Mathematical Colloquium
Upcoming talks:
| Tue 18 Nov 2025, 16:30: Laurent Jacques (UCLouvain) Implicit neural representations: towards a better understanding of their expressivity on the plane and the sphere |
| Representing and processing data in spherical domains presents unique challenges, primarily due to the curvature of the domain, which complicates the application of classical Euclidean techniques. Implicit neural representations (INRs) have emerged as a promising alternative for high-fidelity data representation; however, to effectively handle spherical domains, these methods must be adapted to the inherent geometry of the sphere to maintain both accuracy and stability. In this context, we propose Herglotz-NET (HNET), a novel INR architecture that employs a harmonic positional encoding based on complex Herglotz mappings. This encoding yields a well-posed representation on the sphere with interpretable and robust spectral properties. Moreover, we present a unified expressivity analysis showing that any spherical-based INR satisfying a mild condition exhibits a predictable spectral expansion that scales with network depth. Our results establish HNET as a scalable and flexible framework for accurate modeling of spherical data. Finally, inspired by the HNET analysis, we propose a common framework to understand the expressivity of the positional encodings used in Euclidean and spherical INRs. ____________________ Invited by Prof. Johannes Maly |
| Theresienstr. 39, München. Room A 027 |
| Wed 17 Dec 2025, 16:30: Tobias Ried (Georgia Tech) TBA |
| TBA ______________________________ Invited by Prof. Phan Thành Nam |
| Theresienstr. 39, München. Room A 027 |
| Tue 20 Jan 2026, 16:30: Sjoerd Dirksen (Utrecht University) TBA |
| TBA ___________________________ Invited by Prof. Johannes Maly |
| Theresienstr. 39, München. Room A 027 |
All lectures are on Tuesdays at 4:30 pm in lecture hall A027 unless otherwise noticed.
Looking for past events? You may find them in the Munich Mathematical Calendar.