Vorträge in der Woche 25.05.2015 bis 31.05.2015

Dienstag, 26.05.2015: The Siegel Upper Half Space, Symplectic Reduction, and Gaussian Wave Packet

Prof. Tomoki Ohsawa (University of Texas, Dallas)

I will talk about the geometry behind the dynamics of the Gaussian wave packet, particularly the role of the Siegel upper half space in parametrizing the Gaussian wave packet. The Siegel upper half space is the set of symmetric complex matrices with positive-definite imaginary parts. Understanding the geometry of this space gives insights into the description of the dynamics of the Gaussian wave packet. I will show how the Siegel upper half space fits into the setting of symplectic reduction. The result is useful in understanding the relationship between two different formulations of Gaussian wave packet dynamics as Hamiltonian dynamical systems.