Courses

Current courses at Loyola University Chicago.

Cursos

Cursos este semestre en Loyola University Chicago.

MATH 313/413 Abstract Algebra

This 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.

MATH 108 Real World Modeling


This course investigates mathematical modeling applied to a variety of topics such as linear programming, coding information, probability and statistics, scheduling problems and social choice.

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.
    Discrete Comput Geom 70, 1593–1631 (2023).

  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. R. S. González D'León, A. H. Morales, E. Philippe, D. Tamayo Jiménez, M. Yip. Realizing the s-Permutahedron via Flow Polytopes (extended abstract) .
    Sém. Lothar. Combin. 91B (2024), Art. 60, 12 pp. Proceedings of FPSAC 2024

  16. 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

  17. 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

  18. 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

  19. 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.

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

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

    22. Thesis and dissertations

    Tesis

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

  23. 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..

    Funded grants and projects

    Subvenciones y proyectos financiados

  1. AMS-Simons Research Enhancement Grants for PUI Faculty. PI: R. S. González D'León. Award amount 10800 USD.2024-2027

  2. NSF Conference: Research School: Bridges between Algebra and Combinatorics. PI: R. S. González D'León. DMS Award Number:2416063, Award amount 27000 USD. Start Date:05/01/2024

  3. MATH-AmSud collaboration. 22-MATH-01 ALGONCOMB: Algebraic structures supported in families of combinatorial objects.. International coordinator: R. S. González D'León. Local group coordinators: M. Ronco (Chile), A. Gonzalez (Uruguay), Y. Vargas (Venezuela), P.-L. Giscard (France), V. Pons (France), V. Pilaud (France). Award amount: 19300 EUR. 2022-2023

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

Activities

Actividades

Upcoming and recent seminars, conferences and meetings.

Seminarios, conferencias y encuentros próximos y recientes.

  • Oct 23, 2024. NC State Algebra & Combinatorics seminar. North Carolina State University, Raleigh, NC, USA
  • Sep 6, 2024. Colloquium of the Department of Mathematical Sciences. University of Wisconsin-Milwaukee, Milwaukee, WI, USA
  • June 17-28 2024, Encuentro Colombiano de Combinatoria ECCO 2024. http://ecco2024.combinatoria.co/. Universidad del Cauca, Popayán, Colombia.
  • June 10 - 14, 2024. Collaborate@ICERM Connections between Alcoved and Flow polytopes. The Institute for Computational and Experimental Research in Mathematics, Providence, RI, USA.
  • May 6-10, 2024. ISM Discovery School, Geometry and Combinatorics of Flow polytopes. http://ism.uqam.ca/flow/en/. Institut des sciences mathématiques Université du Québec à Montréal. Montréal, Québec, Canada.
  • Apr 20-21, 2024. Special Session on Posets in algebraic and geometric combinatorics, AMS Central Sectional Meeting. University of Wisconsin-Milwaukee, Milwaukee, WI, USA
  • Feb 25-27, 2024. Conference on Enumerative and Algebraic Combinatorics. University of Florida, Gainesville, FL, USA
  • Nov 29, 2023. Institute for mathematical and statistical innovation IMSI. Chicago, IL, USA
  • Nov 3, 2023. Carolina Math Seminar. Allen University, Columbia, SC, USA
  • Oct 16, 2023. Combinatorics seminar. Washington University St. Louis, St. Louis, MO, USA
  • Oct 30-31, 2023. Minisimposio álgebras, categorías, y combinatoria. Universidad Nacional de Colombia sede Medellín. Medellín, Colombia. https://sites.google.com/view/minisimposioacc2023/inicio
  • Oct 16, 2023. Combinatorics seminar. Washington University St. Louis, St. Louis, MO, USA
  • 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.

Co3

Comunidad Colombiana de Combinatoria.

ECCO

Encuentro Colombiano de Combinatoria

DIAS

Días de Combinatoria

Other activities of the community

Otras actividades de la comunidad

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