Electronic structure theory is the study of correlated fermionic quantum many-body systems. In this framework, algebraic varieties in high-dimensional spaces are a language for expressing the polynomials and tensors that describe these systems and for revealing the symmetries in their structure. These algebraic and geometric structures are only partially understood, offering opportunities for discovery at the interface of quantum chemistry and algebraic geometry. In the workshop, attention will be given to how new mathematics can bring about computational strategies for simulating correlated quantum systems.
This workshop will bring together researchers from these fields to develop new algebraic frameworks and computational tools for strongly correlated systems. Topics will include the tensor structures and representation theory of many-body wave functions, where Hamiltonians and ground states of quantum systems lead to the study of Kalman varieties. Coupled-cluster theory gives rise to truncation varieties, including Grassmannians, flag varieties, and their spin adaptations. Discussions will address polynomial optimization, differential algebra for many-body Green’s function methods, and the complexity of computational algebraic geometry methods in electronic structure theory. Additional topics will include Weyl algebras and their applications to bosonic systems.
This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.
Fabian Faulstich
(Rensselaer Polytechnic Institute)
Anna Seigal
(Harvard University)
Luca Sodomaco
(Max Planck Institute for Mathematics in the Sciences )
Bernd Sturmfels
(Max-Planck-Institut fĂĽr Mathematik in den Naturwissenschaften)
Svala Sverrisdottir
(University of California, Berkeley (UC Berkeley))
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