OS Reelle Algebra & KWIM: Coupled Cluster Degree of the Grassmannian

Freitag, 19. Juli 2024
13:30 bis 15 Uhr


Veranstaltet von
Mateusz Michalek

Vortragende Person/Vortragende Personen:
Viktoriia Borovik

We determine the number of complex solutions to a nonlinear eigenvalue problem on the Grassmannian in its Plücker embedding. This is motivated by quantum chemistry, where it represents the truncation to single electrons in coupled cluster theory. In the case of the Grassmannian of lines, we obtain an explicit formula for the number of complex solutions, which involves Catalan numbers and is the volume of the Cayley sum of the Gelfand-Cetlin polytope with simplex. This rests on the geometry of the graph of a birational parametrization of the Grassmannian. This is joint work with Bernd Sturmfels and Svala Sverrisdóttir.