Karin Melnick

Karin Melnick is a Full Professor in Mathematics at the University of Luxembourg, Faculty of Science, Technology and Medicine, Department of Mathematics. She heads the research group Group Actions, Geometric Structures, and Smooth Dynamics. Previously, she held positions at the University of Maryland (2009–2023), where she advanced from Assistant Professor to Professor and Associate Chair for Faculty Affairs, and at Yale University (2006–2009).

Education:

• PhD and Master's degrees from the University of Chicago

Research Interests: Her work spans differential-geometric rigidity, Lorentzian geometry, conformal pseudo-Riemannian structures, parabolic Cartan geometries, and smooth dynamical systems. She investigates symmetries of geometric structures, classification of manifolds with prescribed curvature properties, and dynamics of group actions on differentiable manifolds.

Publications: Melnick's 15 most recent articles (2011–2025) predominantly explore rigidity phenomena in geometric structures, conformal/Lorentzian geometry, and dynamical systems. Key themes include automorphism groups of parabolic geometries, embedding theorems for tractor bundles, non-existence results for quasihomogeneous metrics, and applications of Frobenius-type theorems to Cartan geometries.

Academic Leadership: She organizes major conferences including the upcoming BeNeLux Mathematical Congress (2026) and Lorentzian, Affine, and Hyperbolic Geometry: In Memory of Todd Drumm (2025). She frequently delivers invited talks at institutions like IHES Paris, Isaac Newton Institute, and Universität Hamburg.

Teaching: Currently instructs Géométrie des courbes et des surfaces (Summer 2025).