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BEGIN:VEVENT
SUMMARY:Tere M-Seara (UPC\, Barcelona)
DTSTART;VALUE=DATE-TIME:20200630T123000Z
DTEND;VALUE=DATE-TIME:20200630T133000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/1
DESCRIPTION:Title: Mechanism of instability in Hamiltonian Systems: Skipping
along a normally hyperbolic invariant manifold\nby Tere M-Seara (UPC\,
Barcelona) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLectur
e held in Via Microsoft Teams.\n\nAbstract\nWe describe a recent method to
show instability in Hamiltonian systems. The mechanism works if some expl
icit and verifiable transversality conditions are satisfied. The hypothesi
s can be verified by just checking that some Melnikov type integrals have
non-degenerate zeros. This holds for Baire generic sets of perturbations i
n the C^r topology.\n\nThe method uses these hypotheses to conclude the ex
istence of orbits\, in near integrable Hamiltonian Systems\, which change
the action coordinate by a quantity independent of the size of the perturb
ation.\n\nnstructions: the Seminar will be held in streaming\, as a videoc
onference on-line\, via Microsoft Teams.\nLink: https://teams.microsoft.co
m/l/meetup-join/19%3a851c456a7d9d47caae6f7d5534a315f3%40thread.tacv2/15928
45825482?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22
%2c%22Oid%22%3a%229bfb10cf-6b03-47dc-906c-d23eb368824c%22%7d\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Devillanova (Politecnico di Bari)
DTSTART;VALUE=DATE-TIME:20201029T130000Z
DTEND;VALUE=DATE-TIME:20201029T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/2
DESCRIPTION:Title: Profile decomposition and applications\nby Giuseppe De
villanova (Politecnico di Bari) as part of Analysis Seminar @ Univ. Rome T
or Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nAbstract.
A brief survey on the evolution of concentration - com-\npactness theorems
in the last 30 years is given. Starting from the\npioneering results by P
-L Lions in [5] and M. Struwe in [8] for\nP.S. sequences and relative gene
ralizations to bounded sequences\nin [6]\, with their “wavelet based”
counterpart in [3] and [4] (see\n[2] for a comparison between the two appr
oaches in Lp spaces)\,\nthe research path has evolved till [7] where the r
esults are given\nin a more general context (uniformly convex Banach space
s). In\nthe spirit of the “compactness and contradiction” argument by
T.\nTao [9]\, some applications are provided in [1] to prove existence of\
ninfinitely many solutions to some elliptic equations.\nReferences\n[1] G.
Devillanova\, S. Solimini\, Infinitely many positive solutions to some no
n-\nsymmetric scalar field equations: the planar case. Calculus of Variati
ons and\nPartial Differential Equations 52 (2015)\, Issue 3-4\, 857-898.\n
[2] G. Devillanova\, S. Solimini\, Some Remarks on Profile Decomposition T
heo-\nrems. preprint.\n[3] P. G ́erard\, Description du d ́efaut de comp
acit ́e de l’injection de Sobolev.\nESAIM: Control\, Optimisation and C
alculus of Variations 3 (1998)\, 213-233.\n[4] S. Jaffard\, Analysis of th
e lack of compactness in the critical Sobolev embed-\ndings J. Funct. Anal
.\, 161 (1999)\, pp. 384–396.\n[5] P-L. Lions\, The concentration-compac
tness principle in the calculus of vari-\nations. The locally compact case
. Parts 1 and 2\, Annales de l’IHP\, Analyse\nnon-lin ́eaire\, I (1984)
\, 109-145 and 224-283.\n[6] S. Solimini\, A note on Compactness-type prop
erties with respect to Lorentz\nnorms of bounded subsets of a Sobolev spac
e. Ann. Inst. Henry Poincar ́e 12\, 3\n(1995)\, 319–337.\n[7] S. Solimi
ni\, K. Tintarev\, Concentration analysis in Banach spaces.\nCommunication
s\n in\n Contemporary\n Mathematics\n (2015)\,\n DOI:\n10.1142/S0219199715
500388.\n[8] M. Struwe\, A global compactness result for elliptic boundary
value problems\ninvolving limiting nonlinearities. Math. Z. 187 (1984)\,
pp. 511-517.\n[9] T. Tao\, Compactness and contradiction.\nhttps://terryta
o.files.wordpress.com/2011/06/blog-book.pdf\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudianor Alves (Universidade Federal de Campina Grande)
DTSTART;VALUE=DATE-TIME:20201112T130000Z
DTEND;VALUE=DATE-TIME:20201112T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/3
DESCRIPTION:Title: Super-critical Neumann problems on unbounded domains\n
by Claudianor Alves (Universidade Federal de Campina Grande) as part of An
alysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft T
eams.\n\nAbstract\nIn this paper\, by making use of a new variational pr
inciple\, we prove existence of nontrivial solutions for two different
types of semilinear problems with Neumann boundary conditions in unbo
unded domains. Namely\, we study elliptic equations and Hamiltonian syst
ems on the unbounded domain $\\Omega=\\R^{m}\\times
B_r$ where $B_r$ is a ball centered at the origin with radius $r$
in $\\mathbb{R}^{n}$. Our proofs con
sist of several new and novel ideas that can be used in broader contexts.
This is a joint work with Abbas Moameni that was accepted for publication
in Nonlinearity.\n\n** N.B.: this talk is part of the activity of the Ita
lian MIUR Excellence Department Project CUP E83C18000100006**\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Daneri (Gran Sasso Science Institute)
DTSTART;VALUE=DATE-TIME:20201119T130000Z
DTEND;VALUE=DATE-TIME:20201119T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/4
DESCRIPTION:Title: Symmetry breaking for local/nonlocal interaction functiona
ls\nby Sara Daneri (Gran Sasso Science Institute) as part of Analysis
Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n
\nAbstract\nIn this talk I will review some recent results obtained in col
laboration with E. Runa and A. Kerschbaum on the one-dimensionality of the
minimizers of a family of continuous local/nonlocal interaction functiona
ls in general dimension. Such functionals have a local term\, typically th
e perimeter or its Modica-Mortola approximation\, which penalizes interfac
es\, and a nonlocal term favouring oscillations which are high in frequenc
y and in amplitude. The competition between the two terms is expected by e
xperiments and simulations to give rise to periodic patterns at equilibriu
m. Functionals of this type are used to model pattern formation\, either i
n material science or in biology. The difficulty in proving the emergence
of such structures is due to the fact that the functionals are symmetric w
ith respect to permutation of coordinates\, while minimizers are not. We w
ill present new techniques and results showing that for two classes of fun
ctionals (used to model generalized anti-ferromagnetic systems\, respectiv
ely colloidal suspensions)\, both in sharp interface and in diffuse interf
ace models\, minimizers are one-dimensional and periodic\, in general dime
nsion. In the discrete setting such results had been previously obtained f
or a smaller set of functionals with a different approach by Giuliani and
Seiringer. \n** N.B.: this talk is part of the activity of the MIUR Excel
lence Department Project CUP E83C18000100006 **\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elsa Marchini (Politecnico di Milano)
DTSTART;VALUE=DATE-TIME:20201126T130000Z
DTEND;VALUE=DATE-TIME:20201126T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/5
DESCRIPTION:Title: Minimal time optimal control for the moon lander problem<
/a>\nby Elsa Marchini (Politecnico di Milano) as part of Analysis Seminar
@ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstra
ct\nWe study a variant of the classical safe landing optimal control probl
em in aerospace\, introduced by Miele in the Sixties\, where the target wa
s to land a spacecraft on the moon by minimizing the consumption of fuel.
Assuming that the spacecraft has a failure and that the thrust (representi
ng the control) can act in both vertical directions\, the new target becom
es to land safely by minimizing time\, no matter of what the consumption i
s. In dependence of the initial data (height\, velocity\, and fuel)\, we p
rove that the optimal control can be of four different kinds\, all being p
iecewise constant. Our analysis covers all possible situations\, including
the nonexistence of a safe landing strategy due to the lack of fuel or fo
r heights/velocities for which also a total braking is insufficient to sto
p the spacecraft.\n

\nTalk based on a joint work with Filippo Gazzola\n

\n** N.B.: this talk is part of the activity of the MIUR Excellence D
epartment Project CUP E83C18000100006 **\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Benedetti (Heidelberg University)
DTSTART;VALUE=DATE-TIME:20201210T130000Z
DTEND;VALUE=DATE-TIME:20201210T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/6
DESCRIPTION:Title: Strong magnetic fields on surfaces: trapped motions and fu
lly periodic systems\nby Gabriele Benedetti (Heidelberg University) as
part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via
Microsoft Teams.\n\nAbstract\nIt is a central problem in experimental phys
ics to design magnetic fields that trap charged particles in a region of s
pace. In this talk\, we show how to use the KAM theorem to trap particles
constrained on a surface if the magnetic field is strong and certain non-d
egenerate conditions on the field or on the curvature of the surface are s
atisfied. Using similar ideas we show that the motion of a particle in a s
trong magnetic field is periodic for every initial condition if and only i
f the field is constant and the surface has constant curvature. This is jo
int work with Luca Asselle.\n\nMS Teams Link for the streaming: \nhttps://
teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145dfae91372d186b1cd9%40
thread.tacv2/1606733297311?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-99
75-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88e4-99bf4cf68fe9%2
2%7d\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vitaly Moroz (Swansea University)
DTSTART;VALUE=DATE-TIME:20201210T130000Z
DTEND;VALUE=DATE-TIME:20201210T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/7
DESCRIPTION:Title: Asymptotic profiles of groundstates for a class of Choquar
d equations\nby Vitaly Moroz (Swansea University) as part of Analysis
Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n
\nAbstract\nWe study the asymptotic behaviour of groundstates for a class
of singularly perturbed Choquard type equations with a local repulsion ter
m. We identify seven different asymptotic regimes and provide a characteri
sation of the limit profiles of the groundstates when perturbation paramet
er is small. We also outline the behaviour of groundstates when perturbati
on is strong. This is a joint work with Zeng Liu (Suzhou\, China).\n\n**
NB **: *this talk is part of the activity of the MIUR Excellence Depar
tment Project CUP E83C18000100006*\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Muratori (Politecnico di Milano)
DTSTART;VALUE=DATE-TIME:20210114T130000Z
DTEND;VALUE=DATE-TIME:20210114T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/8
DESCRIPTION:Title: Nonlinear diffusion equations on noncompact manifolds and
relations with stochastic completeness\nby Matteo Muratori (Politecnic
o di Milano) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLectu
re held in Via Microsoft Teams.\n\nAbstract\nWe prove that the mass conser
vation property for the heat flow on a complete\, connected\, noncompact R
iemannian manifold $M$\, namely stochastic completeness\, is equivalent to
the uniqueness of nonnegative bounded solutions for a certain class of no
nlinear evolution equations. Such a connection was well known in the pure
linear case only\, i.e. for the heat equation itself. Here we consider equ
ations of the type of $u_t=\\Delta(\\phi(u))$\, where $\\phi$ is any nonne
gative\, concave\, increasing function\, $C^1$ away from the origin and sa
tisfying $ \\phi(0)=0 $. We provide optimal criteria for uniqueness/nonuni
queness of nonnegative\, bounded (distributional) solutions taking general
nonnegative\, bounded initial data $u_0$. In particular our results apply
to the fast diffusion equation $u_t=\\Delta(u^m)$ (where $m \\in (0\,1)$)
\, and they show that there is a large class of manifolds in which uniquen
ess actually fails. This is in sharp contrast\, for instance\, with the Eu
clidean case\, where existence and uniqueness hold for merely $L^1_{loc}$
initial data thanks to the theory developed by M.A. Herrero and M. Pierre
in the '80s. We will also address existence/nonexistence of nonnegative\,
nontrivial\, bounded solutions to a strictly related nonlinear elliptic eq
uation and\, if time allows\, some work in progress devoted to removing th
e concavity assumption. \n\n\nThe talk is based on joint projects with G.
Grillo\, K. Ishige and F. Punzo.\n\n**Note**: *This talk is part of t
he activity of the MIUR Excellence Department Project CUP E83C18000100006<
/i>\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandra Pluda (University of Pisa)
DTSTART;VALUE=DATE-TIME:20210121T130000Z
DTEND;VALUE=DATE-TIME:20210121T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/9
DESCRIPTION:Title: Motion by curvature of networks: analysis of singularities
and “restarting” theorems\nby Alessandra Pluda (University of Pis
a) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in
Via Microsoft Teams.\n\nAbstract\nA regular network is a finite union of
sufficiently smooth\ncurves whose end points meet in\ntriple junctions. I
will present the state-of-the-art of the problem of\nthe motion by curvatu
re of a regular network\nin the plane mainly focusing on singularity forma
tion. Then I will\ndiscuss the need of a “restarting”\ntheorem for net
works with multiple junctions of order bigger than three\nand I will give
an idea of a possible strategy to prove it.\nThis is a research in collabo
ration with Jorge Lira (University of\nFortaleza)\, Rafe Mazzeo (Stanford
University) and Mariel Saez (P.\nUniversidad Catolica de Chile).\n\nNote:
This talk is part of the activity of the MIUR Excellence Department Proje
ct MATH@TOV CUP E83C18000100006\n\nThe talk will be streamed via MS Teams:
\nhttps://teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145dfae91372d1
86b1cd9%40thread.tacv2/1610381100098?context=%7b%22Tid%22%3a%2224c5be2a-d7
64-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88e4-99bf
4cf68fe9%22%7d\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Valvo (University of Rome Tor Vergata)
DTSTART;VALUE=DATE-TIME:20210204T130000Z
DTEND;VALUE=DATE-TIME:20210204T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/10
DESCRIPTION:Title: Hamiltonian Control of Magnetic Field Lines: Computer Ass
isted Results Proving the Existence of KAM Barriers\nby Lorenzo Valvo
(University of Rome Tor Vergata) as part of Analysis Seminar @ Univ. Rome
Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nA control
theory for Hamiltonian systems\, based on KAM theory\, was introduced in
[Ciraolo\, 2004] and applied to a model of magnetic field in [Chandre\, 20
06]. By a combination of Frequency Analysis and of a rigorous (Computer As
sisted) KAM algorithm we show that in the phase space of the magnetic fiel
d\, due to the control term\, a set of invariant tori appears\, and it act
s as a transport barrier. Our analysis\, which is common (but often also l
imited) to celestial mechanics\, is very general and can be applied to qua
si-integrable Hamiltonian systems satisfying a few additional mild assumpt
ions.\n\nNote: This talk is part of the activity of the MIUR Excellence De
partment Project MATH@TOV CUP E83C18000100006\n\nThe talk will be streamed
via MS Teams:\nhttps://teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1
145dfae91372d186b1cd9%40thread.tacv2/1611256564820?context=%7b%22Tid%22%3a
%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-
4c35-88e4-99bf4cf68fe9%22%7d\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Martinazzi (Universita' di Padova)
DTSTART;VALUE=DATE-TIME:20210211T130000Z
DTEND;VALUE=DATE-TIME:20210211T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/11
DESCRIPTION:Title: Entire solutions to a prescribed curvature equation in R^
4 and the Nirenberg problem\nby Luca Martinazzi (Universita' di Padova
) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in
Via Microsoft Teams.\n\nAbstract\nSeveral existence and non-existence resu
lts for the Nirenberg problem of prescribing the Gauss curvature on a clos
ed surface are classically known. In higher dimension\, analog results hol
d with the Q-curvature replacing the Gauss curvature. In many cases a non-
existence result is associated with a blow-up phenomenon which leads to en
tire solutions of the Liouville equation $-\\Delta u = e^{2u}
$ in dimension 2 or higher-dimensional analogs. On the other hand\,
Borer\, Galimberti and Struwe studied a blow-up phenomenon which could lea
d to solutions to the equation\n$$-\\Delta u =(1-|x|^2)e^{2u}
in R^2$$ (1)\nor\n$$\\Delta^2 u =(1-|x|^2)e^{4u}
in R^4$$ (2)\nWhile non-existence results have been shown for (1) by Stru
we\, the question remained opened for (2). We recently gave a positive ans
wer with A. Hyder\, giving sharp conditions under which (2) admits solutio
ns with controlled behaviour at infinity\, hence answering an open questio
n by Struwe. More related open questions will be discussed.\n\n***N.B.**
*This talk is part of the activity of the MIUR Excellence Department Pr
oject CUP E83C18000100006*.\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacopo Bellazzini (Università di Pisa)
DTSTART;VALUE=DATE-TIME:20210225T130000Z
DTEND;VALUE=DATE-TIME:20210225T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/12
DESCRIPTION:Title: Ground state energy threshold and blow-up for NLS with co
mpeting nonlinearities\nby Jacopo Bellazzini (Università di Pisa) as
part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via M
icrosoft Teams.\n\nAbstract\nAim of the talk is to discuss qualitative pro
perties of the nonlinear Schr\\"odinger equation with combined nonlinearit
ies\, where the leading term is an intracritical focusing power-type nonli
nearity\, and the perturbation is given by a power-type defocusing one. F
ixed the mass of the problem\, we completely answer the question wether th
e ground state energy \, which is a threshold between global existence and
formation of singularities\, is achieved. As a byproduct of the variation
al characterization of the ground state energy\, we show the existence of
blowing-up solutions in finite time\, for any initial data with energy bel
ow the ground state energy threshold in case of cylindrical symmetry.\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weiwei Ao (Wuhan University)
DTSTART;VALUE=DATE-TIME:20210304T130000Z
DTEND;VALUE=DATE-TIME:20210304T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/13
DESCRIPTION:Title: Symmetry and symmetry breaking for the fractional Caffare
lli-Kohn-Nirenberg inequality\nby Weiwei Ao (Wuhan University) as part
of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Micro
soft Teams.\n\nAbstract\nWe first study the existence and nonexistence of
extremal solutions. We also show some results for the symmetry and symmetr
y breaking region for the minimizers. In order to get these result we refo
rmulate the fractional Caffarelli-Kohn-Nirenberg inequality in cylindrical
variables. We also get the non-degeneracy and uniqueness of minimizers in
the radial symmetry class. This is joint work with Azahara DelaTorre and
Maria del Mar Gonzalez.\n

\n**N.B.**: \;*this talk is part of
the activity of the MIUR Excellence Department Project CUP E83C1800010000
6*\n\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohameden Ahmedou (Universität Gießen)
DTSTART;VALUE=DATE-TIME:20210311T130000Z
DTEND;VALUE=DATE-TIME:20210311T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/14
DESCRIPTION:Title: New blow up phenomena for the Nirenberg's problem
on half spheres\nby Mohameden Ahmedou (Universität Gießen) as part
of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Micro
soft Teams.\n\nAbstract\nIn this talk I will report on a refined blow
up analysis of finite energy approximated solutions to the Nirenberg's
problem on half spheres. The later consists of prescribing under mi
nimal boundary conditions the scalar curvature to be a given function. I
n particular we give a precise location of blow up points and blow up ra
tes. Such an analysis shows that the blow up picture of the Nirenberg's
problem on half spheres is far more complicated that in the case of clos
ed spheres. Indeed besides the combination of interior and boundary blow
ups\, there are "non simples blow ups" for subcritical solutions ha
ving zero or nonzero weak limit. The formation of such non simple
blow ups is governed by a vortex problem\, unveiling an unexpected con
nection with Euler equations in fluid dynamic and mean fields type equ
ations in mathematical physics.\nThis is joint work with Mohamed Ben
Ayed (Sfax University).

\n**NB**:*This talk is part of the act
ivity of the MIUR Excellence Department Project MATH@TOV CUP E83C180001000
06*\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Santilli (University of Augsburg)
DTSTART;VALUE=DATE-TIME:20210318T130000Z
DTEND;VALUE=DATE-TIME:20210318T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/15
DESCRIPTION:Title: Regularity of distance functions from arbitrary clo
sed sets\nby Mario Santilli (University of Augsburg) as part of Analy
sis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Team
s.\n\nAbstract\nLet $ \\phi $ be a non-Euclidean uniformly convex norm. We
show that the gradient of an anisotropic $\\phi$-distance function $\\del
ta^\\phi_K $ from an arbitrary closed subset $K$ of $R^n$ satisfies a loca
l Lipschitz property on the complement of the $\\phi$-cut-locus of K\; nam
ely on $R^n \\setminus (K \\cup Cut^\\phi(K))$. Then we study the geometri
c properties of the set points where the distance function is second-order
pointwise differentiable. The available known results allow only to con
clude that the gradient of $ \\delta^\\phi_K $ is locally Lipschitz on t
he interior of $R^n \\setminus (K \\cup Cut^\\phi(K))$\, which might be em
pty even if K is a $C^{1\,\\alpha}$ hypersurface or K is
the complementary of a convex body with $C^1 $ boundary.\n

\n**NB
**:*This talk is part of the activity of the MIUR Excellence Departmen
t Project MATH@TOV CUP E83C18000100006*\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Caponigro (Università di Roma "Tor Vergata")
DTSTART;VALUE=DATE-TIME:20210325T130000Z
DTEND;VALUE=DATE-TIME:20210325T140000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/16
DESCRIPTION:Title: Geometric controllability of the bilinear Schrödinger eq
uation\nby Marco Caponigro (Università di Roma "Tor Vergata") as part
of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Micro
soft Teams.\n\nAbstract\nWe consider the bilinear Schrödinger equation wi
th a discrete-spectrum free Hamiltonian and we present a general method fo
r the approximate controllability based on Lie-algebraic control technique
s applied to suitable finite dimensional approximation of the Galerkin-typ
e. Under some regularity assumptions on the Hamiltonians and generic condi
tions on the controllability of the finite dimensional Galerkin approximat
ions we show exact controllability in projection on an arbitrary given num
ber of eigenstates.\n \n\n

\n**NB**:*This talk is part of the acti
vity of the MIUR Excellence Department Project MATH@TOV CUP E83C1800010000
6*\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Jeanjean (University of Bourgogne Franche-Comté)
DTSTART;VALUE=DATE-TIME:20210401T120000Z
DTEND;VALUE=DATE-TIME:20210401T130000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/17
DESCRIPTION:Title: Prescribed norm solutions of Schrödinger equations with
mixed power nonlinearities\nby Louis Jeanjean (University of Bourgogne
Franche-Comté) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nL
ecture held in Via Microsoft Teams.\n\nAbstract\nIn this talk\, I will pre
sent some recent results concerning the existence of prescribed norm solut
ions in problems where the associated nonlinearity is the sum of two power
s\, one which is mass-subcritical and one mass-supercritical. This leads t
o consider a constrained variational problem presenting a so-called convex
-concave geometry. The issues of existence\, multiplicity and orbital stab
ility of solutions will be addressed with a special emphasize on the cases
where the mass-supercritical power is Sobolev critical. \n

\nThe cont
ent of this talk is based on some jointed work with J. Jendrej\, T. T. Le
and N. Visciglia.\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberta Ghezzi (Università di Roma "Tor Vergata")
DTSTART;VALUE=DATE-TIME:20210415T120000Z
DTEND;VALUE=DATE-TIME:20210415T130000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/18
DESCRIPTION:Title: Regularization of chattering phenomena via bounded
variation controls\nby Roberta Ghezzi (Università di Roma "Tor Verga
ta") as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held
in Via Microsoft Teams.\n\nAbstract\nIn control theory\, chattering refers
to fast oscillations of controls\, such as accumulation of switchings in
finite time. This behavior is rather typical\, as it is the case for the c
lass of single-input control-affine problems\, and may be a serious obstac
le to convergence of standard numerical methods to detect optimal solution
s.\n\nWe propose a general regularization procedure\, consisting of penali
zing the cost functional with a total variation term. Under appropriate as
sumptions of small-time local controllability\, we prove that the optimal
cost and any optimal solution of the regularized problem converge respecti
vely to the optimal cost and an optimal solution of the initial problem. O
ur approach is valid for general classes of nonlinear optimal control prob
lems and applies to chattering phenomena appearing in constrained problems
as well as to switching systems. We also quantify the error in terms of t
he rate of convergence of the sequence of switching times\, for systems wi
th regular time-optimal map.\n\n**Note**: *This talk is part of the a
ctivity of the MIUR Excellence Department Project MATH@TOV CUP E83C1800010
0006*\n\n\n\n__________________________________________________________
______________________\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleks Jevnikar (Università di Udine)
DTSTART;VALUE=DATE-TIME:20210429T120000Z
DTEND;VALUE=DATE-TIME:20210429T130000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/19
DESCRIPTION:Title: Existence results for super-Liouville equations\nby A
leks Jevnikar (Università di Udine) as part of Analysis Seminar @ Univ. R
ome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nWe co
nsider super-Liouville equations on closed surfaces\, which have a variati
onal structure with a strongly-indefinite functional. We obtain the first
existence results by making use of min-max methods and bifurcation theory.
Joint project with Andrea Malchiodi and Ruijun Wu.\n

\n**NB**:*Th
is talk is part of the activity of the MIUR Excellence Department Project
MATH@TOV CUP E83C18000100006*\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margherita Nolasco (Università degli Studi dell'Aquila)
DTSTART;VALUE=DATE-TIME:20210506T120000Z
DTEND;VALUE=DATE-TIME:20210506T130000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/20
DESCRIPTION:Title: A variational principle for a charge-normalized solitary
wave for the Maxwell-Dirac equations\nby Margherita Nolasco (Univers
ità degli Studi dell'Aquila) as part of Analysis Seminar @ Univ. Rome Tor
Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nIn the conte
xt of classical field theory\, the solitary wave solutions of the Euler-La
grange equations describe "extended" particles. The existence of a charge-
normalized solitary wave solution of the coupled Maxwell-Dirac equations\,
describing the spin-1/2 charged particle (electron) with self-interaction
\, has been an open problem for a long time. The first existence result
of (not necessarily normalized) solitary waves was given by Esteban\,
Georgiev and Séré (Calc.Var. PDE (1996)) by using a variational method\
, as critical points of an energy functional which is strongly indefinite
and presents a lack of compactness. In this talk we discuss the existence
of a charge-normalized solitary wave obtained with a different variationa
l principle inspired by the min-max characterization of eigenvalues of Dir
ac operators. In particular\, we provide a variational characterization
of the normalized solitary wave as a minimizer of an effective "renormali
zed" energy functional.\n\nNote: This talk is part of the activity of the
MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006\n\nMicr
osoft Teams Link:\nhttps://teams.microsoft.com/l/meetup-join/19%3a7f273a2a
ff1145dfae91372d186b1cd9%40thread.tacv2/1619704157047?context=%7b%22Tid%22
%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e
4d-4c35-88e4-99bf4cf68fe9%22%7d\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Secchi (Università di Milano Bicocca)
DTSTART;VALUE=DATE-TIME:20210513T120000Z
DTEND;VALUE=DATE-TIME:20210513T130000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/21
DESCRIPTION:Title: Concentration phenomena for the Schroedinger-Poisson syst
em in R^2\nby Simone Secchi (Università di Milano Bicocca) as part of
Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsof
t Teams.\n\nAbstract\nWe present some recent results obtain in collaborati
on with Denis Bonheure (Bruxelles\, Belgium) and Silvia Cingolani (Bari\,
Italy) about a semiclassical analysis for a planar Schroedinger-Poisson sy
stem with potential functions.\n

\n**NB**:*This talk is par
t of the activity of the MIUR Excellence Department Project MATH@TOV CUP E
83C18000100006*\n\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Molica Bisci (Università degli Studi di Urbino)
DTSTART;VALUE=DATE-TIME:20210520T120000Z
DTEND;VALUE=DATE-TIME:20210520T130000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/22
DESCRIPTION:Title: Nonsmooth functionals in the Calculus of Variations\n
by Giovanni Molica Bisci (Università degli Studi di Urbino) as part of An
alysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft T
eams.\n\nAbstract\nIn the last years\, elliptic equations involving a nons
mooth term have attracted several outstanding mathematicians and the inter
est towards this kind of problems has grown more and more\, not only for t
heir intriguing analytical structure\, but also in view of their applicati
ons in a wide range of contexts. Motivated by this wide interest in\\end{a
bstract}\n\n the literature\, the leading purpose of this talk is to prese
nt some recent results on nonsmooth elliptic equations\, mainly related to
a wide class of functionals defined through multiple integrals of Calculu
s of Variations\; see\, among others\, the papers \\cite{arbo0\, arbo\, ar
bo2\, ArCar}. Applications to\nquasilinear boundary value problems will be
presented and some open problems briefly discussed\; see \\cite{MolicaBis
ci} and \\cite[Chapter 8]{MolicaBisciPucci} for related topics.\n\n\\bibit
em{arbo0} {\\sc D. Arcoya and L. Boccardo}\, \\emph{A min--max theorem for
multiple integrals of\nthe Calculus of Variations and applications}\, Ren
d. Mat. Acc. Lincei\, \\textbf{6} (1995)\n29--35.\n\n\\bibitem{arbo} {\\sc
D. Arcoya and L. Boccardo}\,\n{\\em Critical points for multiple integral
s of Calculus of Variations}\,\n{Arch. Rat. Mech. Anal.} {\\bf134} (1996)\
, 249--274.\n\n\\bibitem{arbo2} {\\sc D. Arcoya and L. Boccardo}\,\n{\\em
Some remarks on critical point theory for nondifferentiable functionals}\
,\n{Nonlinear Differential Equations and Applications NoDEA} {\\bf6} (1999
)\, 79--100.\n\n\n\\bibitem{ArCar} {\\sc D. Arcoya and J. Carmona}\,\n{\\
em A nondifferentiable extension of a theorem\nof Pucci and Serrin and app
lications}\,\n{J. Differential Equations } {\\bf235} (2007)\, 683--700.\n
\n\\bibitem{MolicaBisci} {\\sc G. Molica Bisci}\,\n\\textit{Local minima f
or some functionals in the Calculus of Variations}\,\nsubmitted for public
ation (2021)\, 1--53.\n\n\\bibitem{MolicaBisciPucci} {\\sc G. Molica Bisci
and P. Pucci}\,\nNonlinear Problems with Lack of Compactness\, De Gruyter
Series\nin Nonlinear Analysis and Applications \\textbf{36} (2021)\, i+vi
i\, 1--266.\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Costante Bellettini (University College London (UK))
DTSTART;VALUE=DATE-TIME:20210527T120000Z
DTEND;VALUE=DATE-TIME:20210527T130000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/23
DESCRIPTION:Title: Existence of hypersurfaces with prescribed-mean-curvature
\nby Costante Bellettini (University College London (UK)) as part of A
nalysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft
Teams.\n\nAbstract\nLet N be a compact Riemannian manifold of dimension 3
or higher\, and g a Lipschitz non-negative (or non-positive) function on N
. We prove that there exists a closed hypersurface M whose mean curvature
attains the values prescribed by g (joint work with Neshan Wickramasekera\
, Cambridge). Except possibly for a small singular set (of codimension 7 o
r higher)\, the hypersurface M is C^2 immersed and two-sided (it admits a
global unit normal)\; the scalar mean curvature at x is g(x) with respect
to a global choice of unit normal. More precisely\, the immersion is a qua
si-embedding\, namely the only non-embedded points are caused by tangentia
l self-intersections: around such a non-embedded point\, the local structu
re is given by two disks\, lying on one side of each other\, and intersect
ing tangentially (as in the case of two spherical caps touching at a point
). A special case of PMC (prescribed-mean-curvature) hypersurfaces is obta
ined when g is a constant\, in which the above result gives a CMC (constan
t-mean-curvature) hypersurface for any prescribed value of the mean curvat
ure.\nThe construction of M is carried out largely by means of PDE princip
les: (i) a minmax for an Allen--Cahn (or Modica-Mortola) energy\, involvin
g a parameter that\, when sent to 0\, leads to an interface from which the
desired PMC hypersurface is extracted\; (ii) quasi-linear elliptic PDE an
d geometric-measure-theory arguments\, to obtain regularity conclusions fo
r said interface\; (iii) parabolic semi-linear PDE (together with specific
features of the Allen-Cahn framework)\, to tackle cancellation phenomena
that can happen when sending to 0 the Allen-Cahn parameter.\n\nNote: This
talk is part of the activity of the MIUR Department of Excellence Project
MATH@TOV CUP E83C18000100006\n\nLink for the streaming (MS Teams):\nhttps:
//teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145dfae91372d186b1cd9%
40thread.tacv2/1621517541296?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-
9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88e4-99bf4cf68fe9
%22%7d\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Carlotta Chittaro (Université de Toulon)
DTSTART;VALUE=DATE-TIME:20210603T120000Z
DTEND;VALUE=DATE-TIME:20210603T130000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/24
DESCRIPTION:Title: Hamiltonian approach to sufficient optimality conditions<
/a>\nby Francesca Carlotta Chittaro (Université de Toulon) as part of Ana
lysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Te
ams.\n\nAbstract\nThe celebrated Pontryagin Maximum Principle (PMP) provid
es a (first order) necessary condition for the optimality of trajectories
of optimal control problems. In most cases\, however\, a trajectory satisf
ying PMP is not optimal. For these reasons\, additional optimality conditi
ons are required.\nIn this context\, Hamiltonian methods are quite effecti
ve in establishing sufficient optimality conditions. In this talk\, after
a brief review of the main ideas of the general method\, we will focus on
optimal control problems associated with control-affine dynamics and costs
of the form\n\\[\n\\int_0^T |u(t)| |\\varphi( X(t))| dt\n\\]\n\nCosts of
these form are very common in problems modeling neurobiology\, mechanics a
nd fuel-consumption.\n\nNote: This talk is part of the activity of the MIU
R Excellence Department Project MATH@TOV CUP E83C18000100006\n\nMS Teams L
ink:\nhttps://teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145dfae913
72d186b1cd9%40thread.tacv2/1622121687579?context=%7b%22Tid%22%3a%2224c5be2
a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88e4-
99bf4cf68fe9%22%7d\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Palmurella (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20210610T120000Z
DTEND;VALUE=DATE-TIME:20210610T130000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/25
DESCRIPTION:Title: The parametric approach to the Willmore flow\nby Fran
cesco Palmurella (ETH Zürich) as part of Analysis Seminar @ Univ. Rome To
r Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nWe introduc
e a parametric framework for the study of Willmore gradient flows which en
ables to consider a general class of weak\, energy-level solutions and ope
ns the possibility to study energy quantization and finite-time singularit
ies. In this first work we restrict to a small-energy regime and prove tha
t\, for small-energy weak immersions\, the Cauchy problem in this class ad
mits a unique solution. Joint work with T. Rivière.\n

\n \n
**NB**:*This talk is part of the activity of the MIUR Excellence Dep
artment Project MATH@TOV CUP E83C18000100006*\n \n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carina Geldhauser (University of Lund\, Sweden)
DTSTART;VALUE=DATE-TIME:20211019T140000Z
DTEND;VALUE=DATE-TIME:20211019T150000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/26
DESCRIPTION:Title: Discrete models for atmospheric turbulence\nby Carina
Geldhauser (University of Lund\, Sweden) as part of Analysis Seminar @ Un
iv. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\n
n this talk we discuss a family of discrete models for atmospheric turbule
nce\, often called point vortex models.\n\nPoint vortices provide an appro
ximation of solutions to generalized surface quasi-geostrophic models\, a
family of fractional PDEs which interpolate between 2D Euler equations and
the more irregular SQG equation.\n\nWe state some of it basic properties
and see how variational methods and tools from probability theory together
can help us to obtain more information about turbulence phenomena.\n\nThe
content of this talk is based on work in collaboration with Marco Romito
(University of Pisa)\, the presentation tries to avoid technicalities and
to be accessible to a mixed audience.\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rafael Soriano-Lopez (Universidad Carlos III Madrid)
DTSTART;VALUE=DATE-TIME:20211123T150000Z
DTEND;VALUE=DATE-TIME:20211123T160000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/27
DESCRIPTION:Title: Bound and ground states for an elliptic system with doubl
e criticality\nby Rafael Soriano-Lopez (Universidad Carlos III Madrid)
as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in V
ia Microsoft Teams.\n\nAbstract\nWe will consider a nonlinear elliptic sys
tem in $\\mathbb{R}^N$.\nThe interest of
this problem is based on the presence of critical power\nnonlinea
rities and a nonlinear coupling\, possibly critical\, as well as\
nHardy-type singular potentials. By means of variational methods\, we will
\nfocus on the existence of solutions. More precisely\, we shall derive ne
w\nresults on bound and ground states of the underlying energy f
unctional.\nFinally\, we extend our results to the special case o
f\n``Schrödinger-Korteweg-de Vries'' coupling type term.\n\nThis sem
inar is based on a couple of works in collaboration with\nEduard
o Colorado and Alejandro Ortega (UC3M).\n

\n \n **
NB**:*This talk is part of the activity of the MIUR Excellence Departm
ent Project MATH@TOV CUP E83C18000100006*\n \n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joost Hulshof (Vrije Universiteit Amsterdam)
DTSTART;VALUE=DATE-TIME:20211130T150000Z
DTEND;VALUE=DATE-TIME:20211130T160000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/28
DESCRIPTION:Title: Advancing front solutions in a degenerate reaction-diffus
ion system\nby Joost Hulshof (Vrije Universiteit Amsterdam) as part of
Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsof
t Teams.\n\nAbstract\nWe are interested in planar travelling wave solution
s of the system\n$$\nu_t=\\varepsilon\\\,\\nabla\\cdot u\\nabla u+uv\,\\qu
ad v_t=\\nabla\\cdot\\nabla u-uv\,\n$$\nwith nonnegative profiles $U$ an
d $V$ that satisfy $U(-\\infty)=V(+\\infty)=0$ and $U(\\infty)=V(-\\infty)
=1$.\nThe corresponding solutions have $u\\to1$ and $v\\to0$ as $t\\to\\in
fty$.\nAmong these traveling wave profiles there's one with $U\\equiv0$ on
the left and $U>0$ on the right.\nWe discuss its existence and an approac
h towards its stability analysis\, using a linearisation technique that we
developed for the Porous Medium Fischer equation $u_t=(uu_x)_x+u(1-u)$ (P
MF).\nThis is part of an ongoing research project with Michiel Bertsch\, L
orenzo Giacomelli and others\, suggested to us by Mayan Mimura.\nThe ultim
ate goal is to show that for small $\\varepsilon>0$ the front solutions ar
e stable in 1D but unstable in 2D.\nFor now it seems that the results for
(PMF) are nontrivial and new.\n

\n \n **NB**:*This
talk is part of the activity of the MIUR Excellence Department Project MAT
H@TOV CUP E83C18000100006*\n \n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tien Khai Nguyen (North Carolina State University)
DTSTART;VALUE=DATE-TIME:20210803T140000Z
DTEND;VALUE=DATE-TIME:20210803T150000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/29
DESCRIPTION:Title: Differential Game Models of Optimal Debt Management\n
by Tien Khai Nguyen (North Carolina State University) as part of Analysis
Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tien Khai Nguyen (North Carolina State University)
DTSTART;VALUE=DATE-TIME:20211207T150000Z
DTEND;VALUE=DATE-TIME:20211207T160000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/30
DESCRIPTION:Title: Differential Game Models of Optimal Debt Management\n
by Tien Khai Nguyen (North Carolina State University) as part of Analysis
Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n
\nAbstract\nIn this talk\, I will present recent results on game theoreti
cal formulation of optimal debt management problems in an infinite time ho
rizon with exponential discount\, modeled as a noncooperative interaction
between a borrower and a pool of risk-neutral lenders. Here\, the yearly i
ncome of the borrower is governed by a stochastic process and bankruptcy i
nstantly occurs when the debt-to-income ratio reaches a threshold. Since t
he borrower may go bankrupt in finite time\, the risk-neutral lenders will
charge a higher interest rate in order to compensate for this possible lo
ss of their investment. Thus\, a "solution" must be understood as a Nash e
quilibrium\, where the strategy implemented by the borrower represents the
best reply to the strategy adopted by the lenders\, and conversely. This
leads to highly nonstandard optimization process

\n \n <
b>NB:*This talk is part of the activity of the MIUR Excellence Depar
tment Project MATH@TOV CUP E83C18000100006*\n \n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azahara DelaTorre (Universita' di Roma "La Sapienza")
DTSTART;VALUE=DATE-TIME:20220208T150000Z
DTEND;VALUE=DATE-TIME:20220208T160000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/31
DESCRIPTION:Title: The fractional Yamabe problem with singularities\nby
Azahara DelaTorre (Universita' di Roma "La Sapienza") as part of Analysis
Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n
\nAbstract\nThe so called Yamabe problem in Conformal Geometry consists in
finding a metric conformal to a given one and which has constant scalar c
urvature. From the analytic point of view\, this problem becomes a semilin
ear elliptic PDE with critical (for the Sobolev embedding) power non-linea
rity. If we study the problem in the Euclidean space\, allowing the presen
ce of nonzero-dimensional singularities can be transformed into reducing t
he non-linearity to a Sobolev-subcritical power. A quite recent notion of
non-local curvature gives rise to a parallel study which weakens the geome
tric assumptions giving rise to a non-local semilinear elliptic PDE. \n\nI
n this talk\, we will focus on metrics which are singular along nonzero-di
mensional singularities. In collaboration with Ao\, Chan\, Fontelos\, Gonz
ález and Wei\, we covered the construction of solutions which are singula
r along (zero and positive dimensional) smooth submanifolds in this fracti
onal setting. This was done through the development of new methods coming
from conformal geometry and Scattering theory for the study of non-local O
DEs. Due to the limitations of the techniques we used\, the particular cas
e of ``maximal’’ dimension for the singularity was not covered. In a r
ecent work\, in collaboration with H. Chan\, we cover this specific dimens
ion constructing and studying singular solutions of critical dimension. \n

\n \n **NB**:*This talk is part of the activity of
the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006*\n
\n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Augier (CNRS-LAAS\, Toulouse)
DTSTART;VALUE=DATE-TIME:20220215T150000Z
DTEND;VALUE=DATE-TIME:20220215T160000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/32
DESCRIPTION:Title: On the use of quasi-static controls and duplication of co
ntrols for quantum systems\nby Nicolas Augier (CNRS-LAAS\, Toulouse) a
s part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via
Microsoft Teams.\n\nAbstract\nIn a first part of the talk\, I will presen
t some geometric techniques allowing to control quantum systems using slow
ly-varying controls\, in the so-called adiabatic regime. The latter provid
es strong control results only when the system is driven by at least two c
ontrols\, which is a strong requirement in practice. The second part of th
e talk will be dedicated to an averaging approximation (Rotating Wave Appr
oximation) which allows to duplicate controls in this setting.\n

\n
\n **NB**:*This talk is part of the activity of the MIUR
Excellence Department Project MATH@TOV CUP E83C18000100006*\n \n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Fidaleo (Università di Roma "Tor Vergata")
DTSTART;VALUE=DATE-TIME:20220503T140000Z
DTEND;VALUE=DATE-TIME:20220503T150000Z
DTSTAMP;VALUE=DATE-TIME:20230925T233339Z
UID:AnalysisSeminarRomeTorV/33
DESCRIPTION:Title: Spectral actions for q-particles and their asymptotic
\nby Francesco Fidaleo (Università di Roma "Tor Vergata") as part of Anal
ysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Tea
ms.\n\nAbstract\nFor spectral actions made of the average number of partic
les and arising from open systems made of general free $q$-particles (incl
uding Bose\, Fermi and classical ones corresponding to $q=\\pm1$ and $0$\,
respectively) in thermal equilibrium\, we compute the asymptotic expansio
n with respect to the natural cut-off. We treat both relevant situations r
elative to massless and massive particles\, where the natural cut-off is $
1/\\beta=k_{\\rm B}T$ and $1/\\sqrt{\\beta}$\, respectively. \nWe show th
at the massless situation enjoys less regularity properties than the massi
ve one. We also consider the passage to the continuum describing infinitel
y extended open systems in thermal equilibrium. We briefly discuss the app
earance of condensation phenomena occurring for Bose-like $q$-particles\,
for which $q\\in(0\,1]$\, after passing to the continuum. We also compare
the arising results for the finite volume situation (discrete spectrum) wi
th the corresponding infinite volume one (continuous spectrum).\n

\
n \n **NB**:*This talk is part of the activity of the MIUR
Excellence Department Project MATH@TOV CUP E83C18000100006*\n \n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chaona Zhu (Chinese Academy of Sciences and Roma "Tor Vergata")
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UID:AnalysisSeminarRomeTorV/34
DESCRIPTION:Title: Prescribing scalar curvatures: the negative case\nby
Chaona Zhu (Chinese Academy of Sciences and Roma "Tor Vergata") as part of
Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsof
t Teams.\n\nAbstract\nThe problem of prescribing conformally the scalar cu
rvature on a closed manifold of negative Yamabe invariant is always solvab
le\, if the function to be prescribed is strictly negative\, while suffici
ent and necessary conditions are known in the case that function is non po
sitive. Still in the case of a negative Yamabe invariant\, Rauzy (Trans. A
mer. Math. Soc. 1995) showed solvability\, if the function to be prescribe
d is not too positive\, as quantified by Aubin-Bismuth (J. Funct. Anal. 19
97) later on. In this talk we will review these results variationally and
shed some light on the case\, when Rauzy’s conditions fail. This talk is
joint work with Martin Mayer.\n

\n \n **NB**:*Th
is talk is part of the activity of the MIUR Excellence Department Project
MATH@TOV CUP E83C18000100006*\n \n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/34/
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SUMMARY:Marta Calanchi (Università degli studi di Milano)
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UID:AnalysisSeminarRomeTorV/35
DESCRIPTION:Title: Bifurcation of positive solution for a Neumann problem wi
th indefinite weights\nby Marta Calanchi (Università degli studi di M
ilano) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture hel
d in Via Microsoft Teams.\n\nAbstract\nWe consider eigenvalue problems and
bifurcation of positive solutions for elliptic equations with indefinite
weights and with Neumann boundary conditions. We give complete results con
cerning the existence and non- existence of positive solutions for the sup
erlinear coercive and non-coercive problems\, showing a surprising complem
entarity of the respective results.\nJoint work with Bernhard Ruf (Univers
ità degli Studi di Milano).\n

\n \n **NB**:*This
talk is part of the activity of the MIUR Excellence Department Project MAT
H@TOV CUP E83C18000100006*\n \n
LOCATION:https://researchseminars.org/talk/AnalysisSeminarRomeTorV/35/
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