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Dr. Kyle Broder, a researcher from the University of Brisbane in Australia, has been awarded the prestigious Marie Skłodowska-Curie postdoctoral fellowship. As part of this fellowship, he will conduct research on the curvature aspects of rigidity and flexibility of complex manifolds at the Faculty of Mathematics and Physics, University of Ljubljana, under the mentorship of professor Franc Forstnerič.

This research program will address the curvature properties of two important classes of complex manifolds: Kobayashi hyperbolic manifolds and Oka manifolds. These manifolds are characterized by a degree of holomorphic rigidity and flexibility, respectively, and have appeared in many branches of mathematics, from number theory to algebraic and differential geometry. A grasp of the curvature properties of these manifolds will offer valuable insights into their geometry, facilitate the generation of examples, and elucidate their relationship to important classes of manifolds - for instance, rationally connected manifolds, which play a central role in algebraic geometry.  

The experienced postdoctoral researcher has established major improvements in the Schwarz lemma, which is one of the main techniques that are used in the differential geometric study of Kobayashi hyperbolic manifolds. On the other hand, the field of Oka manifolds has seen tremendous growth primarily from the work of the host supervisor prof. Forstnerič, who is the world leader in the subject, and a world leader in complex analysis more generally.

Kyle Broder, who will be joining the UL FMF team in 2025, is currently working as a postdoctoral researcher at the University of Queensland, previously obtaining his doctorate through a joint program between the Australian National University and the University of Beijing.

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