Press & Research Highlights

What do drone navigation, shape analysis, and AI algorithms have in common? They all rely on computing optimal paths in curved geometric spaces. Among these, the Stiefel manifold—a mathematical space representing sets of orthonormal frames—plays a key role. Despite its importance, a crucial geometric quantity known as the injectivity radius had remained elusive—until now. Researchers from UCLouvain have cracked this problem, offering new insights that bridge deep theoretical geometry and real-world optimization methods.

Exoplanets are planets orbiting stars outside our solar system and are difficult to detect due to their faintness and the bright light of host stars. Traditional detection methods struggle to isolate planetary signals from noise. A team led by Professors Pierre-Antoine Absil, Laurent Jacques, and Nicolas Gillis, along with Dr. Hazan Daglayan Sevim, developed a low-rank approximation approach that utilizes sparse modeling and matrix completion to improve the separation of planetary signals from background noise. This method enhances signal-to-noise ratios, aiding in identifying hidden exoplanets, though it also presents new computational challenges related to accuracy and adaptability across different telescopes.