BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Sathya Rengaswami (UTK)
DTSTART:20210216T195000Z
DTEND:20210216T210500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/1
DESCRIPTION:Title: Rotationally symmetric translators of curvature flows\nby Sathy
a Rengaswami (UTK) as part of UTK Geometric Analysis Seminar\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Lynch (Tubingen University)
DTSTART:20210223T195000Z
DTEND:20210223T210500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/2
DESCRIPTION:Title: Convex ancient solutions of mean curvature flow with Type I curvatu
re growth\nby Stephen Lynch (Tubingen University) as part of UTK Geome
tric Analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Santilli (Augsburg University)
DTSTART:20210302T195000Z
DTEND:20210302T210500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/3
DESCRIPTION:Title: Soap bubble theorems in Convex Geometry and Geometric Measure Theor
y.\nby Mario Santilli (Augsburg University) as part of UTK Geometric A
nalysis Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Tinaglia (King’s College London)
DTSTART:20210309T195000Z
DTEND:20210309T210500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/4
DESCRIPTION:Title: The geometry of constant mean curvature surfaces in Euclidean space
.\nby Giuseppe Tinaglia (King’s College London) as part of UTK Geome
tric Analysis Seminar\n\n\nAbstract\nI will begin by reviewing classical g
eometric properties of constant mean curvature surfaces\, H>0\, in R^3. I
will then talk about several more recent results for surfaces embedded in
R^3 with constant mean curvature\, such as curvature and radius estimates
for simply-connected surfaces embedded in R^3 with constant mean curvature
. Finally I will show applications of such estimates including a character
ization of the round sphere as the only simply-connected surface embedded
in R^3 with constant mean curvature and area estimates for compact surface
s embedded in a flat torus with constant mean curvature and finite genus.
This is joint work with Meeks.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alec Payne (Courant Institute)
DTSTART:20210316T185000Z
DTEND:20210316T200500Z
DTSTAMP:20260422T230721Z
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://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:20260422T230721Z
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://researchseminars.org/talk/UTK-GA-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debora Impera (Politecnico di Torino)
DTSTART:20210330T185000Z
DTEND:20210330T200500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/7
DESCRIPTION:Title: Quantitative index bounds for f-minimal hypersurfaces in the Euclid
ean space\nby Debora Impera (Politecnico di Torino) as part of UTK Geo
metric Analysis Seminar\n\n\nAbstract\nThe recent developments in the exis
tence theory for minimal immersions have motivated a renewed interest in s
tudying estimates on the Morse index of these objects. One possible way to
control instability is through topological invariants (in particular thro
ugh the first Betti number) of the minimal hypersurface. This was first in
vestigated by A. Ros for immersed minimal surfaces in $R^3$\, or a quotien
t 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 we will
first discuss how the method used by Savo can be generalized to study the
Morse index of self-shrinkers for the mean curvature flow and\, more gener
ally\, of weighted minimal hypersurfaces in a Euclidean space endowed with
a convex weight. In particular\, when the hypersurface is compact\, we wi
ll 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 bound is
in terms of the dimension of the space of weighted square integrable f-har
monic 1-forms. In particular\, in dimension 2\, the procedure gives an ind
ex estimate in terms of the genus of the surface. \n\nCombining this techn
ique with an adaptation to the weighted setting of well-known results by P
. Li and L. F. Tam\, we will also discuss how to obtain quantitative estim
ates on the Morse index of translators for the mean curvature flow with bo
unded norm of the second fundamental form via the number of ends of the hy
persurface.\n\nThis talk is based on joint works with Michele Rimoldi and
Alessandro Savo.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Halilaj (University of Ioannina)
DTSTART:20210406T185000Z
DTEND:20210406T200500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/8
DESCRIPTION:Title: Minimal maps\, MCF and isotopy problems\nby Andreas Halilaj (Un
iversity of Ioannina) as part of UTK Geometric Analysis Seminar\n\n\nAbstr
act\nI will discuss the mean curvature flow (MCF) of graphical submanifold
s generated\nby smooth maps between Riemannian manifolds. I will demonstra
te applications related to\nthe homotopy type of smooth maps between compa
ct manifolds. I will also show some rigidity\nresults concerning the Hopf
fibrations.\n
LOCATION:https://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:20260422T230721Z
UID:UTK-GA-seminar/9
DESCRIPTION:Title: An isometric flow of G2 structures\nby Panagiotis Gianniotis (N
ational and Kapodistrian University of Athens) as part of UTK Geometric An
alysis Seminar\n\n\nAbstract\nA G2 structure on a 7 manifold is a three fo
rm that determines\, in a nonlinear way\, a Riemannian metric. Our interes
t in such structures comes from the fact that when they are parallel with
respect to the associated Levi-Civita connection then the metric is automa
tically Ricci flat with holonomy contained in the Lie group G2. Parallel G
2 structures can be considered as the optimal such structures on a given s
mooth manifold\, however there may not exist since there are several obstr
uctions. Unfortunately\, despite the construction of many examples of para
llel G2 structures\, there is at the moment no conjecture regarding which
smooth 7 manifolds admit holonomy G2 metrics. On the other hand\, any Riem
annian metric on a manifold admitting G2 structures is induced by many -
isometric - G2 structures\, and a natural question is to find whether ther
e exists an optimal representative in a\ngiven isometric class. In this ta
lk I will discuss a geometric flow approach to this problem\, initially pr
oposed by Grigorian\, and present joint work with Dwivedi and Karigiannis
in which we develop the foundational theory for this flow.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Espinar (Cadiz University)
DTSTART:20210420T185000Z
DTEND:20210420T200500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/10
DESCRIPTION:Title: On non-compact free boundary minimal hypersurfaces in the Riemanni
an Schwarzschild spaces.\nby Jose Espinar (Cadiz University) as part o
f UTK Geometric Analysis Seminar\n\n\nAbstract\nWe will show that\, in con
trast with the 3-dimensional case\, the Morse index of a free boundary rot
ationally symmetric totally geodesic hypersurface of the nnn-dimensional R
iemannnian Schwarzschild space with respect to variations that are tangent
ial along the horizon is zero\, for $n\\geq 4$. Moreover\, we will show th
at there exist non-compact free boundary minimal hypersurfaces which are n
ot totally geodesic\, $n\\geq 8$\, with Morse index equal to zero. Also\,
for $n\\geq 4$\, there exist infinitely many non-compact free boundary min
imal hypersurfaces\, which are not congruent to each other\, with infinite
Morse index. Finally\, we will discuss the density at infinity of a free
boundary minimal hypersurface with respect to a minimal cone constructed o
ver 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 hypersu
rface and the area of the minimal hypersurface in the unit sphere. This lo
wer bound is optimal in the sense that only minimal cones achieve it.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Scharrer (University of Warwick)
DTSTART:20210427T185000Z
DTEND:20210427T200500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/11
DESCRIPTION:Title: Isoperimetric constrained Willmore tori\nby Christian Scharrer
(University of Warwick) as part of UTK Geometric Analysis Seminar\n\n\nAb
stract\nIn order to explain the bi-concave shape of red blood cells\, Helf
rich proposed the minimisation of a bending energy amongst closed surfaces
with given fixed area and volume. In the homogeneous case\, the Helfrich
functional reduces to the scaling invariant Willmore functional. Thus\, fo
r the minimisation\, the constraints on area and volume reduce to a single
constraint on the scaling invariant isoperimetric ratio. This talk is abo
ut two strict inequalities that lead to existence of isoperimetric constra
ined Willmore tori.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melanie Rupflin (University of Oxford)
DTSTART:20210921T185000Z
DTEND:20210921T200500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/12
DESCRIPTION:Title: Lojasiewicz inequalities near simple bubble trees\nby Melanie
Rupflin (University of Oxford) as part of UTK Geometric Analysis Seminar\n
\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Lambert (Technische Universitaet Darmstadt)
DTSTART:20210928T185000Z
DTEND:20210928T200500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/13
DESCRIPTION:Title: Lagrangian Mean Curvature Flow with Boundary\nby Ben Lambert (
Technische Universitaet Darmstadt) as part of UTK Geometric Analysis Semin
ar\n\n\nAbstract\nThe foundational result of Lagrangian Mean Curvature Flo
w (LMCF) is that in Calabi–Yau manifolds\, high codimensional mean curva
ture flow preserves the Lagrangian condition. A natural question is then t
o ask if this can this be generalised to manifolds with boundary. Equivale
ntly\, 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 re
sulting flow exhibits good behaviour in two model situations\, namely with
boundary on the Lawlor neck and Clifford Torus respectively. No prior kno
wledge of geometric flows will be assumed. This work is joint with Chris E
vans and Albert Wood.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Blatt (Paris-Lodron University Salzburg)
DTSTART:20211026T185000Z
DTEND:20211026T200500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/14
DESCRIPTION:Title: Analyticity of solutions to fractional partial differential equati
ons\nby Simon Blatt (Paris-Lodron University Salzburg) as part of UTK
Geometric Analysis Seminar\n\n\nAbstract\nWe will discuss an old topic in
the field of partial differential equations in a new context: The question
of analyticity of solutions to elliptic equations. While first results fo
r classical elliptic partial differential equations were already obtained
by Bernstein in 1904\, in the context of fractional and non-local equation
s only partial results or results for very special cases like the Hartree-
Fock equations and the Boltzmann equation are known up to now.\nAfter pres
enting some known results\, we will discuss our recent findings for so-cal
led knot energies and general semi-linear integro-differential equations.
The main ingredients in the proof of these results are Cauchy's method of
majorants and a new estimate for the long range interactions of these equa
tions. Partly joint with Nicole Vorderobermeier.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Magdalena Rodriguez (Universidad de Granada)
DTSTART:20211109T195000Z
DTEND:20211109T210500Z
DTSTAMP:20260422T230721Z
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 Ge
ometric Analysis Seminar\n\n\nAbstract\nAbstract: The theory of constant m
ean curvature $H>0$ surfaces ($H$-surfaces) in $\\mathbb{H}^2\\times\\math
bb{R}$ became very active after the seminal work by Abresch and Rosenberg
where they described a Hopf-type holomorphic quadratic differential on any
such surface and classified the rotational $H$-spheres. The critical valu
e for $H$ in $\\mathbb{H}^2\\times\\mathbb{R}$ is $\\frac 12$\, in the sen
se that there exist compact examples only when $H>\\frac 12$ and entire gr
aphs (i.e. graphs defined on the whole $\\mathbb{H}^2$) if $H\\leq\\frac 1
2$. When $H>\\frac 12$\, the geometric behaviour of the H-surfaces in $\\m
athbb{H}^2\\times\\mathbb{R}$ is analogous\, in some sense\, to the surfac
es of positive constant mean curvature in $\\mathbb{R}^3$. In this talk
we will prove that a properly embedded $H$-surface in $\\mathbb{H}^2\\time
s\\mathbb{R}$ with $0The mean curvature flow in null hypersurfaces and the detection of
MOTS\nby Julian Scheuer (Cardiff University) as part of UTK Geometric
Analysis Seminar\n\n\nAbstract\nThis talk is based on joint work with Hen
ri Roesch. We discuss the mean curvature flow in 3-dimensional null hypers
urfaces. In a spacetime a hypersurface is called null\, if its induced met
ric is degenerate. The speed of the mean curvature flow of spacelike surfa
ces in a null hypersurface is the projection of the codimension-two mean c
urvature vector onto the null hypersurface. Under fairly mild conditions w
e obtain that for an outer un-trapped initial surface\, a condition which
resembles the mean-convexity of a surface in Euclidean space\, the mean cu
rvature flow exists for all times and converges smoothly to a marginally o
uter trapped surface (MOTS). As an application we obtain the existence of
a smooth local foliation of the past of an outermost MOTS.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhongshan An (University of Connecticut)
DTSTART:20210907T185000Z
DTEND:20210907T200500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/18
DESCRIPTION:Title: Static vacuum extensions of Bartnik boundary data near flat domain
s\nby Zhongshan An (University of Connecticut) as part of UTK Geometri
c Analysis Seminar\n\n\nAbstract\nThe Bartnik boundary data of a Riemannia
n manifold with nonempty boundary consists of the induced metric and extri
nsic mean curvature of the boundary manifold. Existence of static vacuum R
iemannian metrics with prescribed Bartnik data is one of the most fundamen
tal problems in Riemannian geometry related to general relativity. It is a
lso a very interesting problem on the global solvability of a natural geom
etric boundary value problem. In this talk I will first discuss the basic
properties of static vacuum metrics and their boundary geometry. Then I wi
ll present some recent progress towards the existence problem based on a j
oint work with Lan-Hsuan Huang.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Schulze (University of Warwick)
DTSTART:20211130T195000Z
DTEND:20211130T210500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/19
DESCRIPTION:Title: Mean curvature flow with generic initial data\nby Felix Schulz
e (University of Warwick) as part of UTK Geometric Analysis Seminar\n\n\nA
bstract\nMean curvature flow is the gradient flow of the area functional a
nd constitutes a natural geometric heat equation on the space of hypersurf
aces 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 t
o approach several fundamental conjectures in geometry. The obstacle for t
hese applications is that the flow develops singularities\, which one in g
eneral might not be able to classify completely. Nevertheless\, a well-kno
wn 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 spheres a
nd cylinders are the only linearly stable singularity models. As a second
step toward Huisken's conjecture we show that mean curvature flow of gener
ic initial closed surfaces in R^3 avoids asymptotically conical and non-sp
herical compact singularities. The main technical ingredient is a long-tim
e existence and uniqueness result for ancient mean curvature flows that li
e on one side of asymptotically conical or compact self-similarly shrinkin
g solutions. This is joint work with Otis Chodosh\, Kyeongsu Choi and Chri
stos Mantoulidis.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ao Sun (University of Chicago)
DTSTART:20220301T195000Z
DTEND:20220301T210500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/20
DESCRIPTION:Title: Existence of minimal hypersurfaces with arbitrarily large area
\nby Ao Sun (University of Chicago) as part of UTK Geometric Analysis Semi
nar\n\n\nAbstract\nI will present an approach to find minimal hypersurface
s with arbitrarily large area in a closed manifold with dimension between
3 and 7. The method is based on the novel Almgren-Pitts min-max theory\,
and its further development by Marques-Neves\, Song and Zhou. Among the ap
plications\, we can show that there exist minimal hypersurfaces with arbit
rarily large area in an analytic manifold. In the case where this approach
does not work\, it is surprising that the space of minimal hypersurfaces
has a Cantor set fractal structure. This is joint work with James Stevens
(UChicago).\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Saez (Pontificia Universidad Católica de Chile)
DTSTART:20220308T195000Z
DTEND:20220308T210500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/21
DESCRIPTION:Title: Uniqueness of entire graphs evolving by mean curvature flow\nb
y Mariel Saez (Pontificia Universidad Católica de Chile) as part of UTK G
eometric Analysis Seminar\n\n\nAbstract\nIn this talk I will discuss the u
niqueness of graphical mean curvature flow. We consider as initial conditi
ons graphs of locally Lipschitz functions and prove that in the one dimens
ional case solutions are unique without any further assumptions. This resu
lt is then generalized for rotationally symmetric solutions. In the genera
l n- dimensional case\, we prove uniqueness under additional conditions: w
e require a uniform lower bound on the second fundamental form and the hei
ght function. The latter result extends to initial conditions that are pro
per graphs over subdomains of $\\mathbb R^n$. (Joint with P. Daskalopoulos
)\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Lai (Stanford University)
DTSTART:20220503T185000Z
DTEND:20220503T200500Z
DTSTAMP:20260422T230721Z
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\nAbstr
act\nFor any 3D steady gradient Ricci soliton\, if it is asymptotic to a r
ay we prove that it must be isometric to the Bryant soliton. Otherwise\, i
t is asymptotic to a sector and called a flying wing. We show that all fly
ing wings are O(2)-symmetric. Hence\, all 3D steady gradient Ricci soliton
s are O(2)-symmetric.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Mäder-Baumdicker (Technische Universität Darmstadt)
DTSTART:20220426T185000Z
DTEND:20220426T200500Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/23
DESCRIPTION:Title: The area preserving curve shortening flow in a free boundary setti
ng\nby Elena Mäder-Baumdicker (Technische Universität Darmstadt) as
part of UTK Geometric Analysis Seminar\n\n\nAbstract\nA convex\, simple cl
osed plane curve moving by the area preserving curve shortening flow (APCS
F) converges smoothly to a circle with the same enclosed area as the initi
al curve (Gage 1986). Note that the circle is the solution of the isoperim
etric problem in the Euclidean plane. Corresponding to the relative (outer
) isoperimetric problem we present results concerning the APCSF with Neuma
nn free boundary conditions outside of a convex domain. Under certain cond
itions on the initial curve the flow does not develop a singularity and su
bconverges smoothly to an arc of a circle sitting outside of the given con
vex domain and enclosing the same area as the initial curve. On the other
hand\, there are many examples of convex initial curves developing a singu
larity in finite time. In all these cases\, the singularity is of type II\
, and we conjecture that some curves developing a singularity stay embedde
d under the flow. In general\, we will point out similarities and differen
ces of the APCSF to the well-known curve shortening flow.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keaton Naff (MIT)
DTSTART:20220419T160000Z
DTEND:20220419T170000Z
DTSTAMP:20260422T230721Z
UID:UTK-GA-seminar/24
DESCRIPTION:Title: Immersed mean convex mean curvature flows with noncollapsed singul
arities\nby Keaton Naff (MIT) as part of UTK Geometric Analysis Semina
r\n\n\nAbstract\nIn the mean curvature flow of hypersurfaces\, noncollapsi
ng has proven to be a powerful and useful assumption when studying singula
rities and high curvature regions. In particular\, the assumption of nonco
llapsing has been used to prove a wide range of local a priori estimates\,
and has led to classification results for certain classes of singularity
models. Less is known for immersed mean-convex flows. In this talk\, I wou
ld like to survey recent results and discuss outstanding conjectures for i
mmersed mean-convex flows that begin to bridge the gap between the embedde
d and immersed mean-convex settings. The talk is based on joint work with
S. Brendle and ongoing work with S. Lynch.\n
LOCATION:https://researchseminars.org/talk/UTK-GA-seminar/24/
END:VEVENT
END:VCALENDAR