Colloquium: Algebraic Varieties in Quantum Chemistry - Bernd Sturmfels
Abstract: We discuss the algebraic geometry behind coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schroedinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Pluecker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations. This is joint work with Fabian Faulstich and Svala Sverrisdóttir.
Bio: Bernd Sturmfels received doctoral degrees in 1987 from the University of Washington and the Technical University Darmstadt, and an honorary doctorate in 2015 from the Goethe University Frankfurt. After postdoctoral years in Minneapolis and Linz, he taught at Cornell University, before joining UC Berkeley in 1995, where he served as Professor of Mathematics, Statistics and Computer Science. Since 2017 he is a director at the Max-Planck Institute for Mathematics in the Sciences, Leipzig. In 2018 he became Honarary Professor at Technical University Berlin and University of Leipzig. His awards include a David and Lucile Packard Fellowship, a Humboldt Senior Research Prize, the SIAM von Neumann Lecturership, the Sarlo Distinguished Mentoring Award, and the George David Birkhoff Prize in Applied Mathematics. He is a fellow of the AMS and SIAM, and a member of the Berlin-Brandenburg Academy of Sciences. In 2022 he spoke at the International Congress of Mathematicians. Sturmfels mentored 60 doctoral students and numerous postdocs, and he authored 11 books and 300 research articles, in combinatorics, commutative algebra, algebraic geometry, and their applications to fields like statistics, optimization, and computational biology.
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"Adventures in Mentoring": https://math.berkeley.edu/~bernd/mentoring.pdf
"Excellence through Diversity": https://www.europeanwomeninmaths.org/nlalg-mpi-mis/