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Oberseminar: Calculus of Variations and Applications

Organizers: Phan Thành Nam, Arnaud Triay

Past semesters

Summer semester 2026

• 06.05.2026: Avy Soffer (Rutgers University).
  
  Title: Global Self-Similar solutions, Breakdown of Asymptotic Completeness-New Physics?
  
  Abstract: For Schrödinger-type equations with time-dependent, spatially local interactions — including nonlinear cases — there exist solutions that are neither localized nor scattering. These solutions exhibit sub-ballistic spreading, yet are global, asymptotically stable, and transport mass (the L^2-norm) to infinity. I will describe the construction of such self-similar solutions and discuss some of their physical implications.
• 20.05.2026: Ian Jauslin (Rutgers University).
  
  Title: TBA
• 09.06.2026: Domenico Cafiero (Politecnico di Milano).
  
  Title: Three-body Hamiltonian for abelian anyons with zero-range interactions
  
  Abstract: Anyons are 2d identical quantum particles with an intermediate exchange symmetry characterized by representations of the braid group. In the abelian case, they can be modeled through the so-called magnetic representation, namely as a system of bosons with an Aharonov-Bohm flux attached to each particle. In this talk, I will discuss the construction of self-adjoint Hamiltonians, different from the Friedrichs realization, for a system of three abelian anyons. I will focus in particular on the Ter-Martirosyan-Skornyakov extensions. This family of Hamiltonians turns out to be parametrized by a suitable boundary operator; I will present a complete classification of its self-adjoint realizations and compute the negative spectrum for the specific case of interest. These results shed light on the possible occurrence of Thomas instability in the three-anyon model. Joint work with Michele Correggi (PoliMi) and Davide Fermi (PoliMi)