BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Camillo Brena (IAS) DTSTART:20251113T130000Z DTEND:20251113T143000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/1 DESCRIPTION:Title: Regularity for stationary varifolds\nby Camillo Br ena (IAS) as part of SISSA's Analysis seminars\n\nLecture held in 133.\n\n Abstract\nStationary varifolds generalize minimal surfaces and can exhibit singularities. The most general regularity theorem in this context is the celebrated Allard's Regularity Theorem\, which asserts that the set of si ngular points has empty interior. However\, it is believed that the set of singular points should have codimension (at least) one. Despite more than 50 years having passed since Allard's breakthrough\, stronger results hav e remained elusive. In this talk\, after a brief discussion about the regu larity theory for stationary varifolds\, I will discuss the principle of u nique continuation and the topic of rectifiability\, both of which are lin ked to understanding the structure of singularities. This discussion is ba sed on joint works with Stefano Decio\, Camillo De Lellis\, and Federico F ranceschini.\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jules Pitcho (GSSI) DTSTART:20251118T130000Z DTEND:20251118T143000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/2 DESCRIPTION:Title: Non-uniqueness and recovery of uniqueness for the tran sport equation\nby Jules Pitcho (GSSI) as part of SISSA's Analysis sem inars\n\nLecture held in 133.\n\nAbstract\nI will discuss recent non-uniqu eness results for the transport equation and in the specific case of vecto r fields singular at the initial time\, I will explain how uniqueness can be recovered\, both at the Eulerian and Lagrangian level.\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Luigi De Rosa (GSSI) DTSTART:20251210T130000Z DTEND:20251210T143000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/3 DESCRIPTION:Title: On the Dissipation Measure in Turbulent Flows\nby Luigi De Rosa (GSSI) as part of SISSA's Analysis seminars\n\nLecture held in 133.\n\nAbstract\nThe persistence of kinetic energy dissipation in the inviscid limit is known as "anomalous dissipation" and it is central to ou r current understanding of turbulent flows. This results in a non-trivial finite measure quantifying the kinetic energy loss\, the "Dissipation Meas ure". The geometric and analytic structures that such measure can sustain remain poorly understood. It will be shown how\, in any space dimension\, quantitative bounds on the Hausdorff dimension of the dissipation can be obtained by leveraging on the regularity of the solution. Although there are good reasons to believe in their sharpness in the ideal (i.e. with no viscosity) setting\, for physically realizable weak solutions the problem is extremely different if settled in dimension two or three. Indeed\, for two-dimensional fluids the results can be pushed much more\, with almost n o assumption on the weak solutions. This is due to the "inverse cascade" i nduced by the higher order formally conserved quantities. We will present the physical background\, explain the main ideas behind the proofs\, discu ss the sharpness of the results and how they fit in the mathematical lite rature.\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Federico Pasqualotto (UC San Diego) DTSTART:20251218T100000Z DTEND:20251218T113000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/4 DESCRIPTION:Title: From instability to singularity formation in incompres sible fluids\nby Federico Pasqualotto (UC San Diego) as part of SISSA' s Analysis seminars\n\nLecture held in 133.\n\nAbstract\nIn this talk\, I will first review the singularity formation problem in incompressible flui d dynamics\, describing how particle transport poses the main challenge in constructing blow-up solutions for the incompressible 3d Euler equations. I will then outline a new mechanism that allows us to overcome the effect s of particle transport\, leveraging the instability seen in the classical Taylor--Couette experiment. Using this mechanism\, we construct the first swirl-driven singularity for the incompressible Euler equations in R^3. T his is joint work with Tarek Elgindi (Duke University).\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Inversi (University of Basel) DTSTART:20260128T130000Z DTEND:20260128T143000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/5 DESCRIPTION:Title: Some dissipative properties of Euler solutions\nby Marco Inversi (University of Basel) as part of SISSA's Analysis seminars\ n\nLecture held in 133.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Federico Renzi (SNS) DTSTART:20260114T130000Z DTEND:20260114T143000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/6 DESCRIPTION:Title: The superposition principle for local 1-dimensional cu rrents\nby Federico Renzi (SNS) as part of SISSA's Analysis seminars\n \nLecture held in 133.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxime Van De Moortel (Rutgers University) DTSTART:20260226T130000Z DTEND:20260226T143000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/7 DESCRIPTION:Title: The Klein-Gordon equation on a black hole\nby Maxi me Van De Moortel (Rutgers University) as part of SISSA's Analysis seminar s\n\nLecture held in 133.\n\nAbstract\nThe (linear) Klein-Gordon equation on a Schwarzschild background combines the most fundamental model for mass ive matter evolving on the simplest type of black hole. Yet\, unlike massl ess fields (the wave equation) which are now well-understood on a black ho le\, the large-time asymptotics of Klein-Gordon solutions have long remain ed elusive.\nPhysically\, the Klein-Gordon dynamics presents a geometric o bstruction: the stable trapping of massive particles\, which was conjectur ed to prevent decay. In this talk\, we disprove this expectation and estab lish that solutions with localized initial data actually decay polynomiall y in time. We will highlight the proof's most surprising ingredient: the u se of analytic number theory--specifically\, bounds on exponential sums si milar to the Riemann zeta function.\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Dolce (EPFL) DTSTART:20260305T130000Z DTEND:20260305T143000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/8 DESCRIPTION:Title: Instability of the 2D Taylor-Green vortex\nby Mich ele Dolce (EPFL) as part of SISSA's Analysis seminars\n\nLecture held in 1 33.\n\nAbstract\nThe 2D Taylor-Green (TG) vortex is the prototypical examp le of an Euler steady state on T^2 possessing truly two-dimensional featur es\, namely elliptic and hyperbolic stagnation points. Its streamfunction\ , sin(x)sin(y)\, lives on the second Fourier shell\, making it susceptible to large-scale destabilizing mechanisms. Despite the apparent simplicity of the steady state\, a proof of its spectral instability has long remaine d elusive\, and was only recently observed numerically. To solve this prob lem\, I will introduce a new criterion to detect unstable eigenvalues for a wide class of linear Hamiltonian operators. We apply this to prove the s tability of the TG vortex with respect to odd perturbations. In the subspa ce of functions even in both variables\, we combine our criterion with a r igorous computer-assisted argument to locate two unstable eigenvalues. Thi s fully characterizes the unstable spectrum of the TG vortex and implies n onlinear instability in velocity.\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Oliver Edtmair DTSTART:20260416T120000Z DTEND:20260416T133000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/9 DESCRIPTION:by Oliver Edtmair as part of SISSA's Analysis seminars\n\nLect ure held in 133.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Bozhidar Velichkov (Università di Pisa) DTSTART:20260310T130000Z DTEND:20260310T143000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/10 DESCRIPTION:Title: On the structure of the two-phase free boundaries in dimension two\nby Bozhidar Velichkov (Università di Pisa) as part of SISSA's Analysis seminars\n\nLecture held in 133.\n\nAbstract\nThis talk i s dedicated to the regularity and the fine structure of the free boundarie s of the two-phase Bernoulli problem. I will start from the classical resu lt of Alt-Caffarelli-Friedman and the Lipschitz continuity of the solution s\, then I will discuss the regularity of the free boundaries obtained via an epiperimetric inequality. Finally\, I will present a recent result abo ut the number of contact points between the positive and the negative phas es.\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Massimo Sorella (Imperial College) DTSTART:20260410T090000Z DTEND:20260410T103000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/11 DESCRIPTION:Title: Fast dynamo action on the 3-torus for pulsed-diffusio ns\nby Massimo Sorella (Imperial College) as part of SISSA's Analysis seminars\n\nLecture held in 133.\n\nAbstract\nFor the passive vector equat ion\, the fast dynamo conjecture predicts exponential-in-time growth of th e L^2 norm of the solution under a Lipschitz flow of a vector field\, at a rate independent of the resistivity. We establish this conjecture for the pulsed diffusion model with a time-periodic stretch-fold-shear (SFS) vect or field. Our approach uses anisotropic Banach spaces adapted to the dynam ics of the underlying flow to prove the existence of a discrete eigenvalue with positive real part in this distributional setting.\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Luciano Mari (University of Milan) DTSTART:20260430T120000Z DTEND:20260430T133000Z DTSTAMP:20260404T095500Z UID:SissaAnalysisSeminar/12 DESCRIPTION:Title: Prescribing the Lorentzian mean curvature of a spacel ike hypersurface\, and the Born-Infeld model\nby Luciano Mari (Univers ity of Milan) as part of SISSA's Analysis seminars\n\nLecture held in 133. \n\nAbstract\nThe talk aims to discuss the existence and regularity proble m for spacelike hypersurfaces $M$ in Lorentzian manifolds whose mean curva ture is a prescribed\, possibly singular distribution. When considering am bient Minkowski space\, this leads to study the following Dirichlet proble m for the function that (locally) describes $M$ as a graph\, which we call $(\\mathcal{BI})$:\n \n\\[\n \\left\\{ \\begin{array}{ll}\n -{\\rm div } \\left( \\frac{Du}{\\sqrt{1-|Du|^2}}\\right) = \\rho & \\quad \\text{in a domain } \\\, \\Omega \\Subset \\R^n\, \\\\[0.5cm]\n u = \\phi & \\qua d \\text{on } \\\, \\partial \\Omega\, \n \\end{array}\n \\right.\n\\] \n\nfor a given measure $\\rho$ (the prescribed mean curvature) and bounda ry data $\\phi$. Problem $(\\mathcal{BI})$ also appears in Born-Infeld's t heory of electrostatics\, according to which $u$ describes the electric po tential generated by the charge $\\rho$. Even though $(\\mathcal{BI})$ is formally the Euler-Lagrange equation of a nice convex functional $I_\\rho$ \, the lack of smoothness of $I_\\rho$ where $|Du|=1$ (i.e. where the grap h of $u$ becomes lighlike) may prevent the unique variational minimizer $u _\\rho$ to solve $(\\mathcal{BI})$. As we shall see\, this possibility act ually occurs. We shall describe both existence and non-existence results h elping to guess the possible sharp thresholds on $\\rho$. A chief difficul ty comes from the possible presence of ``light segments" in the graph of $ u_\\rho$\, a fact that we will investigate in detail. Various open problem s and research directions will be discussed.\n\nThe talk is based on joint works with J. Byeon\, N. Ikoma\, A. Malchiodi and L. Maniscalco\, availab le at arXiv:2112.11283 and arXiv:2512.17670.\n LOCATION:https://stable.researchseminars.org/talk/SissaAnalysisSeminar/12/ END:VEVENT END:VCALENDAR