Sean Boros
Portrait of Sean Boros

Sean Boros

PhD Student, Department of Mathematics
Louisiana State University

I am a PhD student in mathematics at LSU working in matroid theory under the supervision of Prof. James Oxley. My research focuses on matroid connectivity.

Curriculum Vitae (PDF) sboros1@lsu.edu

Research

  1. On k-connected sets in matroids
    S. Boros and J. Oxley
    Submitted, arXiv:2610.29979, 2026. PDF arXiv
    Abstract

    In 1966, Tutte defined k-connected matroids for each k ≥ 2. Robertson and Seymour built on Tutte’s idea to define tangles as a way to identify highly connected parts of a matroid. Motivated by tangles, a set Z in a matroid M has been defined to be 3-connected if, for each j in {1, 2}, there is no j-separation (X, Y) of M such that each of |Z ∩ X| and |Z ∩ Y| is at least j. This paper solves a problem of Whittle for k = 3 by proving that a minor-minimal matroid having Z as a 3-connected set has at most 3|Z| − 4 elements. We also identify the matroids for which this bound is attained.

  2. On some structural properties of graphs with non-negative resistance curvature
    G. Agrahari, C. Bibby, S. Boros, H. Garcia, F. Heidercheidt, and Z. Wang
    Preprint, arXiv:2607.13169, 2026. PDF arXiv
    Abstract

    A graph is called resistance nonnegative (RN), respectively resistance positive (RP), if it admits positive edge weights such that all vertex resistance curvatures are nonnegative, respectively positive. In this paper, we study the structure of RN and RP graphs in relation to toughness, traceability, and Cartesian products. First, we disprove a conjecture of Fiedler and answer a question of Devriendt in the negative by constructing, for every n ≥ 11, an n-vertex 1-tough graph that is not RN. Second, we show that RP graphs need not be traceable by proving that the Thomassen 34-graph is RP but not traceable. Finally, we resolve a conjecture of Devriendt on grid graphs by proving that all Cartesian products of paths are RN.

Teaching

Calculus II: Lecture Series

Thirty recorded lectures from my five-week Summer 2026 MATH 1552 course, covering techniques of integration, improper integrals, sequences and series, power and Taylor series, parametric and polar curves, vectors and the geometry of space, and vector functions.

Watch on YouTube →

Teaching at LSU

Instructor of record

Recitation instructor

Mentoring

Contact

Department of Mathematics
Louisiana State University
349 Lockett Hall
Baton Rouge, LA 70803
sboros1@lsu.edu