federico ardila mantilla
chair in combinatorics . queen mary university of london
professor of mathematics . san francisco state university (on leave)


. research . teaching . society . outreach . cv . personal . interviews .

      . writing . talks .

            . research . expository .


Selected videos of research talks.

Cosmohedra.
        (Institute for Advanced Study, 2025)

Inequalities for trees and matroids.
        (Instituto de Matematica Pura e Aplicada, 2025)

Intersection theory of matroids: variations on a theme.
        (Institute for Advanced Study, 2025)

Intersection theory and combinatorics.
        (Latinx in Math, 2025)
        (with some story time on my math journey)

Non-linear spaces from linear spaces.
        (Harvard CMSA, 2023)

The geometry of geometries: matroid theory, old and new.
        (International Congress of Mathematicians, 2022)

Lagrangian geometry of matroids.
        (Mathematical Sciences Research Institute, 2020)
        (for an audience of algebraists)

Lagrangian geometry of matroids.
        (Matroid Seminar, 2020)
        (for an audience of combinatorialists)

The bipermutohedron and the harmonic polytope.
        (Max Planck Institute, 2021)

Cómo medir poliedros simétricos: los permutaedros de Coxeter.
        (Ceremonia de posesión, Academia Colombiana de Ciencias, 2021)

Algebraic structures on polytopes.
        (AMS Invited Address, Joint Mathematics Meetings 2018)

The geometry of matroids.
        (Tutte Distinguished Lecture Series, University of Waterloo, 2018)

Moving a robotic arm in a tunnel.
        (Mathematical Sciences Research Institute, 2017)

Matroids and tropical geometry.
        (Mathematical Sciences Research Institute, 2017)

Linearity in the tropics I.
Linearity in the tropics II.
        (Mathematical Sciences Research Institute, 2009)

Bergman Complexes and Coxeter Arrangements.
        (Mathematical Sciences Research Institute, 2004)


Selected slides from research talks.

The geometry of geometries: matroid theory, old and new.
        (International Congress of Mathematicians, 2022)

The Lagrangian geometry of matroids.
        (Arrangements at Home, 2020)

Measuring polytopes through their algebraic structure.
        (Algebra, Geometry, and Combinatorics Colloquium, 2020)

The equivariant Ehrhart theory of the permutahedron.
        (Seminario Sabanero de Combinatoria, 2019)

The geometry of matroids.
        (Tutte Distinguished Lecture Series, 2018)

The algebraic and combinatorial structure of generalized permutahedra.
        (plenary talk, Joint Math Meetings, 2018)

Using CAT(0) cube complexes to move robots efficiently.
        (MSRI, 2017)

Positroids, non-crossing partitions, and a conjecture of da Silva.
        (Princeton, 2015)

The closure of a linear space in a product of projective lines.
        (MIT, 2015)

Computing arithmetic Tutte polynomials.
        (plenary talk, Congreso Colombiano de Matematicas 2013)

Lifted generalized permutahedra and composition polynomials.
        (Joint Math. Meetings 2012)

Marked poset polytopes in representation theory.
        (FPSAC 2011)

Severi degrees of toric surfaces are eventually polynomial.
        (MIT 2010)

Combinatorics and geometry of power ideals.
        (FPSAC 2009)

Tropical linear spaces.
        (MSRI minicourse 2009)

Tropical oriented matroids.
        (MIT 2007)

Flag arrangements and triangulations of products of simplices.
        (Berkeley 2006)

Bergman complexes.
        (Latin American Algebra Colloquium 2005)

Computing the Tutte polynomial of a hyperplane arrangement.
        (FPSAC 2002)



Selected expository videos.

Hidden patterns: the shape of multiplication
        (2023 MAA Distinguished Lecture Series)

The cross ratio and Roberto Carlos's famous goal
        (Numberphile YouTube channel)

Combinatorics and higher dimensions
        (Numberphile YouTube channel)

The math of fútbol stickers and its second part and a bit of story time.
        (Numberphile YouTube channel)

Looking at perfect shuffles and its second part
        (Numberphile YouTube channel)

¿Las matematicas son inofensivas?
        (Derivando YouTube channel)

Robots, geometry, and society
        (Young Mathematicians Conference, 2021)

Cómo medir poliedros simétricos: los permutaedros de Coxeter.
        (Ceremonia de posesión, Academia Colombiana de Ciencias, 2021)

Cómo usamos la forma para conocer el mundo
        (Ciencia en Bicicleta, Parque Explora, 2016)


Selected slides from expository talks.

Hidden patterns: the shape of multiplication.
        (public talk, Museum of Mathematics, New York, 2022)

La matemática del mundial de fútbol.
        (public talk, Universidad del Norte, Barranquilla, 2018)

¿Cómo usamos la forma para conocer el mundo?
        (public talk, Ciencia en Bicicleta, Parque Explora, Medellin, 2016)

Matroids and Tutte polynomials.
        (SACNAS 2013)

Tilings.
        (International Mathematics Olympiad 2013)

Counting lattice points in polytopes.
        (SACNAS 2011)