Hopf algebras

For every locally compact abelian group G, the set of characters is also a locally compact abelian group and the Pontrjagin theorem says that the double dual is isomorphic to the original group G. For a non-abelian group, a generalized dual can no longer be defined in the form of a group. One has to look for a larger category, namely quantum groups in the form of Hopf algebras. The objective is to study Hopf algebras in the setting of C*-algebras and von Neumann algebras such that a generalization of Pontrjagin duality is obtained.

Learning Partial Differential Equations with fMRI Data

In this project, we apply an appropriate data-driven method to derive the potential partial differential equation model hidden in an fMRI dataset collected by Visconti di Oleggio Castello, Matteo et al. (2020). This dataset records the responses of 25 subjects who watched part of the feature film "The Grand Budapest Hotel" by Wes Anderson.