Felix Gotti

UC Berkeley

Research Interest:

Algebra and Combinatorics: In algebra, I am mostly interested in the study of the phenomenon of non-uniqueness of factorizations into irreducibles in integral domains and atomic monoids using techniques of number theory, combinatorics, and convex geometry. My research in combinatorics focuses on posets and matroids. I am also interested in polytopes, cluster algebras, finite groups, and graphs.

Scientific Publications:

  1. On the system of sets of lengths and the elasticity of submonoids of a finite-rank free commutative monoid
    Journal of Algebra and Its Applications (to appear)
    Available on Arxiv: https://arxiv.org/pdf/1806.11273.pdf
  2. The elasticity of Puiseux monoids
    (with C. O'Neill)
    Journal of Commutative Algebra (to appear)
    DOI: https://projecteuclid.org/euclid.jca/1523433696
  3. On the molecules of numerical semigroups, Puiseux monoids, and Puiseux algebras
    (with M. Gotti)
    Springer INdAM Series: Proceedings of the IMNS (to appear)
    Available on Arxiv: https://arxiv.org/pdf/1702.08270.pdf
  4. Increasing positive monoids of ordered fields are FF-monoids
    Journal of Algebra, Vol. 518 (2019) 40-56.
  5. Systems of sets of lengths of Puiseux monoids
    Journal of Pure and Applied Algebra, Vol. 223 (2019) 1856-1868.
  6. How do elements really factor in Z[sqrt(-5)]?
    (with S. Chapman and M. Gotti),
    In: Advances in Commutative Algebra (2019), Eds. A. Badawi and J. Coykendall
    Springer Trends in Mathematics, Birkhäuser, Singapore.
  7. Puiseux monoids and transfer homomorphisms
    Journal of Algebra, Vol. 516 (2018) 95-114.
  8. Minimal presentations of shifted numerical semigroups
    (with R. Conaway, J. Horton, C. O'Neill, R. Pelayo, M. Williams, and B. Wissman)
    International Journal of Algebra and Computations, Vol. 28 (2018) 53-68.
  9. Atomicity and boundedness of monotone Puiseux monoids
    (with M. Gotti)
    Semigroup Forum, Vol. 96 (2018) 536-552.
  10. Dyck paths and positroids from unit interval orders
    (with A. Chavez)
    Journal of Combinatorial Theory Series A, Vol. 154 (2018) 507-532.
  11. On the atomic structure of Puiseux monoids
    Journal of Algebra and its Applications, Vol. 16 (2017) 1750126.
  12. On delta sets and their realizable subsets in Krull monoids with cyclic class groups
    (with S. Chapman and R. Pelayo)
    Colloquium Mathematicum, Vol. 137 (2014), 137-146.
  13. On positroids induced by rational Dyck paths
    Séminaire Lotharingien de Combinatoire, Vol. 80B (2018) 12pp.
  14. Dyck paths and positroids from unit interval orders
    (with A. Chavez)
    Séminaire Lotharingien de Combinatoire, Vol. 78B (2017) 12pp.
  15. Manuscripts Submitted to Peer-Reviewed Journals:

  16. Atomic and antimatter semigroup algebras with rational exponents
  17. Factorization invariants of Puiseux monoids generated by geometric sequences
    (with S. T. Chapman and M. Gotti)
  18. Tilings and matroids on regular subdivisions of a triangle
    (with H. Polo)
  19. Positroids induced by rational Dyck paths