Advancing Quantum Mechanics with Mathematics and Statistics - Tutorials

Explore advanced quantum mechanics through a comprehensive tutorial series that bridges mathematics, statistics, and computational methods. Designed for participants with diverse scientific backgrounds, this four-day program provides foundational knowledge across major themes in quantum mechanical research. Delve into electronic structure calculations including Hartree-Fock and density functional theory, mathematical models of electronic systems, and many-body perturbation theory from both physics and mathematical perspectives. Master ab initio quantum chemistry approaches for nonequilibrium molecular interactions and discover randomized methods for quantum many-body problems. Learn classical and quantum Monte Carlo methods for many-body systems, understand the physical and chemical motivations behind quantum embedding theories, and gain mathematical insights into embedding frameworks. Acquire essential machine learning techniques relevant to quantum systems, explore Green's function methods and many-body perturbation theory, and examine eigenvalue problems with error control considerations. Investigate field theory methods for multiscale quantum system descriptions and deepen understanding of molecular interaction theory through expert-led sessions from leading researchers in computational quantum mechanics and mathematical physics.

Syllabus

Kieron Burke - Elements of electronic structure calculations: HF and DFT - IPAM at UCLA
Jianfeng Lu - Mathematical Models of Electronic Structure - IPAM at UCLA
Alexandre Tkatchenko - Many-body perturbation theory and wavefunction methods: A Physics perspective
Prineha Narang - Ab initio quantum chemistry approaches to nonequilibrium interactions in molecules
Robert Webber - Randomized methods for quantum many-body problems: a mathematical primer
David Ceperley - Introduction to Classical and Quantum Monte Carlo methods for Many-Body systems
Dominika Zgid - A physical/chemical motivation behind quantum embedding theories - IPAM at UCLA
Lin Lin - A mathematical introduction to quantum embedding theory - IPAM at UCLA
Stefan Chmiela - Machine learning basics: A speedrun - IPAM at UCLA
Michael Lindsey - Many-body perturbation theory and Green's function methods - IPAM at UCLA
Benjamin Stamm - Eigenvalue problems and error control - IPAM at UCLA
Matteo Gori - Field theory methods for multiscale description of quantum systems - IPAM at UCLA
Alexandre Tkatchenko - Theory of Molecular Interactions - IPAM at UCLA