Title:
Coherent state representations of exponential Lie groups
Abstract:
For an exponential Lie group G and an irreducible unitary representation π of G on a Hilbert space H, we consider the natural action defined by π on the projective space of H and show that the stabilisers of this action coincide with the projective kernel of π.
Using this, we prove that, if G is unimodular, then π admits a symplectic projective orbit, that is, π is a coherent state representation, if and only if π is square-integrable modulo its projective kernel. We also discuss the existence of coherent frames in the orbit of the action mentioned above.
This talk reports on joint work with J.T. van Velthoven (Univ. Vienna).
Title:
PDE techniques in Image Processing
Abstract:
Partial differential equations (PDEs) offer a powerful framework for understanding and processing images. In this talk, we present how ideas from geometry and optimization can be used to smooth images and detect meaningful structures. We introduce curvature-driven flows for shape regularization, variational approaches for image segmentation, and simple iterative algorithms such as the Merriman–Bence–Osher (MBO) scheme, which alternates diffusion and thresholding steps. We illustrate how these methods extend to a wide range of real-world applications, including the automated analysis of Scanning Tunneling Microscopy (STM) images, medical imaging, surface topography, and the restoration of degraded or historical documents.
Title:
Generic subsystems of a Smale Space
Abstract: TBA
Title:
Nets and realizability
Abstract:
We discuss the occurrence of symmetrical structures of matroids of net type as intersection lattices of arrangements of lines and we present several consequences of the existence of these structures on arrangements of lines.
Title:
Rational points on modular curves
Abstract:
The endeavor of provably computing rational points on curves stretches back millennia. In this talk, we focus on a particularly interesting class of curves—modular curves. These are moduli spaces that parametrize elliptic curves equipped with additional structure, and they offer a powerful setting in which to study rational points.