~bcody/
Photo of Brent Cody
fig. 1 — the author

Brent Cody

Associate Professor, Department of Mathematics and Statistics

Virginia Commonwealth University

email: bmcody@vcu.edu cv: Cody_CV_2026.pdf elsewhere: Google Scholar · arXiv · VCU · ORCID

§1

Research Overview

My primary research is in set theory, especially large cardinals and forcing. Much of my recent work centers on higher (or diagonal) indescribability and its connections to the Ramsey and ineffability hierarchies [13], [15] and to derived topologies on ordinals [18], [23]. Current work studies diagonal square principles and indescribability in \(L\) [a]. Two of my set theory papers are joint with students [16], [19].

I also work in graph theory. My interest in this area grew out of connections between mathematics and music theory, specifically maximally even sets and Euclidean rhythms [20], [21]. Much of my graph theory research, on extremal vertex sets and metric general position problems, is joint with students [20]–[22], [24], [25], [b].

Recent activity

  • May 2027Local organizer, Virginia Academy of Science Annual Meeting at VCU.
  • Summer 2026Dean’s Research Grant funding summer research with undergraduates Rose Detore and Garrett Moore.
  • May 2026Rose Detore won the Best Poster Award at the Virginia Academy of Science Annual Meeting for our joint work [25], [b].
  • Mar 2026Invited talk, AMS Western Sectional Meeting, Boise State University.
  • 2026“Two-cardinal derived topologies, indescribability and Ramseyness” (with Lambie-Hanson and Zhang) appeared in the Journal of Symbolic Logic [23].
§2

Papers

2012–present

* undergraduate and † graduate student coauthors

In preparation

  1. [a]
    Diagonal hypersquares. (with Joan Bagaria) In preparation.
  2. [b]
    Metric general position graph invariants and graph powers. (with Rose Detore*) In preparation.

Submitted & published

  1. [25]
    Metric general position extensions of classical graph invariants and perfection. (with Rose Detore*) Submitted [pdf]
  2. [24]
    The Wiener index of vertex colorings. (with Viktoriya Bardenova†, Neal Bushaw, Paul Fay† and Maya Tennant†) Submitted [pdf]
  3. [23]
    Two-cardinal derived topologies, indescribability and Ramseyness. (with Chris Lambie-Hanson and Jing Zhang) Journal of Symbolic Logic, 91 (3): 1260–1288, 2026. [doi] [pdf]
  4. [22]
    The \(k\)-general \(d\)-position problem for graphs. (with Garrett Moore*) Discrete Applied Mathematics, 366: 135–151, 2025. [doi] [pdf]
  5. [21]
    Sets of vertices with extremal energy. (with Neal Bushaw and Chris Leffler*) Discrete Mathematics, 348 (7): Paper No. 114466, 17 pp., 2025. [doi] [pdf]
  6. [20]
    The Music and Mathematics of Maximally Even Sets. (with Neal Bushaw, Luke Freeman* and Tobias Whitaker) Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture, pp. 61–68, 2024. [pdf]
  7. [19]
    Two-cardinal ideal operators and indescribability. (with Philip White†) Annals of Pure and Applied Logic, 175 (8): Paper No. 103463, 17 pp., 2024. [doi] [pdf]
  8. [18]
    Higher indescribability and derived topologies. Journal of Mathematical Logic, 24 (1): Paper No. 2350001, 48 pp., 2024. [doi] [pdf]
  9. [17]
    Large cardinal ideals. Research Trends in Contemporary Logic (College Publications), accepted 2020; volume forthcoming. 49 pp. [pdf]
  10. [16]
    Sparse analytic systems. (with Sean Cox and Kayla Lee*) Forum of Mathematics, Sigma, 11: Paper No. e58, 9 pp., 2023. [doi] [pdf]
  11. [15]
    Ideal operators and higher indescribability. (with Peter Holy) Journal of Symbolic Logic, 88 (2): 835–873, 2023. [doi] [pdf]
  12. [14]
    Forcing a \(\square(\kappa)\)-like principle to hold at a weakly compact cardinal. (with Victoria Gitman and Chris Lambie-Hanson) Annals of Pure and Applied Logic, 172 (7): 102960, 26 pp., 2021. [doi] [pdf]
  13. [13]
    A refinement of the Ramsey hierarchy via indescribability. Journal of Symbolic Logic, 85 (2): 773–808, 2020. [doi] [pdf]
  14. [12]
    Characterizations of the weakly compact ideal on \(P_\kappa\lambda\). Annals of Pure and Applied Logic, 171 (6): Paper No. 102791, 23 pp., 2020. [doi] [pdf]
  15. [11]
    The weakly compact reflection principle need not imply a high order of weak compactness. (with Hiroshi Sakai) Archive for Mathematical Logic, 59 (1): 179–196, 2020. [doi] [pdf]
  16. [10]
    Adding a non-reflecting weakly compact set. Notre Dame Journal of Formal Logic, 60 (3): 503–521, 2019. [doi] [pdf]
  17. [9]
    Rigid ideals. (with Monroe Eskew) Israel Journal of Mathematics, 224 (1): 343–366, 2018. [doi] [pdf]
  18. [8]
    Indestructibility of generically strong cardinals. (with Sean Cox) Fundamenta Mathematicae, 232 (2): 131–149, 2016. [doi] [pdf]
  19. [7]
    The least weakly compact cardinal can be unfoldable, weakly measurable and nearly \(\theta\)-supercompact. (with Moti Gitik, Joel David Hamkins, and Jason Schanker) Archive for Mathematical Logic, 54 (5–6): 491–510, 2015. [doi] [pdf]
  20. [6]
    Easton's theorem for Ramsey and strongly Ramsey cardinals. (with Victoria Gitman) Annals of Pure and Applied Logic, 166 (9): 934–952, 2015. [doi] [pdf]
  21. [5]
    Easton functions and supercompactness. (with Sy Friedman and Radek Honzik) Fundamenta Mathematicae, 226 (3): 279–296, 2014. [doi] [pdf]
  22. [4]
    On Supercompactness and the continuum function. (with Menachem Magidor) Annals of Pure and Applied Logic, 165 (2): 620–630, 2014. [doi] [pdf]
  23. [3]
    Easton's Theorem in the presence of Woodin cardinals. Archive for Mathematical Logic, 52 (5–6): 569–591, 2013. [doi] [pdf]
  24. [2]
    Consecutive singular cardinals and the continuum function. (with A. W. Apter) Notre Dame Journal of Formal Logic, 54 (2): 125–136, 2013. [doi] [pdf]
  25. [1]
    The failure of GCH at a degree of supercompactness. Mathematical Logic Quarterly, 58 (1–2): 83–94, 2012. [doi] [pdf]

Pictures from the papers

Diagram with j(κ), κ, j(θ), the image j''H, a generic g and a set A, illustrating how a generic ultrafilter is modified to lift an elementary embedding
fig. 2Modifying generic ultrafilters to lift elementary embeddings [1], [4], [5], [8].
Tree diagram comparing the Ramsey operator applied to two indescribability ideals, with height alpha equal to ot(beta_1 minus beta_0) times omega
fig. 3The Ramsey hierarchy and transfinite indescribability [13], [15], [19], [23].
Three Möbius ladders with minimal energy vertex subsets shaded black
fig. 4Minimizers on Möbius ladders [21].
Formula defining the restriction of an infinitary formula phi to alpha as a conjunction of restrictions of formulas psi
fig. 5Restrictions of infinitary formulas [18], [15], [a].
Diagram of heptatonic scales drawn as seven-vertex subsets of a 12-cycle, connected in order of increasing energy
fig. 6Heptatonic (seven-note) scales arranged in order of increasing energy from left to right, from [20].
Diagram of triads drawn as three-vertex subsets of a 12-cycle, with their energies, in order of increasing energy
fig. 7Triads arranged in order of increasing energy from left to right, from [20].
§3

Research With Students

I have worked on research projects in set theory and graph theory with many undergraduate and graduate students. Students have co-authored seven of my papers, five published and two submitted [16], [19]–[22], [24], [25], with another in preparation [b]. Student research has been supported by VCU’s Undergraduate Research Opportunities Program (UROP) and a College of Humanities and Sciences Dean’s Research Grant.

Student highlight: Rose Detore won the Best Poster Award at the Virginia Academy of Science Annual Meeting in May 2026, chosen from roughly 50 student posters across all areas of science. See [25], [b].

  • Ky-Quan Pham2026
  • Rose Detore [25] [b]2025–2026
  • Maya Tennant [24]2024–2025
  • Paul Fay [24]2024–2025
  • Viktoriya Bardenova [24]2024–2025
  • Garrett Moore [22]2024 & 2026
  • Alex Johnson2024
  • Chris Leffler [21]2023–2024
  • Luke Freeman [20]2023–2024
  • Kayla Lee [16]2022
  • Philip White [19]2020–2021
A graph G on eight vertices, properly colored with four colors, and its square G squared
fig. 8A \((2,2)\)-perfect graph \(G\) (left) with \(G^2\) (right) not perfect [25].

Master's Thesis Advised

Philip White, Some intuition behind large cardinal axioms, their characterization, and related results, 2019

Students interested in a research project, including a summer UROP project (please contact me by December), are welcome to email me.

§4

Teaching

CourseTitleSyllabi & notes
MATH 201Calculus with Analytic Geometry IIspring 2026, spring 2022, fall 2020
MATH 300Introduction to Mathematical Reasoningspring 2025, fall 2023, fall 2016
MATH 301Differential Equationsspring 2019
MATH 310Linear Algebrafall 2026, spring 2022, spring 2019
MATH 407Advanced Calculusfall 2021
MATH 409General Topologyfall 2019
MATH 490Mathematical Expositionsspring 2021, fall 2020, spring 2018
MATH 492Independent StudySpring 2015 computability theory and Gödel’s Incompleteness Theorems with Philip White; Fall 2014 forcing with Samuel Dworetzky; Spring 2014 set theory with Samuel Dworetzky
MATH 493Mathematical Sciences InternshipSpring 2016 with Lynh Tran, Spring 2018 with Tobechi Okoli
MATH 502Abstract Algebra Ifall 2023
MATH 556Graph Theoryfall 2026
MATH 591Topics – Filters, ultrafilters and applicationspring 2017, taught jointly with Sean Cox and Monroe Eskew
MATH 591Topics – Logic and Mathematical Structuresspring 2014, taught jointly with Sean Cox, notes
MATH 602Abstract Algebra IIspring 2020
MATH 697Directed Researchforcing and large cardinals with Philip White
MATH 698ThesisPhilip White's thesis has been cited by Buhagiar and Dz̆amonja