condit
ions: we require a uniform lower bound on the second fundamental form and
the height function. The latter result extends to initial conditions that
are proper graphs over subdomains of $\\mathbb R^n$. (Joint with P. Daskal
opoulos)\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Lai (Stanford University)
DTSTART:20220503T185000Z
DTEND:20220503T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/22
DESCRIPTION:Title: O(2)-symmetry of 3D steady gradient Ricci solitons\nby
Yi Lai (Stanford University) as part of UTK Geometric Analysis Seminar\n\n
\nAbstract\nFor any 3D steady gradient Ricci soliton\, if it is asymptotic
to a ray we prove that it must be isometric to the Bryant soliton. Otherw
ise\, it is asymptotic to a sector and called a flying wing. We show that
all flying wings are O(2)-symmetric. Hence\, all 3D steady gradient Ricci
solitons are O(2)-symmetric.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Mäder-Baumdicker (Technische Universität Darmstadt)
DTSTART:20220426T185000Z
DTEND:20220426T200500Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/23
DESCRIPTION:Title: The area preserving curve shortening flow in a free boundar
y setting\nby Elena Mäder-Baumdicker (Technische Universität Darmsta
dt) as part of UTK Geometric Analysis Seminar\n\n\nAbstract\nA convex\, si
mple closed plane curve moving by the area preserving curve shortening flo
w (APCSF) converges smoothly to a circle with the same enclosed area as th
e initial curve (Gage 1986). Note that the circle is the solution of the i
soperimetric problem in the Euclidean plane. Corresponding to the relative
(outer) isoperimetric problem we present results concerning the APCSF wit
h Neumann free boundary conditions outside of a convex domain. Under certa
in conditions on the initial curve the flow does not develop a singularity
and subconverges smoothly to an arc of a circle sitting outside of the gi
ven convex domain and enclosing the same area as the initial curve. On the
other hand\, there are many examples of convex initial curves developing
a singularity in finite time. In all these cases\, the singularity is of t
ype II\, and we conjecture that some curves developing a singularity stay
embedded under the flow. In general\, we will point out similarities and d
ifferences of the APCSF to the well-known curve shortening flow.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keaton Naff (MIT)
DTSTART:20220419T160000Z
DTEND:20220419T170000Z
DTSTAMP:20260404T111331Z
UID:UTK-GA-seminar/24
DESCRIPTION:Title: Immersed mean convex mean curvature flows with noncollapsed
singularities\nby Keaton Naff (MIT) as part of UTK Geometric Analysis
Seminar\n\n\nAbstract\nIn the mean curvature flow of hypersurfaces\, nonc
ollapsing has proven to be a powerful and useful assumption when studying
singularities and high curvature regions. In particular\, the assumption o
f noncollapsing has been used to prove a wide range of local a priori esti
mates\, and has led to classification results for certain classes of singu
larity models. Less is known for immersed mean-convex flows. In this talk\
, I would like to survey recent results and discuss outstanding conjecture
s for immersed mean-convex flows that begin to bridge the gap between the
embedded and immersed mean-convex settings. The talk is based on joint wor
k with S. Brendle and ongoing work with S. Lynch.\n
LOCATION:https://stable.researchseminars.org/talk/UTK-GA-seminar/24/
END:VEVENT
END:VCALENDAR