Courses

Current courses at Loyola University Chicago.

Cursos

Cursos este semestre en Loyola University Chicago.

MATH 212 Linear Algebra

An introduction to linear algebra in abstract vector spaces with particular emphasis on Rn. Topics include: Gaussian elimination, matrix algebra, linear independence, span, basis, linear transformations, determinants, eigenvalues, eigenvectors, and diagonalization. Some of the basic theorems will be proved rigorously; other results will be demonstrated informally.

MATH 313/413 Abstract Algebra

TThis course provides a rigorous introduction to the study of structures such as groups, rings, and fields; emphasis is on the theory of groups with topics such as subgroups, cyclic groups, Abelian groups, permutation groups, homomorphisms, cosets, and factor groups.

Past courses

Cursos pasados

Research

Investigación

Articles, students and projects.

Artículos, estudiantes y proyectos.

    Preprints and publications

    Preimpresiones y publicaciones

  1. R. S. González D'León, J. Hallam., Y. A. Quiceno D. Whitney Twins, Whitney Duals, and Operadic Partition Posets.
    Arxiv:2307.07480

  2. R. S. González D'León, A. H. Morales, E. Philippe, D. Tamayo Jiménez, M. Yip. Realizing the s-permutahedron via flow polytopes.
    Arxiv:2307.03474

  3. R. S. González D'León, C. R. H. Hanusa, A. H. Morales, M. Yip. Column convex matrices, G-cyclic orders, and flow polytopes.
    Arxiv:2107.07326. Accepted for publication in Discrete Comput. Geom.

  4. M. von Bell, R. S. González D'León, F. A. Mayorga Cetina, M. Yip. A unifying framework for the ν-Tamari lattice and principal order ideals in Young's lattice .
    Combinatorica volume 43, pages479–504 (2023).

  5. N. Bergeron, R. S. González D'León, S. X. Li, C. Y. A. Pang, Y. Vargas. Hopf algebras of parking functions and decorated planar trees.
    Adv. Appl. Math. Volume 143, February 2023, 102436.

  6. R. S. González D'León, J. Hallam. The Whitney duals of a graded poset.
    J. Combin. Theory Ser. A. Volume 177, January 2021.

  7. C. Benedetti, R. S. González D'León, C. R. H. Hanusa, P. E. Harris, A. Khare, A. H. Morales, M. Yip. A combinatorial model for computing volumes of flow polytopes.
    Trans. Amer. Math. Soc. Volume 372, Number 5, 1 September 2019, Pages 3369–3404.

  8. C. Ceballos, R. S. González D'León. Signature Catalan Combinatorics.
    J. Comb. Volume 10, Number 4, 725–773, 2019.

  9. R. S. González D'León. A family of symmetric functions associated with Stirling permutations.
    J. Comb. Volume 10, Number 4, 675–709, 2019.

  10. R. S. González D'León. The colored symmetric and exterior algebras.
    J. Algebra 496 (2018), 187–215.

  11. R. S. González D'León. A note on the γ-coefficients of the tree Eulerian polynomial.
    Electron. J. Combin. Volume 23, Issue 1 (2016).

  12. R. S. González D'León, M. L. Wachs. On the (co)homology of the poset of weighted partitions.
    Trans. Amer. Math. Soc. 368 (2016) 6779-6818.

  13. R. S. González D'León. On the free Lie algebra with multiple brackets.
    Adv. Appl. Math. 79 (2016) 37-97.

  14. P. Brändén, R. S. González D'León. On the half-plane property and the Tutte-group of a matroid.
    J. Combin. Theory Ser. B. 100 - 2010.

    15. Refereed conference proceedings

    Artículos en conferencias evaluados por pares

  15. M. von Bell, R. S. González D'León, F. A. Mayorga Cetina, M. Yip. On framed triangulations of flow polytopes, the nu-Tamari lattice and Young's lattice .
    Sém. Lothar. Combin. 85B (2021), Art. 42, 12 pp. Proceedings of FPSAC 2021

  16. C. Benedetti, R. S. González D'León, C. R. H. Hanusa, P. E. Harris, A. Khare, A. H. Morales, M. Yip. The volume of the caracol polytope.
    Sém. Lothar. Combin. 80B (2018), Art. 87, 12 pp. Proceedings of FPSAC 2018

  17. R. S. González D'León, J. Hallam. Whitney labelings and 0-Hecke algebra actions on graded posets.
    Sém. Lothar. Combin. 80B (2018), Art. 88, 12 pp. Proceedings of FPSAC 2018

  18. R. S. González D'León, J. Hallam. Whitney duals of geometric lattices.
    Sém. Lothar. Combin. 78B (2017), Art. 82, 12 pp. Proceedings of FPSAC 2017.

  19. R. S. González D'León. The colored symmetric and exterior algebras (extended abstract).
    DMTCS proceedings BC, 2016, 575–586. Proceedings of FPSAC 2016.

  20. R. S. González D'León, M. L. Wachs. On the poset of weighted partitions.
    DMTCS Proceedings 01 (2013) 1029-1040. Proceedings of FPSAC 2013.

    21. Thesis and dissertations

    Tesis

  21. R. S. González D'León. Ph.D. Thesis - On the combinatorics of the free Lie algebra with multiple brackets.
    University of Miami, June 2014.

  22. R. S. González D'León. Master Thesis - Representing matroids by polynomials with the half-plane property.
    Kungliga Tekniska Högskolan, May 2009.

    Ongoing projects

    Projectos en curso

  1. R. S. González D'León, M. Wachs. (Co)homology of weighted bond posets, characteristic symmetric functions and tree associahedra.

  2. R. S. González D'León, J. Hallam. CW-labelings and the rooted forests semilattice.

  3. N. Avila Ramirez, S. Carrillo, R. S. González D'León. The \(\mu\)-polynomials of nestohedra..

  4. R. S. González D'León, J. Hallam, A. M. Giraldo, J. A. Samper. On minimal Whitney dual classes of geometric lattices..

  5. MATH-AmSud collaboration. ALGONCOMB: Algebraic structures supported in families of combinatorial objects..

    Students

    Estudiantes

  1. Andres Molina Giraldo - Pontificia Universidad Javeriana. Undergraduate thesis: On Whitney Duals of Geometric Lattices. June 5 of 2023.

  2. Sergio A. Fernández de Soto Guerrero. U. del Valle. Master thesis: A combinatorial connection between the nonnegative Grassmannian and the multilinear component of the bicolored exterior algebra. September 20 of 2022.

  3. Luis Alfonso Contreras Ordoñezo - U. Sergio Arboleda. Undergraduate thesis: Cover monoidal categories on species and free cover monoids. July 15 of 2022.

  4. Nicolas Avila Ramirez - U. Sergio Arboleda (coadvised with Sergio Carrillo).Undergraduate thesis: The \(\mu\)-polynomials of graph associahedra. June 30 of 2022.

  5. Edward Julian Salamanca Valencia. U. Sergio Arboleda. Master degree project: Sobre el método de reescritura en el estudio de operads no simétricos. April 19 of 2022.

  6. Camilo A. Hurtado Erasso. U. Sergio Arboleda. Master degree project: Generating pseudoknotted RNA skeleta using the combinatorics of Catalan objects and irreducible chord diagrams. August 4 of 2021.

  7. Yeison Quiceno. U. Nacional de Colombia sede Medellín. Master thesis: On Whitney duals of operadic posets. June 18 of 2020.

  8. Cesar Orozco - U. Sergio Arboleda. Undergraduate thesis: On Hopf algebras related to Segre powers of a partially ordered set on weak compositions and a family of generalizations of the Riemann zeta function. June 4 of 2020.

  9. Francisco Alfonso Mayorga Cetina - U. Sergio Arboleda. Undergraduate thesis: Characterizing dual graphs associated to triangulations of the Caracol flow polytope. March 10 of 2020.

    10. In progress
    En curso
  10. Zachary George - Loyola University Chicago. On the plethystic inverse of a combinatorial species.

  11. Brahayan Suarez- Pontificia Universidad Javeriana. Master degree project: Random generation of combinatorial families.

Activities

Actividades

Upcoming seminars, conferences and meetings.

Próximos seminarios, conferencias y encuentros.

  • Jul 28, 2023. Math REU DePaul University. Chicago, IL, USA
  • Jul 25, 2023. MathIly daily gather. Bryn Mawr College, Bryn Mawr, PA, USA
  • Jul 17 - 21, 2023. FPSAC - 35th International Conference on Formal Power Series and Algebraic Combinatorics. UC Davis, Davis, CA, USA
  • Jul 3 - 4, 2023. Journées Annuelles du GT CombAlg 2023. Paris, France
  • Jun 26 - 27, 2023. IV AlCoVE - Algebraic Combinatorics Virtual Expedition.
  • Jun 26, 2023. Seminar GT Combi du Plateau de Saclay. Saclay, France
  • Jun 21, 2023. Geometry Seminar. TU Graz, Graz, Austria
  • May 15 - 19, 2023. Collaborate@ICERM Computing Volumes of Flow Polytopes. The Institute for Computational and Experimental Research in Mathematics, Providence, RI, USA.
  • Apr 28, 2023. DePaul Algebra, Combinatorics, and Number Theory Seminar. Chicago, IL, USA
  • Apr 15, 2023. ALGECOM XXIII Algebra, Geometry and Combinatorics Day. ULoyola University Chicago, Chicago, IL, USA
  • Mar 2, 2023. Mathematics and Statistics Department Colloquium. Reed College, Portland, OR, USA
  • Feb 27, 2023. Department of Mathematics and Statistics Teaching Seminar. Loyola University Chicago, Chicago, IL, USA
  • Feb 6, 2023. Applied Algebra Seminar. York University, Toronto, ON, CA
  • Oct 14, 2022. Club de Matemática. Pontificia Universidad Católica de Chile, Santiago, Chile
  • Oct 11, 2022. Jornada de Matemáticas discretas. Universidad del Cauca, Popayán, Colombia
  • Oct 1 - 2, 2022. AMS Fall Eastern Sectional Meeting. University of Massachusetts-Amherst, Amherst, MA, USA
  • Sep 28, 2022. TACO Topology, Algebra, Combinatorics and Operators. Loyola University Chicago, Chicago, IL, USA
  • June 14-25 2022, Encuentro Colombiano de Combinatoria ECCO 2022. http://ecco2022.combinatoria.co/. Universidad de los Andes, Pontificia Universidad Javeriana y Universidad Sergio Arboleda, Bogotá, Colombia.
  • May 9 - 13, 2022. AIM workshop Ehrhart polynomials: inequalities and extremal constructions. American Institute of Mathematics, San Jose, CA, USA.
  • Program Committee FPSAC 2022 http://fpsac.org/confs/fpsac-2022/. Indian Institute of Science, Bangalore (India)
  • February 16, 2022 MSU Combinatorics and Graph Theory (C&GT) Seminar. Michigan State University, MI, USA.
  • September 13-17, 2021 Sesión temática en Combinatoria algebraica de funciones simétricas, cuasisimétricas y aplicaciones https://www.clam2020.cmat.edu.uy/. VI Congreso latinoamericano de Matemáticos. Universidad de la República, Montevideo, Uruguay.
  • May 28, 2021 Canadian Discrete and Algorithmic Mathematics Conference CANADAM, Online meeting, Canada.
  • March 15, 2021 Día internacional de las matemáticas. Politécnico Grancolombiano, Bogotá, Colombia.
  • March 12, 2021 Combinatorics, Algebra and Geometry Seminar (CAGS). George Mason University, Fairfax, VA, USA.
  • February 24, 2021 Coloquio Sergista de Matemáticas https://sites.google.com/view/colmatsergista/coloquios-de-matem%C3%A1ticas-universidad-sergio-arboleda/coloquio-sergista. Universidad Sergio Arboleda, Bogotá, Colombia.

Co3

Comunidad Colombiana de Combinatoria.

ECCO

Encuentro Colombiano de Combinatoria

DIAS

Días de Combinatoria

SeSaCo

Seminario Sabanero de Combinatoria

Contact

Contacto

Rafael S. González D'León

Assistant Professor

Department of Mathematics and Statistics
College of Arts & Sciences
Loyola University Chicago
1032 W. Sheridan Rd., Chicago, IL 60660, USA
Email: rgonzalezdleon at luc.edu