Federico Castillo

Email: efecastillo [dot] math [at] gmail [dot] com


I am a Profesor Asistente at the Departamento de Matemáticas de la Universidad Católica de Chile.

I received my PhD in June 2017 from University of California, Davis under the guidance of Fu Liu. I spent the Fall of 2017 at MSRI as a postdoc fellow. From 2018 to summer 2020 I was a Postdoc in the Department of Mathematics at the University of Kansas. And from fall 2020 to summer 2021 I was a postdoctoral researcher in the Nonlinear Algebra group of Bernd Sturmfels, at Max-Planck-Institut für Mathematik in den Naturwissenschaften (MiS) in Leipzig.

Here is my CV.


Research

My research interests lie in discrete geometry and algebraic combinatorics.

Preprints:

  1. Double Schubert polynomials do have saturated Newton polytopes, with Yairon Cid-Ruiz, Fatemeh Mohammadi, and Jonathan Montaño

  2. The permuto-associahedron revisited, with with Fu Liu.

  3. Common tangents to polytopes, with Joseph Doolittle, and Jose Samper

  4. An effective solution to convex 1-body N-representability, with Jean-Philippe Labbé, Julia Liebert, Arnau Padrol, Eva Philippe, and Christian Schilling.

  5. Foundation of one-particle reduced density matrix functional theory for excited states, with Jean-Philippe Labbé, Julia Liebert, and Christian Schilling.

  6. Minkowski summands of cubes, with Joseph Doolittle, Bennet Goeckner, Michael S. Ross, and Li Ying.

  7. Hopf monoids of ordered simplicial complexes, with Jose Samper and Jeremy Martin.


Publications:

  1. On the Todd Class of the Permutohedral variety, with Fu Liu.

    • Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 387-407. (2021).

  2. Finiteness theorems for Matroid Complexes with prescribed topology, with Jose Samper.

    • European Journal of Combinatorics (2021).

  3. When are multidegrees positive?, with Yairon Cid-Ruiz, Binglin Li, Jonathan Montaño and Naizhen Zhang.

    • Advances in Mathematics 374 (2020)

  4. Deformation cones of nested Braid fans, with Fu Liu.

    • International Math. Research Notices, (2020).

  5. Coxeter submodular functions and deformations of Coxeter permutahedra, with Federico Ardila, Chris Eur, and Alexander Postnikov.

    • Advances in Mathematics 365 (2020)

  6. A pithy look at the polytope algebra:

    • Proceedings of The 2018 Summer Workshop on Lattice Polytopes, Osaka University (2018).

  7. Smooth polytopes with negative Ehrhart coefficients, with Fu Liu, Benjamin Nill, and Andreas Paffenholz:

    • Journal of Combinatorial Theory Ser. A 160 (2018), 316-331

  8. Berline-Vergne valuation and generalized permutohedra, with Fu Liu:

  9. The topology of the external activity complex of a matroid, with Federico Ardila and Jose Samper:

    • Electronic Journal of Combinatorics, 23 (2016), P3.8.

  10. The arithmetic Tutte polynomials of the classical root systems, with Federico Ardila and Mike Henley:

    • International Math. Research Notices, (2015) 2015 3830-3877.


Selected Talks: