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Oberseminar: Calculus of Variations and Applications

Organizers: Phan Thành Nam, Arnaud Triay

Past semesters

• Summer semester 25
• Winter semester 24
• Summer semester 24
• Winter semester 23
• Summer semester 23
• Winter semester 22

Winter Semester 2025

• 15.10.2025: Jinyeop Lee (University of Basel).
  
  Title: Derivation of the Chern–Simons–Schrödinger equation from the dynamics of an almost-bosonic-anyon gas
  
  Abstract: We study the time evolution of an initial product state in a system of almost-bosonic-extended-anyons in the large-particle limit. We show that the dynamics of this system can be well approximated, in finite time, by a product state evolving under the effective Chern–Simons–Schrödinger equation. Furthermore, we provide a convergence rate for the approximation in terms of the radius R=(logN)^{-½+ε} of the extended anyons. These results establish a rigorous connection between the microscopic dynamics of almost-bosonic-anyon gases and the emergent macroscopic behavior described by the Chern–Simons–Schrödinger equation.
• 22.10.2025: Phan Thanh Nam and David Scholz (LMU Munich).
  
  Title: Compactness of Minimizing Sequences for Sobolev and Hardy–Sobolev–Littlewood Inequalities: Revisited
  
  Abstract: We will revisit the concentration–compactness method. The first speaker will present a simplified proof of the compactness of minimizing sequences associated with the Sobolev inequality, based on a recent joint work with Charlotte Dietze. The second speaker will discuss the extension of this approach to the Hardy–Sobolev–Littlewood inequality.
• 17.12.2025: Tobias Ried (Georgia Tech).
  
  Title: From optimal transport to branched microstructures: a journey through elliptic regularity theory
  
  Abstract: From optimal transport to branched microstructures: a journey through elliptic regularity theoryIn this talk I will present a purely variational approach to the regularity theory of optimal transportation introduced by Goldman and Otto. The approach closely follows De Giorgi's strategy for the regularity theory of minimal surfaces: at its core lies a Campanato iteration, which allows one to transfer the scaling law of the local transport energy to small scales. In regularity theory, this typically leads to Schauder estimates; but the same idea can also be used to study the local energy scaling of minimizers of non-convex variational problems related to branching phenomena in strongly uniaxial ferromagnets and type-I superconductors in the intermediate state. I will highlight this connection and give a brief overview of further recent developments and point out some other interesting applications.
• 21.01.2026: Thomas Gamet (ENS Lyon).
  
  Title: Semi-classical limit of a trapped dilute Fermi gas
  
  Abstract: In this talk, I will discuss the semi classical limit of a dilute Fermi gas in a fixed trapping potential. The ground state energy of such a system with very short-range interactions and spin 1/2 particles converges to the Thomas Fermi energy of the system, with a perturbative term corresponding to the interactions. The main difficulty of this problem is the lack of explicit diagonalization of the one-particle Hamiltonian.