Federico Castillo

Federico Castillo is an Assistant Professor in the Department of Mathematics at the Pontificia Universidad Católica de Chile. He holds a PhD from the University of California, Davis (2017), and has held postdoctoral positions at the University of Kansas (2018–2020) and the Max Planck Institute for Mathematics in the Sciences (MPI, 2020–2021). His research focuses on polytopes, Minkowski sums, polyhedral subdivisions, and lattice point enumeration, with computational applications in nonlinear algebra.

His academic trajectory includes postdoctoral fellowships at MSRI (2017) and MPI Leipzig (2020–2021). He organizes the Number Theory and Algebra Seminar (SaNTAS) with Giancarlo Lucchini and David Grimm. His work spans theoretical contributions to algebraic geometry and combinatorics, with interdisciplinary applications in mathematical physics and computational algebra.

Education:

• PhD in Mathematics, University of California, Davis (2017), advised by Prof. Fu Liu
• Postdoc, University of Kansas (2018–2020)
• Postdoc, MPI Leipzig Nonlinear Algebra Group (2020–2021)

Research Interests: Castillo’s work centers on polytopes and their combinatorial/geometric properties, including Minkowski decompositions, lattice point enumeration, and computational aspects of nonlinear algebra. He explores applications in algebraic geometry, discrete mathematics, and mathematical physics, often leveraging tools from commutative algebra and combinatorics.

Recent Contributions: His articles (2020–2024) address topics like permutohedra, Coxeter groups, matroid complexes, and N-representability problems in quantum chemistry. These contributions highlight his expertise in bridging abstract algebraic structures with computational methods.

Awards & Grants: No explicit awards listed, though his sustained research output reflects competitive grant support for postdoctoral work and collaborations.

Labs & Teams: Active organizer of events like AGREGA (Algebraic Geometry Research Group in the Andes) and Encuentro Colombiano de Combinatoria (ECCO). Co-organizes the SaNTAS seminar, fostering interdisciplinary dialog in algebra and number theory.