Laura Casabella - From PhD Success to Postdoc

We warmly congratulate Laura on the successful defense of her doctoral dissertation entitled “Regular Subdivisions in Algebraic, Tropical and Metric Geometry.” Her research lies at the intersection of polyhedral and tropical geometry, combinatorics, and commutative algebra, with strong connections to algebraic geometry and the theory of metric spaces.

In her thesis, Laura investigates regular subdivisions of point configurations, a fundamental combinatorial structure that appears across many areas of mathematics. She studies their role in algebraic, tropical and metric geometry, including applications to polynomial systems, tropical curves, and the geometry of hypersimplices. Her work combines deep theoretical insights with large-scale computational methods, pushing current algorithmic techniques to their limits.

Among her key contributions are new results on real solutions of polynomial systems arising from lattice triangulations, a complete classification of smooth tropical elliptic curves in three-dimensional space, and advances in the understanding of secondary fans of hypersimplices and their connection to metric spaces on finite point sets.

Laura obtained her Bachelor's degree in Mathematics from the University of Catania, and a joint Master's degree in Algebra, Geometry, and Number Theory (ALGANT) at University of Padova and University of Bordeaux. Her supervisor was Alessio Sammartano. She completed her PhD at our institute under the supervision of Michael Joswig and Marta Panizzut. Laura has now started a postdoctoral position at Goethe University Frankfurt in the group of Raman Sanyal, funded by the DFG Priority Programme SPP 2458 “Combinatorial Synergies.”

“I am very grateful to the MPI MiS community—for both the scientific and administrative support—for creating such an inspiring and welcoming environment over the past three years”, she says.

We wish Laura all the best in this exciting next step in her academic career and in her personal life.