Department Colloquium February 2024

Christoph Knochenhauer, TUM: 14:30 - 15:30

Partial differential equations are the backbone of many results in applied Mathematical Finance. For example, prices of derivative contracts can be characterized in terms of linear, parabolic, second-order PDEs, and solutions of optimal investment problems are intimately linked to fully nonlinear, parabolic or elliptic second-order equations of Hamilton-Jacobi-Bellman type. In this talk, we discuss to which extend this relationship can also be reversed in that existence, uniqueness, and regulartiy results on certain PDEs can be given a financial interpretation. In particular, we consider several examples including optimal investment problems for institutional or private investors and optimal execution problems for large agents such as hedge funds. We conclude with an outlook on work in progress on a new notion of differentiability designed to construct regular solutions of degenerate second-order PDEs.

Lorenz Panny, TUM: 16:00 - 17:00

The rise of quantum computing threatens the security of currently deployed cryptographic systems that are used, for instance, to secure the internet, as well as pretty much anything else that has a computer chip in it. In this presentation I intend to give a broad overview over the impact of these developments on our cryptographic world and discuss possible solutions to the impending catastrophe, with a particular focus on the mathematical aspects of post-quantum cryptography.