Algebraic Varieties in Quantum Chemistry

Watch a 57-minute conference talk from the CMSA Conference on Mathematics in Science where Bernd Sturmfels from MPI Leipzig explores the intersection of algebraic geometry and quantum chemistry. Delve into the mathematical foundations of coupled cluster (CC) theory and its application to quantum many-body systems. Learn how high-dimensional eigenvalue problems in the electronic Schroedinger equation are approximated using polynomial systems at various truncation levels. Understand the exponential parametrization of eigenstates and their relationship to truncation varieties, which serve as generalizations of Grassmannians in Pluecker embedding. Explore the derivation of Hamiltonians, examine truncation varieties and their CC degrees in detail, and discover current methods for solving CC equations, based on collaborative research with Fabian Faulstich and Svala Sverrisdóttir.