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Organizers: Paolo Antonelli, Gabriele Benomio, Yuri Cacchiò, Sara Daneri, Luigi De Rosa, Francesco Paolo Maiale, Pierangelo Marcati, Stefano Modena, Jules Pitcho, Flavio Rossetti, Eris Runa
Location & time: Gran Sasso Science Institute, weekly on Tuesdays, 2:30-3:30pm (map)
Upcoming Seminars: (see also GSSI Academic Calendar)
18 November 2025, 2:30-3:30pm, GSSI Main Lecture Hall
Speaker: Jonas Lührmann (University of Cologne)
Title: Asymptotic stability of the sine-Gordon kink outside symmetry
Abstract: We consider scalar field theories on the line with Ginzburg-Landau (double-well) self-interaction potentials. Prime examples include the \phi^4 model and the sine-Gordon model. These models feature simple examples of topological solitons called kinks. The study of their asymptotic stability leads to a rich class of problems owing to the combination of weak dispersion in one space dimension, low power nonlinearities, and intriguing spectral features of the linearized operators such as threshold resonances or internal modes. We present a perturbative proof of the full asymptotic stability of the sine-Gordon kink outside symmetry under small perturbations in weighted Sobolev norms. The strategy of our proof combines a space-time resonances approach based on the distorted Fourier transform to capture modified scattering effects with modulation techniques to take into account the invariance under Lorentz transformations and under spatial translations. A major difficulty is the slow local decay of the radiation term caused by the threshold resonances of the non-selfadjoint linearized matrix operator around the modulated kink. Our analysis hinges on two remarkable null structures that we uncover in the quadratic nonlinearities of the evolution equation for the radiation term as well as of the modulation equations. The entire framework of our proof, including the systematic development of the distorted Fourier theory, is general and not specific to the sine-Gordon model. We conclude with a discussion of potential applications in the generic setting (no threshold resonances) and with a discussion of the outstanding challenges posed by internal modes such as in the well-known \phi^4 model. This is joint work with Gong Chen (GeorgiaTech).
25 November 2025, 2:30-3:30pm, GSSI Main Lecture Hall
Speaker: Davide Carazzato (University of Vienna)
Title: A strong quantitative isoperimetric inequality for a capillarity problem
Abstract: During the seminar, we will introduce a stronger version of the quantitative isoperimetric inequality, originally developed by Fusco and Julin. Building on that, we will arrive to the analogous inequality for a capillarity problem using the so-called selection principle, based on the regularity theory for the perimeter functional. We will also highlight the difficulties that arise when we apply Fusco and Julin's method to our situation. This result was obtained in collaboration with Giulio Pascale and Marco Pozzetta.
2 December 2025, 2:30-3:30pm, GSSI Main Lecture Hall
Speaker: Eliot Pacherie (CNRS/CYU)
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9 December 2025, 2:30-3:30pm, GSSI Main Lecture Hall
Speaker: Roberta Bianchini (CNR/IAC)
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