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BEGIN:VEVENT
SUMMARY:Camillo Brena (IAS)
DTSTART:20251113T130000Z
DTEND:20251113T143000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/1
DESCRIPTION:Title: Regularity for stationary varifolds\nby Camillo Brena (IA
S) as part of SISSA's Analysis seminars\n\nLecture held in 133.\n\nAbstrac
t\nStationary varifolds generalize minimal surfaces and can exhibit singul
arities. The most general regularity theorem in this context is the celebr
ated Allard's Regularity Theorem\, which asserts that the set of singular
points has empty interior. However\, it is believed that the set of singul
ar points should have codimension (at least) one. Despite more than 50 yea
rs having passed since Allard's breakthrough\, stronger results have remai
ned elusive. In this talk\, after a brief discussion about the regularity
theory for stationary varifolds\, I will discuss the principle of unique c
ontinuation and the topic of rectifiability\, both of which are linked to
understanding the structure of singularities. This discussion is based on
joint works with Stefano Decio\, Camillo De Lellis\, and Federico Francesc
hini.\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jules Pitcho (GSSI)
DTSTART:20251118T130000Z
DTEND:20251118T143000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/2
DESCRIPTION:Title: Non-uniqueness and recovery of uniqueness for the transport e
quation\nby Jules Pitcho (GSSI) as part of SISSA's Analysis seminars\n
\nLecture held in 133.\n\nAbstract\nI will discuss recent non-uniqueness r
esults for the transport equation and in the specific case of vector field
s singular at the initial time\, I will explain how uniqueness can be reco
vered\, both at the Eulerian and Lagrangian level.\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi De Rosa (GSSI)
DTSTART:20251210T130000Z
DTEND:20251210T143000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/3
DESCRIPTION:Title: On the Dissipation Measure in Turbulent Flows\nby Luigi D
e Rosa (GSSI) as part of SISSA's Analysis seminars\n\nLecture held in 133.
\n\nAbstract\nThe persistence of kinetic energy dissipation in the invisci
d limit is known as "anomalous dissipation" and it is central to our curre
nt understanding of turbulent flows. This results in a non-trivial finite
measure quantifying the kinetic energy loss\, the "Dissipation Measure". T
he geometric and analytic structures that such measure can sustain remain
poorly understood. It will be shown how\, in any space dimension\, quant
itative bounds on the Hausdorff dimension of the dissipation can be obtain
ed by leveraging on the regularity of the solution. Although there are go
od reasons to believe in their sharpness in the ideal (i.e. with no viscos
ity) setting\, for physically realizable weak solutions the problem is ext
remely different if settled in dimension two or three. Indeed\, for two-di
mensional fluids the results can be pushed much more\, with almost no assu
mption on the weak solutions. This is due to the "inverse cascade" induced
by the higher order formally conserved quantities. We will present the ph
ysical background\, explain the main ideas behind the proofs\, discuss the
sharpness of the results and how they fit in the mathematical literature
.\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Pasqualotto (UC San Diego)
DTSTART:20251218T100000Z
DTEND:20251218T113000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/4
DESCRIPTION:Title: From instability to singularity formation in incompressible f
luids\nby Federico Pasqualotto (UC San Diego) as part of SISSA's Analy
sis seminars\n\nLecture held in 133.\n\nAbstract\nIn this talk\, I will fi
rst review the singularity formation problem in incompressible fluid dynam
ics\, describing how particle transport poses the main challenge in constr
ucting blow-up solutions for the incompressible 3d Euler equations. I will
then outline a new mechanism that allows us to overcome the effects of pa
rticle transport\, leveraging the instability seen in the classical Taylor
--Couette experiment. Using this mechanism\, we construct the first swirl-
driven singularity for the incompressible Euler equations in R^3. This is
joint work with Tarek Elgindi (Duke University).\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Inversi (University of Basel)
DTSTART:20260128T130000Z
DTEND:20260128T143000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/5
DESCRIPTION:Title: Some dissipative properties of Euler solutions\nby Marco
Inversi (University of Basel) as part of SISSA's Analysis seminars\n\nLect
ure held in 133.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Renzi (SNS)
DTSTART:20260114T130000Z
DTEND:20260114T143000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/6
DESCRIPTION:Title: The superposition principle for local 1-dimensional currents<
/a>\nby Federico Renzi (SNS) as part of SISSA's Analysis seminars\n\nLectu
re held in 133.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Van De Moortel (Rutgers University)
DTSTART:20260226T130000Z
DTEND:20260226T143000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/7
DESCRIPTION:Title: The Klein-Gordon equation on a black hole\nby Maxime Van
De Moortel (Rutgers University) as part of SISSA's Analysis seminars\n\nLe
cture held in 133.\n\nAbstract\nThe (linear) Klein-Gordon equation on a Sc
hwarzschild background combines the most fundamental model for massive mat
ter evolving on the simplest type of black hole. Yet\, unlike massless fie
lds (the wave equation) which are now well-understood on a black hole\, th
e large-time asymptotics of Klein-Gordon solutions have long remained elus
ive.\nPhysically\, the Klein-Gordon dynamics presents a geometric obstruct
ion: the stable trapping of massive particles\, which was conjectured to p
revent decay. In this talk\, we disprove this expectation and establish th
at solutions with localized initial data actually decay polynomially in ti
me. We will highlight the proof's most surprising ingredient: the use of a
nalytic number theory--specifically\, bounds on exponential sums similar t
o the Riemann zeta function.\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Dolce (EPFL)
DTSTART:20260305T130000Z
DTEND:20260305T143000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/8
DESCRIPTION:Title: Instability of the 2D Taylor-Green vortex\nby Michele Dol
ce (EPFL) as part of SISSA's Analysis seminars\n\nLecture held in 133.\n\n
Abstract\nThe 2D Taylor-Green (TG) vortex is the prototypical example of a
n Euler steady state on T^2 possessing truly two-dimensional features\, na
mely elliptic and hyperbolic stagnation points. Its streamfunction\, sin(x
)sin(y)\, lives on the second Fourier shell\, making it susceptible to lar
ge-scale destabilizing mechanisms. Despite the apparent simplicity of the
steady state\, a proof of its spectral instability has long remained elusi
ve\, and was only recently observed numerically. To solve this problem\, I
will introduce a new criterion to detect unstable eigenvalues for a wide
class of linear Hamiltonian operators. We apply this to prove the stabilit
y of the TG vortex with respect to odd perturbations. In the subspace of f
unctions even in both variables\, we combine our criterion with a rigorous
computer-assisted argument to locate two unstable eigenvalues. This fully
characterizes the unstable spectrum of the TG vortex and implies nonlinea
r instability in velocity.\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Edtmair (ETH Zurich - Institute for Theoretical Studies)
DTSTART:20260416T120000Z
DTEND:20260416T133000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/9
DESCRIPTION:Title: On the topological invariance of helicity\nby Oliver Edtm
air (ETH Zurich - Institute for Theoretical Studies) as part of SISSA's An
alysis seminars\n\nLecture held in 133.\n\nAbstract\nHelicity is an invari
ant of divergence free vector fields on a three-manifold. One of its funda
mental properties is invariance under volume preserving diffeomorphisms. A
rnold\, having derived an ergodic interpretation of helicity as an asympto
tic Hopf invariant\, asked whether helicity remains invariant under volume
preserving homeomorphisms\, and more generally\, whether it admits an ext
ension to topological volume preserving flows. In this talk\, I will prese
nt an affirmative answer to both questions for non-singular flows. The pro
of draws on recent advances in $C^0$ symplectic geometry\, in particular r
egarding the algebraic structure of the group of area preserving homeomorp
hisms\, which I will also survey. This is based on joint work with Sobhan
Seyfaddini.\n\nRoom 134\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bozhidar Velichkov (Università di Pisa)
DTSTART:20260310T130000Z
DTEND:20260310T143000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/10
DESCRIPTION:Title: On the structure of the two-phase free boundaries in dimensi
on two\nby Bozhidar Velichkov (Università di Pisa) as part of SISSA's
Analysis seminars\n\nLecture held in 133.\n\nAbstract\nThis talk is dedic
ated to the regularity and the fine structure of the free boundaries of th
e two-phase Bernoulli problem. I will start from the classical result of A
lt-Caffarelli-Friedman and the Lipschitz continuity of the solutions\, the
n I will discuss the regularity of the free boundaries obtained via an epi
perimetric inequality. Finally\, I will present a recent result about the
number of contact points between the positive and the negative phases.\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Massimo Sorella (Imperial College)
DTSTART:20260410T090000Z
DTEND:20260410T103000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/11
DESCRIPTION:Title: Fast dynamo action on the 3-torus for pulsed-diffusions\
nby Massimo Sorella (Imperial College) as part of SISSA's Analysis seminar
s\n\nLecture held in 133.\n\nAbstract\nFor the passive vector equation\, t
he fast dynamo conjecture predicts exponential-in-time growth of the L^2 n
orm of the solution under a Lipschitz flow of a vector field\, at a rate i
ndependent of the resistivity. We establish this conjecture for the pulsed
diffusion model with a time-periodic stretch-fold-shear (SFS) vector fiel
d. Our approach uses anisotropic Banach spaces adapted to the dynamics of
the underlying flow to prove the existence of a discrete eigenvalue with p
ositive real part in this distributional setting.\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luciano Mari (University of Milan)
DTSTART:20260429T120000Z
DTEND:20260429T133000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/12
DESCRIPTION:Title: Prescribing the Lorentzian mean curvature of a spacelike hyp
ersurface\, and the Born-Infeld model\nby Luciano Mari (University of
Milan) as part of SISSA's Analysis seminars\n\nLecture held in 133.\n\nAbs
tract\nThe talk aims to discuss the existence and regularity problem for s
pacelike hypersurfaces $M$ in Lorentzian manifolds whose mean curvature is
a prescribed\, possibly singular distribution. When considering ambient M
inkowski space\, this leads to study the following Dirichlet problem for t
he function that (locally) describes $M$ as a graph\, which we call $(\\ma
thcal{BI})$:\n \n\\[\n \\left\\{ \\begin{array}{ll}\n -{\\rm div} \\lef
t( \\frac{Du}{\\sqrt{1-|Du|^2}}\\right) = \\rho & \\quad \\text{in a domai
n } \\\, \\Omega \\Subset \\R^n\, \\\\[0.5cm]\n u = \\phi & \\quad \\tex
t{on } \\\, \\partial \\Omega\, \n \\end{array}\n \\right.\n\\]\n\nfor
a given measure $\\rho$ (the prescribed mean curvature) and boundary data
$\\phi$. Problem $(\\mathcal{BI})$ also appears in Born-Infeld's theory o
f electrostatics\, according to which $u$ describes the electric potential
generated by the charge $\\rho$. Even though $(\\mathcal{BI})$ is formall
y the Euler-Lagrange equation of a nice convex functional $I_\\rho$\, the
lack of smoothness of $I_\\rho$ where $|Du|=1$ (i.e. where the graph of $u
$ becomes lighlike) may prevent the unique variational minimizer $u_\\rho$
to solve $(\\mathcal{BI})$. As we shall see\, this possibility actually o
ccurs. We shall describe both existence and non-existence results helping
to guess the possible sharp thresholds on $\\rho$. A chief difficulty come
s from the possible presence of ``light segments" in the graph of $u_\\rho
$\, a fact that we will investigate in detail. Various open problems and r
esearch directions will be discussed.\n\nThe talk is based on joint works
with J. Byeon\, N. Ikoma\, A. Malchiodi and L. Maniscalco\, available at a
rXiv:2112.11283 and arXiv:2512.17670.\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Averil Aussedat (University of Pisa)
DTSTART:20260514T120000Z
DTEND:20260514T133000Z
DTSTAMP:20260422T225723Z
UID:SissaAnalysisSeminar/13
DESCRIPTION:by Averil Aussedat (University of Pisa) as part of SISSA's Ana
lysis seminars\n\nLecture held in 133.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/13/
END:VEVENT
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