Analysis Seminar 2026/27

The Fermi–Pasta–Ulam–Tsingou (FPUT) lattice is a one-dimensional particle chain with nonlinear nearest-neighbour interactions. In this talk, we consider a FPUT-type lattice with long-distance, repulsive forces that decrease with distance. We prove the existence of solitary travelling waves via variational methods and provide a formula for the wave profile in the high-energy limit. This is joint work with Michael Herrmann and Karsten Matthies.

In this talk, we first revisit the vortex filament conjecture for three-dimensional incompressible Euler flows with helical symmetry and no swirl. Using gluing methods, we provide the first construction of a smooth, global-in-time helical vortex filament in $\mathbb{R}^3$ whose cross-sectional vorticity remains compactly supported in $\mathbb{R}^2$ for all times. Building on this construction, we then investigate the leapfrogging phenomenon for helical vortex filaments, in which several interacting helices with a common symmetry axis alternately overtake one another. This is joint work with Monica Musso.