QM Meeting room (Ø10-401-1)
Holonomic functions are omnipresent in the sciences. These are functions that are solutions to sufficiently large systems of linear partial differential equations with polynomial coefficients. As such, they can be tackled by algebraic analysis: holonomic functions can be encoded by left ideals in the Weyl algebra, encoding annihilating differential operators. Examples include A-hypergeometric functions, Feynman integrals as well as some probability distributions, just to name a few. In this talk, I explain how to modify and read fundamental properties of holonomic functions in terms of algebro-geometric methods.
The second part of the talk is based on joint work with Carlos Rodriguez. Motivated from the theory of Hilbert schemes of points, we transfer the concept of border bases from zero-dimensional ideals in polynomial rings to the rational Weyl algebra in order to encode holonomic ideals. As an application, we visit differential equations behind a Feynman integral in dimensional regularization.
- Organizer: Centre for Quantum Mathematics
- Address: Campusvej 55, 5230 Odense M
- Contact Email: qm@sdu.dk
- Add to your calendar: https://eom.sdu.dk:443/events/ical/7ef9ac4d-e337-4e84-83d3-4c5d9d0fedae