MINI-SCHOOL 2017

Mini-school on mathematics in electronic structure theory of GDR CORREL

• Date: 09-11 January 2017

• Location: Université Pierre et Marie Curie (UPMC), Jussieu campus, 4 place Jussieu, 75005, Paris.

Laboratoire Jacques-Louis Lions, corridor 15-16, 3rd floor, room 309

• Lectures: Eric Cancès and Trygve Helgaker
• Organizers: Michel Caffarel, Eric Cancès, Emmanuel Fromager, Julien Toulouse.

• List of registered people

Presentation

• The lectures delivered are intended to be of interest to any person working in the field of electronic structure theory and willing to discover or deepen the mathematical aspects of the methods. PhD students, post-docs or any academic are welcome!

• To provide a detailed presentation of subjects, we have chosen to give a good amount of time to each lecturer. The workshop will thus typically involve only two or three lecturers over a three-day period.

Program

Two lectures will be proposed:

• 1) Operator theory for electronic structure calculation by Eric CANCES, Ecole des Ponts and INRIA, Paris, France

Indicative program (subject to changes and extension):

- Hilbert spaces
- Linear operators on Hilbert spaces
- Self-adjointness
- Spectra of self-adjoint operators: point vs continuous spectrum, discrete vs essential spectrum
- Some examples in quantum chemistry: N-body Schödinger equation, Hartree-Fock and Kohn-Sham hamiltonians
- Some examples in solid state physics: Bloch theory, periodic Kohn-Sham hamiltonians

• 2) Fundamentals of DFT (tentative title) by Trygve HELGAKER Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, Norway

Indicative program (subject to changes and extension):

- Hohenberg–Kohn theory (Hohenberg–Kohn theorem and concavity, Lieb variation principles, v-representable densities, etc.)
- Levy–Lieb constrained-search theory, N-representable densities, the Levy–Lieb constrained-search functional, etc
- Lieb convex-conjugate theory, convex functions and convex conjugation, the Lieb convex-conjugate functional, etc
- Discontinuity and nondifferentiability of the universal functional conditions, etc.
- and much more.

Practical details

• IMPORTANT: To facilitate the participation of young researchers, no registration fees will be asked and housing in student-type accomodation will be offered.