# 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.

## Santiago Number Theory and Algebra Seminar (SaNTAS)

Este semestre estamos organizado santas con Giancarlo Lucchini y David Grimm. Mas informacion AQUI.

## Conferencias

Organizador de Dias de Combinatoria 2023 en la Universidad Industrial de Santander.

## Research

My research interests lie in discrete geometry and algebraic combinatorics.

**Preprints:**

K-polynomials of multiplicity-free varieties, with Yairon Cid-Ruiz, Fatemeh Mohammadi, and Jonathan Montaño

Partial Permutohedra, with Roger Behrend, Anastasia Chavez, Alexander Diaz-Lopez, Laura Escobar, Pamela E. Harris, Erik Insko

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

Common tangents to convex bodies, with Joseph Doolittle, and Jose Samper

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

**Publications:**

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

*Annales Henri Poincaré, to appear.*

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

*Journal of Chemical Theory and Computation,**(2022) , 18, 1, 124–140.*

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

*Bulletin of London Mathematical Society,*(2022), 54: 996-1009.

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

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

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

*European Journal of Combinatorics*(2021).

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

*Advances in Mathematics***374**(2020)

Deformation cones of nested Braid fans, with Fu Liu.

*International Math. Research Notices*, (2020).

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

*Advances in Mathematics***365**(2020)

A pithy look at the polytope algebra.

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

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

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

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

*Discrete and Computational Geometry***60**(2018), no. 4, 885-908. journal online version

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

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

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:**

Todd Class of the permutohedral variety, FPSAC, July 2020.

Newton polytopes of Multidegrees. KUMUNU, September 2019.

Uniqueness of Symmetric McMullen formulas in braid fan. Reed's College Colloquium, April 2018.

Deformation cones of polytopes. BAD math day, October 2017