Seminar

The STyLo seminar is a weekly internal meeting for members of the Systems, Types, and Logic group. It provides a space to present ongoing research, share preliminary results, and discuss papers relevant to the group’s themes such as type systems, categorical semantics, and formal methods for system verification.

When: Mondays at 11:00 (starting from week 38)
Where: Location announced via the mailing list

22 September 2025 – Smooth Maps

Given by Henning

We continue with the introduction to the smooth manifold theory. This time we do smooth maps.

15 September 2025 – Smooth Manifolds

Given by Henning

Today, I start to go through the equivalence between geometry and entropy and I will begin with a general introduction to smooth manifolds.

It is well-known that symplectic manifolds yield a measure, the Liouville measure, against one can define probability distributions and thus entropy. Surprisingly, this geometric structure, the symplectic form, can be reconstructed purely from the entropy. This comes from recent work by Gabriele Carcassi and collaborators, which I aim to go through in detail in the coming weeks. This will include the basics of symplectic manifolds and I aim to develop some category theoretical understanding around this result as well.

Reading

• John M. Lee, Introduction to Smooth Manifolds, vol. 218. in Graduate Texts in Mathematics, vol. 218. New York, NY: Springer, 2012. doi.
• P. Iglesias-Zemmour, Diffeology, 2nd edn. Beijing World Publishing Corporation, 2022. doi: 10.1090/surv/185. Download
• G. Carcassi and C. A. Aidala, ‘Hamiltonian mechanics is conservation of information entropy’, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, vol. 71, pp. 60–71, Aug. 2020, doi.