LLP-IP at the Faculty of Mathematics and Computer Sciences 2013

This Intensive Programme is designed to provide educational and research experience for advanced undergraduate and beginning graduate students of mathematics, physics and other subjects applying mathematics. The scientific program consists of seven mini-courses, problem sessions, and projects with computer lab and theoretical components. Projects will be performed in teams with students from different countries to provide a first-hand international experience.

Ablaufplan

Schedule (final version) (PDF)

Mini-courses


  • Introductory course on periodic structures (in the first week) (Ingo Witt, Göttingen)
    • Spectral theory for selfadjoint operators
    • The spectral theorem
    • Bloch-Floquet theory for periodic differential operators
    • Bloch waves



  • Mathematics of photonic crystals (Michael Plum, Karlsruhe)
    • Physical and operator theoretical modelling of photonic crystals
    • Application of Floquet-Bloch theory
    • Eigenvalue bounds by verified numerical methods
    • A computer-assisted proof of a spectral band gap



  • Phononic crystals (Natalia Movchan, Liverpool)
    • Mathematical modeling
    • Continuous versus lattice structures
    • Layered media
    • Wave propagation in phononic crystals



  • Local perturbations of periodic media (Sonia Fliss, Paris)
    • Helmholtz equation with absorption term
    • Exact boundary conditions for wave propagation
    • Bloch-Floquet transformation



  • Inverse Scattering Problems for Periodic Structures (Thorsten Hohage, Göttingen)
    • Well-posedness of forward problems
    • Uniqueness results
    • Iterative reconstruction methods
    • Sampling methods



  • Allen-Cahn equations in periodic media (Enrico Valdinoci, Milan)
    • Variational approach and asymptotics
    • Critical points of energy functionals, periodic minimizers
    • Rigidity and symmetry
    • Multi-bump solutions, laminations and foliations



  • Semiclassical analysis for periodic media (in the second week) (Ingo Witt, Göttingen)
    • Semiclassical operators with periodic potentials
    • Functional formulas and Grushin reduction
    • Effective description and reminder estimates
    • Asymptotics of perturbed eigenvalues in unperturbed spectral gaps