federico ardila
matemático
associate professor . san francisco state university
profesor adjunto . universidad de los andes . colombia


. research . teaching . cv . personal . sfsu-colombia combinatorics initiative .



Some recent talks

Computing arithmetic Tutte polynomials. (Congreso Colombiano de Matematicas 2013)
Matroids and Tutte polynomials. (SACNAS 2013)
Tilings. (International Mathematics Olympiad, Colombia 2013)
CAT(0) cubical complexes and moving robots. (MIT 2012)
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)
Double Hurwitz numbers as splines. (Joint Math. Meetings 2010)
The Hopf monoid of generalized permutohedra. (SIAM 2010)
Combinatorics and geometry of power ideals. (FPSAC 2009)
Tropical linear spaces. (MSRI minicourse, PRIMA congress 2008)
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)
Counting lattice points in polytopes. (SACNAS 2011)
Teselaciones. (Colombian Mathematics Congress public lecture 2005)

My research papers and preprints.

The closure of a linear space in a product of lines.
        with Adam Boocher
        (Submitted.)

Positively oriented matroids are representable.
        with Felipe Rincon and Lauren Williams
        (Journal of the European Math. Society, to appear.)

Positroids and non-crossing partitions.
        with Felipe Rincon and Lauren Williams
        (Transactions of the American Math. Society, to appear.)

The arithmetic Tutte polynomials of the classical root systems.
        with Federico Castillo and Mike Henley
        (International Math. Research Notices, to appear.)

Moving robots efficiently using the combinatorics of CAT(0) cubical complexes.
        with Tia Baker and Rika Yatchak
        (SIAM Journal of Discrete and Applied Mathematics 28 (2014) 986?1007.)

Two counterexamples for power ideals of hyperplane arrangements.
        with Alex Postnikov
        (Transactions of the American Mathematical Society, to appear.)

Universal polynomials for Severi degrees of toric surfaces.
        with Florian Block
        (Advances in Mathematics. 237 (2013) 165-193.)

Lifted generalized permutahedra and composition polynomials.
        with Jeff Doker
        (Advances in Applied Mathematics, 50 (2013) 607-633.)

Acyclic systems of permutations and fine mixed subdivisions of simplices.
        with César Ceballos
        (Discrete and Computational Geometry, 49 (2013) 485-510.)

Staircase Schur functions are P-Schur positive.
        with Luis Serrano
        (Journal of Algebraic Combinatorics, 36 (2012) 409-423.)

Geodesics in CAT(0) cubical complexes.
        with Megan Owen and Seth Sullivant
        (Advances in Applied Mathematics, 48 (2012) 142-163.)

Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann-Vinberg polytopes as marked poset polytopes.
        with Thomas Bliem and Dido Salazar
        (Journal of Combinatorial Theory Series A, 118 (2011) 2454-2462.)

Combinatorics and geometry of power ideals.
        with Alex Postnikov
        (Transactions of the American Mathematical Society 362 (2010) 4357-4384..)

Root polytopes and growth series of root lattices.
        with Matt Beck, Serkan Hosten, Julian Pfeifle, and Kim Seashore
        (SIAM Journal of Discrete Mathematics 25 (2011) 360-378.)

Matroid polytopes and their volumes.
        with Carolina Benedetti and Jeff Doker
        (Discrete and Computational Geometry 43 (2010) 841-854.)

When do two planted graphs have the same cotransversal matroid?
        with Amanda Ruiz
        (Boletin de la Sociedad Matematica Mexicana, 16 (2010) 63-73.)

Valuations for matroid polytope subdivisions.
        with Alex Fink and Felipe Rincon
        (Canadian Journal of Mathematics, 62 (2010) 1228-1245.)

Tropical hyperplane arrangements and oriented matroids.
        with Mike Develin
        (Mathematische Zeitschrift, 262 (2009) 795-816.)

Pruning processes and a new characterization of convex geometries.
        with Elitza Maneva
        (Discrete Mathematics, 309 (2009) 3083-3091.)

Flag arrangements and triangulations of products of simplices.
        with Sara Billey
        (Advances in Mathematics, 214 (2007) 495-524.)

Transversal and cotransversal matroids via their representations.
        (Electronic Journal of Combinatorics, 14 (2007), #N6.)

Bergman complexes, Coxeter arrangements, and graph associahedra.
        with Vic Reiner and Lauren Williams
        (Seminaire Lotharingien de Combinatoire, 54A (2006), Article B54Aj)

The positive Bergman complex of an oriented matroid.
        with Carly Klivans and Lauren Williams
        (European Journal of Combinatorics, 27 (2006), 577-591.)

The Bergman complex of a matroid and phylogenetic trees.
        with Carly Klivans
        (Journal of Combinatorial Theory, Series B, 96 (2006), 38-49.)

Subdominant matroid ultrametrics.
        (Annals of Combinatorics, 8 (2004), 379-389.)

Semimatroids and their Tutte polynomial.
        (Revista Colombiana de Matemáticas, 41 (2007) 39-66.)

Computing the Tutte polynomial of a hyperplane arrangement.
        (Pacific Journal of Mathematics, 230 (2007), 1-26.)

The Catalan matroid.
        (Journal of Combinatorial Theory, Series A., 104 (2003), 49-62.)

Enumerative and algebraic aspects of matroids and hyperplane arrangements.
        (my Ph.D. thesis, MIT, 2003).

The number of halving circles.
        (American Mathematical Monthly, 111 (2004), 586-592)

The coefficients of a Fibonacci power series.
        (Fibonacci Quarterly, 42 (2004), 202-204)

A generalization of Euler's R>=2r.
        (Crux Mathematicorum, 21 (1995), 1-2.) (Note.)



My expository papers and preprints.

Tres lecciones en combinatoria algebraica, I. Matrices totalmente negativas y funciones simétricas.
        with Emerson León, Mercedes Rosas, and Marcos Skandera
        (universo.math 1 (2014) No. 1, Artículo 5.)

Tres lecciones en combinatoria algebraica, II. Funciones simétricas y teoría de representaciones.
        with Emerson León, Mercedes Rosas, and Marcos Skandera
        (universo.math 1 (2014) No. 2, Artículo 5.)

Tres lecciones en combinatoria algebraica, III. Arreglos de hiperplanos.
        with Emerson León, Mercedes Rosas, and Marcos Skandera
        (universo.math, to appear.)

Tilings.
        with Richard Stanley
        (Clay Mathematics Institute Online Library; Mathematical Intelligencer 32 (2010) 32-43.)

Pflasterungen.
        translation of "Tilings" to German by Gunter Ziegler
        (Mathematische Semesterberichte, 53 (2006), 17-43.)

Teselaciones.
        translation of "Tilings" to Spanish by Carolina Benedetti
        (Gaceta de la Real Sociedad Matematica Espanola 14 (2011) 463-490.)

Some problems I have proposed.
        (an incomplete list)



My books.

Handbook of Enumerative Combinatorics
        with Miklos Bona et. al.
        (To appear.)

54th International Mathematical Olympiad, Shortlisted Problems with Solutions
        with Ilya Bogdanov, Geza Kós, Carlos Gustavo Tamm de Araújo Moreira and Christian Reiher
        (Santa Marta, Colombia, 2013.)

Problemas y soluciones de los entrenamientos de las Olimpiadas Colombianas de Matemáticas
        with Carlos Caicedo, Mary Falk de Losada and Carlos Vargas
        (Universidad Antonio Nariño, Bogotá, Colombia, yearly publications, 1997-2002.)



These are .pdf files. If you prefer another format, I will gladly send it to you.