Isaac Konan

About me

I am a postdoc researcher in mathematics at Institut Camille Jordan (ICJ), Université Claude Bernard Lyon 1, under the supervision of Jehanne Dousse.
I am working on integer partition theory, a subject at the interface of number theory and combinatorics.
My thesis, entitled Rogers-Ramanujan type identities: bijective proofs and Lie-theoretic approach and supervised by Jeremy Lovejoy, was defended on 4/12/2020 at Université de Paris.

My main research concern is about studying Rogers-Ramanujan type identities and finding some bijections that explain these identities. This research orientation allows having a better understanding of the partitions' structure and permits to go beyond the original identities by generalizing them. I especially have an interest in the identities coming from the representation theory of affine Lie algebras. So far, my contribution has consisted in studying such identities in a combinatorial way and generalizing them, and finally going backward by finding suitable Lie algebras and representation that explain the generalizations of these identities. Some of my works are also related to statistical mechanics and graph theory.

Contact

Postal address :
Institut Camille Jordan
Université Claude Bernard Lyon 1
43 Boulevard du 11 novembre 1918
69622 Villeurbanne Cedex
France

e-mail : konan [at] math.univ-lyon1.fr

Papers and preprints

  1. Systematic study of Schmidt-type partitions via weighted words
    In preparation.
  2. The arithmetical combinatorics of k,l-regular partitions
    Preprint.
  3. A bijective proof and generalization of the non-negative crank- odd mex identity
    Preprint.
  4. Partitions identities from higher level crystals of A_1^{(1)} (with J. Dousse and L. Hardiman)
    Preprint.
  5. The (k,l)-Euler theorem and the combinatorics of (k,l)-sequences
    European journal of Combinatorics, 103 (2022), 103524.
  6. Multi-grounded partitions and character formulas (with J. Dousse)
    Advances in Mathematics, 400 (2022), 108275.
  7. Weighted words at degree two, II: flat partitions, regular partitions, and application to level one perfect crystals
    Electronic Journal of Combinatorics, 29 (2022), P1.54.
  8. Weighted words at degree two, I: Bressoud's algorithm as an energy transfer
    To appear in AIHPD.
  9. Generalisation of Capparelli's and Primc's identities, II: perfect A_{n-1}^{(1)} crystals and explicit character formulas (with J. Dousse)
    Preprint.
  10. Generalisation of Capparelli's and Primc's identities, I: coloured Frobenius partitions and combinatorial proofs (with J. Dousse)
    To appear in Advances in Mathematics.
  11. Beyond Gollnitz' Theorem II: arbitrarily many primary colors
    Journal of Combinatorial Theory Series A, 191 (2022), 105640.
  12. Beyond Gollnitz' Theorem I: A Bijective Approach
    Journal of Combinatorial Theory Series A, 180 (2021), 105426.
  13. A bijective proof and generalization of Siladic's Theorem
    European journal of Combinatorics, 87 (2020), 103101.

Publications in conference proceedings

  1. Multi-grounded partitions and character formulas
    FPSAC 2022, with J. Dousse, 12 pp.
  2. Beyond Göllnitz' Theorem I: A Bijective Approach
    FPSAC 2020, Séminaire Lotharingien de Combinatoire, 84B (2020), 12 pp.
  3. A Bijective Proof and Generalization of Siladić's Theorem
    FPSAC 2018, Séminaire Lotharingien de Combinatoire, 80B (2018), 12 pp.

Study projects

  1. Master's thesis, Autour des q-séries, des formes modulaires quantiques et des nœuds toriques ,July 2016 .
  2. Master MFA project, Borne de Weil et graphes de Cayley sur des corps finis , June 2015 .
  3. Licence MFA project, Formule de Pick pour Polygones non croisés avec sommets à coefficients entiers , March 2014 .

For more information (talks in seminars and conferences, teaching, etc) see CV .