Long Programs

This long program aims to forge new connections between applied algebraic geometry and electronic structure theory. Bringing together computational chemists focusing on strongly correlated electronic effects, computer scientists specializing in machine learning, and numerical algebraists, we seek to foster interdisciplinary collaboration and innovation to develop new numerical approaches to the fermionic quantum many-body problem.

The fermionic quantum many-body problem is one of the most formidable high-dimensional challenges in science. It is relevant for a wide range of applications, including emission reduction, green chemistry, and the development of materials for renewable energy and energy storage. Computational predictions for such applications require highly accurate results to avoid false-positive predictions that would fail experimentally. Methods that can accommodate these high-accuracy needs incur high computational costs and unfavorable scaling with the system size. A better understanding of the underlying algebraic structures, combined with fresh numerical approaches, opens the way to new computational methods with the potential to address both limitations.

We aim to introduce novel, unexplored lines of research for efficient computation of physical properties and response functions for ground and excited states. We will investigate fundamental and unexplored algebraic-geometric structures inherent in the fermionic quantum many-body problem and the majority of correlated computational methods. Besides increasing numerical efficiency for strongly correlated methods, said algebraic structure may also be exploited by machine learning approaches.

Organizing Committee

Fabian Faulstich (Rensselaer Polytechnic Institute)
Todd Martinez (Stanford University)
Frank Sottile (Texas A&M University - College Station)
Martin Stoehr (Stanford University)
Bernd Sturmfels (Max-Planck-Institut für Mathematik in den Naturwissenschaften)
Guido Falk von Rudorff (University of Kassel)
Julia Westermayr (Universität Leipzig)