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BEGIN:VEVENT
SUMMARY:Alberto Roncoroni
DTSTART;VALUE=DATE-TIME:20210716T020000Z
DTEND;VALUE=DATE-TIME:20210716T030000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130010Z
UID:2ndGAF/1
DESCRIPTION:Title: Q
uantitative Studies of Alexadrov's Theorem\nby Alberto Roncoroni as pa
rt of The 2nd Geometric Analysis Festival\n\n\nAbstract\nAlexandrov's soap
bubbles Theorem states that the spheres are the only closed\, connected\,
and embedded hypersurfaces with constant mean curvature in the Euclidean
space. The theorem holds true also in the so-called space forms and for m
ore general functions of the principal curvatures. \n\nIn the talk we will
present the classical result by Alexandrov together with two proofs: the
original one based on the\, nowadays called\, method of moving planes and
another one based on integral inequalities. Then we will show a quantitati
ve stability result for hypersurfaces with almost constant mean curvature.
In particular\, we will consider hypersurfaces\, satisfying the so-called
uniform touching ball condition\, whose mean curvature is close to a cons
tant and we will quantitatively describe\, in terms of the oscillation of
the mean curvature\, the closedness to a single ball.\n\nThis is based on
a joint work with G. Ciraolo and L. Vezzoni.\n
LOCATION:https://researchseminars.org/talk/2ndGAF/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Rupp
DTSTART;VALUE=DATE-TIME:20210716T010000Z
DTEND;VALUE=DATE-TIME:20210716T020000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130010Z
UID:2ndGAF/3
DESCRIPTION:Title: A
Li-Yau inequality for the 1-dimensional Willmore energy\nby Fabian Ru
pp as part of The 2nd Geometric Analysis Festival\n\n\nAbstract\nBy the cl
assical Li--Yau inequality\, an immersion of a closed surface in $\\mathbb
{R}^n$ with Willmore energy below $8\\pi$ has to be embedded. We discuss a
nalogous results for curves in $\\mathbb{R}^2$\, involving Euler’s elast
ic energy and other possible curvature functionals. Additionally\, we prov
ide applications to associated gradient flows. This is based on a joint wo
rk with Marius M\\"uller (Albert-Ludwigs-Universit\\"at Freiburg).\n
LOCATION:https://researchseminars.org/talk/2ndGAF/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Madnick
DTSTART;VALUE=DATE-TIME:20210715T230000Z
DTEND;VALUE=DATE-TIME:20210716T000000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130010Z
UID:2ndGAF/5
DESCRIPTION:Title: T
he Jacobi Spectrum of Null-Torsion Holomorphic Curves in the 6-Sphere\
nby Jesse Madnick as part of The 2nd Geometric Analysis Festival\n\n\nAbst
ract\nMinimal surfaces are area-minimizing to first order\, but not necess
arily to second-order. The extent to which a minimal surface is (or isn't
) area-minimizing to second-order is encoded by its Jacobi operator. Howev
er\, for a given minimal surface\, computing the spectrum of the Jacobi op
erator — i.e.\, the eigenvalues and their multiplicities — is generall
y a non-trivial task. \n\\indent In this talk\, we will discuss a class of
minimal surfaces in the round 6-sphere known as “null-torsion holomorph
ic curves.” These surfaces are of interest to $G_2$ geometry\, and exis
t in abundance. Indeed\, by a remarkable theorem of Bryant\, extended by
Rowland\, every closed Riemann surface may be conformally embedded as a nu
ll-torsion holomorphic curve in $S^6$. \n\\indent For null-torsion holomor
phic curves of low genus\, we will compute the multiplicity of the first J
acobi eigenvalue. Moreover\, for all genera\, we will give a simple lower
bound for the nullity (the multiplicity of the zero eigenspace) in terms
of the area and genus. We expect that these results will have implication
s for the deformation theory of asymptotically conical associative 3-folds
in euclidean $R^7$.\n
LOCATION:https://researchseminars.org/talk/2ndGAF/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Min Chen
DTSTART;VALUE=DATE-TIME:20210716T000000Z
DTEND;VALUE=DATE-TIME:20210716T010000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130010Z
UID:2ndGAF/7
DESCRIPTION:Title: A
lexandrov-Fenchel type inequalities in the sphere\nby Min Chen as part
of The 2nd Geometric Analysis Festival\n\n\nAbstract\nIn this paper\, we
attempt to use two types of flows to study the relations between quermassi
ntegrals $\\mathcal{A}_k$\, which correspond to the Alexandrov-Fenchel ine
qualities for closed convex $C^2$-hypersurfaces in $\\mathbb{S}_+^{n+1}.$\
n\nPlease\, submit your questions to speakers at https://forms.gle/F8z5Ljf
NNwt3DD4i8\n
LOCATION:https://researchseminars.org/talk/2ndGAF/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Demetre Kazaras
DTSTART;VALUE=DATE-TIME:20210715T150000Z
DTEND;VALUE=DATE-TIME:20210715T200000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130010Z
UID:2ndGAF/8
DESCRIPTION:Title: M
ass of asymptotically Euclidean manifolds using spinors and 1-forms\nb
y Demetre Kazaras as part of The 2nd Geometric Analysis Festival\n\n\nAbst
ract\nThe total mass of an asymptotically Euclidean manifold is an invaria
nt from mathematical General Relativity which has fascinated geometers for
many decades. In these lectures\, we will discus the celebrated Positive
Mass Theorem\, first describing in some detail the proof by Witten which u
ses spinors. I will not assume any prior knowledge of spinors. We will the
n focus on a contemporary approach using 1-forms which arise as the differ
ential of solutions to a certain "spacetime harmonic" equation motivated b
y recent work by Daniel Stern. This second part contains work by myself\,
Hugh Bray\, Sven Hirsch\, Marcus Khuri\, and Yiyue Zhang.\n
LOCATION:https://researchseminars.org/talk/2ndGAF/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davi Maximo
DTSTART;VALUE=DATE-TIME:20210716T060000Z
DTEND;VALUE=DATE-TIME:20210716T080000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130010Z
UID:2ndGAF/13
DESCRIPTION:Title:
On the geometry and topology of 3-manifolds with Positive Scalar Curvature
\nby Davi Maximo as part of The 2nd Geometric Analysis Festival\n\n\nA
bstract\nIn these talks\, we will discuss classical and recent results abo
ut 3-manifolds with positive scalar curvature. We will describe their topo
logy and show how they can be (singularly) foliated by surfaces of control
led area\, diameter and genus.\n
LOCATION:https://researchseminars.org/talk/2ndGAF/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ao Sun
DTSTART;VALUE=DATE-TIME:20210715T200000Z
DTEND;VALUE=DATE-TIME:20210715T230000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130010Z
UID:2ndGAF/16
DESCRIPTION:Title:
Uniqueness problem in geometric analysis and Lojasiewicz inequality\nb
y Ao Sun as part of The 2nd Geometric Analysis Festival\n\n\nAbstract\nLoj
asiewicz inequality is an inequality in real algebraic geometry. It was fi
rst discovered by Leon Simon that Lojasiewicz inequality can be used to pr
ove uniqueness of critical points in the problem of calculus of variation.
In these lectures I will first introduce the Lojasiewicz inequality\; the
n I will discuss the infinite dimensional Lojasiewicz inequality proved by
Leon Simon in the setting of calculus of variations\; then I will discuss
some applications of Lojasiewicz inequality to prove the uniqueness of so
me geometric object\; finally\, I will discuss joint work with Jonathan Zh
u on proving Lojasiewicz inequality finding an explicit power of the Lojas
iewicz inequality near special self-shrinkers of mean curvature flow.\n
LOCATION:https://researchseminars.org/talk/2ndGAF/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otis Chodosh
DTSTART;VALUE=DATE-TIME:20210716T030000Z
DTEND;VALUE=DATE-TIME:20210716T060000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130010Z
UID:2ndGAF/19
DESCRIPTION:Title:
Some new generic regularity results for minimal surfaces and mean curvatur
e flows\nby Otis Chodosh as part of The 2nd Geometric Analysis Festiva
l\n\n\nAbstract\nMinimal surfaces are critical points of the area function
al while mean curvature flow is the gradient flow of the area functional.
Singularities arise in both problems\, and a fundamental issue in geometri
c analysis is to understand such singularities. I will present some recent
work concerning the generic behavior of both problems\, in particular I w
ill discuss the papers (with K. Choi\, C. Mantoulidis\, F. Schulze) arXiv:
2003.14344\, arXiv:2102.11978 as well as (with Y. Liokumovich\, L. Spolao
r) arXiv:2007.11560.\n
LOCATION:https://researchseminars.org/talk/2ndGAF/19/
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