Stability of ferromagnetism in many-electron systems

First part
Title: Stability of ferromagnetism in many-electron systems
Abstract:
I construct a model-independent framework describing stabilities of ferromagnetism in strongly correlated electron systems. Within the new framework, I reinterpret the Marshall-Lieb-Mattis theorem and Lieb’s theorem; in addition, from the new perspective, I prove that Lieb’s theorem still holds true even if the electron-phonon and electron-photon interactions are taken into account. I also examine the NagaokaThouless theorem and its stability. These examples verify the effectiveness of the new viewpoint.

Second part
Title: Order preserving operator inequalities in many-electron systems
Abstract:
In this talk, I will introduce order preserving operator inequalities and explain how these inequalities are applied to the mathematical study of ferromagnetism. As examples of applications, Lieb's theorem of the Hubbard model and its stabilities will be discussed in terms of the inequalities.