Dear Colleagues, We would like to invite you to the following SPASS seminar, *On minimizing curves in a Brownian potential* by Matteo Palmieri (Max Planck Inst. Lepzig), WED 19.11.2025 at 14:00 CET in Saletta Riunioni, Dipartimento di Matematica, UNIPI. Best, Francesco Grotto on behalf of the organizers https://sites.google.com/unipi.it/spass ---------------------------------------------------------------- /Abstract: We study a (1+1)-dimensional semi-discrete random variational problem that can be interpreted as the geometrically linearized version of the critical 2-dimensional random field Ising model (at zero temperature). We show that at every dyadic scale from the system size down to the lattice spacing the minimizer contains at most order-one Dirichlet energy per unit length, leading to a logarithmic scaling of the minimal energy. Using super-additivity in the scales, this allows us to establish a quenched homogenization result in the sense that he leading order of the minimal energy becomes deterministic as the ratio system size/lattice spacing diverges. This is joint work with Felix Otto and Christian Wagner./