Home page | Publications | Oberseminar | Teaching

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)
• 01.07.2026: Arianna Rast (LMU Munich).
  
  Title: Optimization of the Maximum Shear Stress with Isoperimetric-type constraints
  
  Abstract: The torsion function of a bounded domain, arising in the Saint-Venant theory of elasticity, is the solution of \(-\Delta u=1\) that vanishes at the boundary. We refer to the maximum magnitude of the torsion function's gradient as the maximum shear stress. This talk presents the results from Simon Larson's paper ``A Sharp Multidimensional Hermite-Hadamard Inequality'' concerning the shape optimization of the maximum shear stress under a variety of constraints on the volume and perimeter. These results include the establishment of optimal upper and lower bounds and the analysis of optimizing shapes.
• 01.07.2026: Edgardo Stockmeyer (Pontificia Universidad Católica de Chile).
  
  Title: A Spectral Transition in the Stability Theory of the 1-D Soler Model
  
  Abstract: In this talk I will present recent spectral results related to the stability theory of standing waves \( \psi(t,x)=e^{-i\omega t}\phi(x) \) for the one-dimensional Soler model (a nonlinear Dirac equation) with power nonlinearity \[ f(s)=s|s|^{p-1}, \qquad p>0. \] The analysis is motivated by the so-called gap property arising in the stability theory of nonlinear Schrödinger equations. More precisely, we study the spectral structure of the Dirac operators obtained by linearization around standing waves, focusing on the existence of eigenvalues inside the spectral gap and resonances at the thresholds of the essential spectrum. I will describe a sharp spectral transition in the non-linearity at the critical exponent \( p=1 \): threshold resonances present in the Gross--Neveu case generate eigenvalues inside the spectral gap for \( 0< p < 1 \) , whereas no threshold resonances occur for \( p > 1 \).