BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tere M-Seara (UPC\, Barcelona) DTSTART:20200630T123000Z DTEND:20200630T133000Z DTSTAMP:20260422T225826Z 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:20201029T130000Z DTEND:20201029T140000Z DTSTAMP:20260422T225826Z 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:20201112T130000Z DTEND:20201112T140000Z DTSTAMP:20260422T225826Z 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:20201119T130000Z DTEND:20201119T140000Z DTSTAMP:20260422T225826Z 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:20201126T130000Z DTEND:20201126T140000Z DTSTAMP:20260422T225826Z 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:20201210T130000Z DTEND:20201210T140000Z DTSTAMP:20260422T225826Z 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:20201210T130000Z DTEND:20201210T140000Z DTSTAMP:20260422T225826Z 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:20210114T130000Z DTEND:20210114T140000Z DTSTAMP:20260422T225826Z 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\nNote: 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:20210121T130000Z DTEND:20210121T140000Z DTSTAMP:20260422T225826Z 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:20210204T130000Z DTEND:20210204T140000Z DTSTAMP:20260422T225826Z 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:20210211T130000Z DTEND:20210211T140000Z DTSTAMP:20260422T225826Z 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\nN.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:20210225T130000Z DTEND:20210225T140000Z DTSTAMP:20260422T225826Z 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:20210304T130000Z DTEND:20210304T140000Z DTSTAMP:20260422T225826Z 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
\nN.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:20210311T130000Z DTEND:20210311T140000Z DTSTAMP:20260422T225826Z 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).
\nNB: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:20210318T130000Z DTEND:20210318T140000Z DTSTAMP:20260422T225826Z 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

\nNB :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:20210325T130000Z DTEND:20210325T140000Z DTSTAMP:20260422T225826Z 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
\nNB: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:20210401T120000Z DTEND:20210401T130000Z DTSTAMP:20260422T225826Z 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:20210415T120000Z DTEND:20210415T130000Z DTSTAMP:20260422T225826Z 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\nNote: 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:20210429T120000Z DTEND:20210429T130000Z DTSTAMP:20260422T225826Z 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
\nNB: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:20210506T120000Z DTEND:20210506T130000Z DTSTAMP:20260422T225826Z 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:20210513T120000Z DTEND:20210513T130000Z DTSTAMP:20260422T225826Z 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
\nNB: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:20210520T120000Z DTEND:20210520T130000Z DTSTAMP:20260422T225826Z 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:20210527T120000Z DTEND:20210527T130000Z DTSTAMP:20260422T225826Z 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:20210603T120000Z DTEND:20210603T130000Z DTSTAMP:20260422T225826Z 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:20210610T120000Z DTEND:20210610T130000Z DTSTAMP:20260422T225826Z 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:20211019T140000Z DTEND:20211019T150000Z DTSTAMP:20260422T225826Z 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:20211123T150000Z DTEND:20211123T160000Z DTSTAMP:20260422T225826Z 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:20211130T150000Z DTEND:20211130T160000Z DTSTAMP:20260422T225826Z 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:20210803T140000Z DTEND:20210803T150000Z DTSTAMP:20260422T225826Z 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:20211207T150000Z DTEND:20211207T160000Z DTSTAMP:20260422T225826Z 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:20220208T150000Z DTEND:20220208T160000Z DTSTAMP:20260422T225826Z 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:20220215T150000Z DTEND:20220215T160000Z DTSTAMP:20260422T225826Z 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:20220503T140000Z DTEND:20220503T150000Z DTSTAMP:20260422T225826Z 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") DTSTART:20220517T140000Z DTEND:20220517T150000Z DTSTAMP:20260422T225826Z 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/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Calanchi (Università degli studi di Milano) DTSTART:20220524T140000Z DTEND:20220524T150000Z DTSTAMP:20260422T225826Z 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/ END:VEVENT END:VCALENDAR