Explore advanced mathematical and computational approaches to quantum mechanical systems through this comprehensive workshop featuring 22 expert lectures from leading researchers in the field. Delve into cutting-edge topics including machine learning applications for quantum simulation, density functional theory developments, electron-phonon interactions, and quantum embedding methods. Learn about localization techniques, model reduction strategies using DMRG, and quantum continuum mechanics for many-body systems. Examine theoretical foundations through discussions of Dirac-Coulomb operators, Hartree-Fock approximations, and correlation energy calculations for weakly interacting fermions. Discover innovative computational methods including stochastic vector approaches for extended systems, alchemical perturbations for systematic model improvement, and multiscale inverse problems spanning from Schrödinger to Boltzmann equations. Gain insights into practical applications such as electron interactions in condensed matter, quantum dynamics from classical trajectories, and spectral analysis of molecular and crystalline systems. Access presentations covering both fundamental mathematical results and numerical implementations, with particular emphasis on model reduction techniques that bridge quantum mechanical accuracy with computational efficiency.

Syllabus

Eun-Ah Kim - Machine Learning for Quantum Simulation - IPAM at UCLA
Anil Damle - Localization methods: perspectives on initialization and optimization - IPAM at UCLA
Eric Cances - Some mathematical and numerical results on monolayer and twisted bilayer graphene
Nandini Ananth - Quantum dynamics from classical trajectories - IPAM at UCLA
Feliciano Giustino - Methods and software for electron-phonon physics - IPAM at UCLA
Paola Gori-Giorgi - Large-coupling strength expansion in DFT and Hartree-Fock adiabatic connections
Steve White - Model reduction using localized bases and DMRG - IPAM at UCLA
Guido Falk von Rudorff - Systematically improvable models from alchemical perturbations - IPAM UCLA
Lukas Muechler - Quantum embedding methods for correlated excited states of point defects
Andreas Savin - Beyond density functional approximations by lessons from density functional theory
Eric Séré - The ground state of the Dirac-Fock energy for molecules and crystals - IPAM at UCLA
Giovanni Vignale - Quantum continuum mechanics for many-body systems - IPAM at UCLA
Francesco Evangelista - Many-electron effective Hamiltonians from similarity renormalization group
Marco Bernardi - Quantum mechanical calculations of electron interactions in condensed matter
Mathieu Lewin - Recent results in Density Functional Theory - IPAM at UCLA
Stefan Tuefel - Local response in bulk-gapped interacting systems - IPAM at UCLA
Maria Esteban - Spectral results & open problems for Dirac-Coulomb operators w/ charge distributions
Qin Li - Multiscale inverse problem, from Schroedinger to Newton to Boltzmann - IPAM at UCLA
Roi Baer - Stochastic Vector Methods for extended systems - IPAM at UCLA
Garnet Chan - Lattice models and ab initio descriptions of correlated materials - IPAM at UCLA
Benjamin Schlein - Correlation energy of weakly interacting fermions - IPAM at UCLA
Volker Bach - The Hartree-Fock Approximation and its Generalizations - IPAM at UCLA