Research

Research Profiles

arXiv  —  Google Scholar  —  ORCID

Curriculum Vitæ

roi-docampo-cv-2026-04-29.pdf

Preprints

  1. Derived jet and arc spaces, R. Docampo, L. E. Miller and C. E. Overton-Walker, submitted for publication. arXiv:2604.08429
  2. Juggler's friezes, R. Docampo and G. Muller, submitted for publication. arXiv:2208.09025

Publications

  1. On arc fibers of morphisms of schemes, C. Chiu, T. de Fernex and R. Docampo, J. Eur. Math. Soc. 28 (2026), no. 4, 1489–1531. arXiv:2206.08060
  2. Embedding codimension of the space of arcs, C. Chiu, T. de Fernex and R. Docampo, Forum of Mathematics, Pi, 10 (2022), Paper No. e4, 37 pp. arXiv:2001.08377
  3. Nash blow-ups of jet schemes, T. de Fernex and R. Docampo, Ann. Inst. Fourier 69 (2019), no. 6, 2577–2588. arXiv:1712.00911
  4. Differentials on the arc space, T. de Fernex and R. Docampo, Duke Math. J. 169 (2020), no. 2, 353–396. arXiv:1703.07505
  5. The arc space of the Grassmannian, R. Docampo and A. Nigro, Adv. Math. 306 (2017), 1269–1332. arXiv:1510.08833
  6. Terminal valuations and the Nash problem, T. de Fernex and R. Docampo, Invent. Math. 203 (2016), no. 1, 303–331. arXiv:1404.0762
  7. Comparing multiplier ideals to test ideals on numerically Q-Gorenstein varieties, T. de Fernex, R. Docampo, S. Takagi, and K. Tucker, Bull. Lond. Math. Soc. 47 (2015), no. 2, 359–369. arXiv:1401.7946
  8. Jacobian discrepancies and rational singularities, T. de Fernex and R. Docampo, J. Eur. Math. Soc. 16 (2014), no. 1, 165–199. arXiv:1106.2172
  9. Arcs on determinantal varieties, R. Docampo, Trans. Amer. Math. Soc. 365 (2013), no. 5, 2241–2269. arXiv:1011.1930

PhD Thesis

thesis-roi-docampo.pdf

Teaching

Current teaching

Spring 2026 Applied Modern Algebra — Cryptography

Future teaching

Fall 2026 Calculus and Analytic Geometry III
Differential and Integral Calculus II

Past teaching

Fall 2025 Calculus and Analytic Geometry I
Spring 2025 Differential and Integral Calculus II — Honors
Physical Mathematics I
Fall 2024 Physical Mathematics I
Introduction to Differential Geometry I
Spring 2024 Topics in Algebra — Non-Archimedean Analytic Geometry
Fall 2023 Linear Algebra I — Honors
Spring 2023 Physical Mathematics I
Spring 2022 Introduction to Abstract Algebra II
Introduction to Topology
Graduate Algebra Literacy Course — p-adic and Motivic Integration
Fall 2021 Introduction to Abstract Algebra I
Calculus and Analytic Geometry III
Spring 2021 Applied Modern Algebra — Cryptography
Graduate Algebra Literacy Course — Singularities and Links
Fall 2020 Graph Theory
Introduction to Number Theory
Spring 2020 Calculus and Analytic Geometry II
Fall 2019 Senior Mathematics Seminar — Game Theory
Commutative Algebra
Fall 2018 Differential and Integral Calculus II
Abstract Algebra I
Spring 2018 Algebraic Geometry and Commutative Algebra II
Fall 2017 Discrete Math Structures
Algebraic Geometry and Commutative Algebra I
Spring 2017 Differential and Integral Calculus II
Graduate Algebra Literacy Course — Invariant Theory
Fall 2016 Linear Algebra I
Spring 2012 Foundations of Analysis II
Fall 2011 Foundations of Analysis II
Spring 2011 PDE's for Engineers
Special Topics in Algebraic Geometry — Berkovich Spaces
Fall 2010 Complex Variables
Spring 2010 Calculus II
Fall 2009 Calculus I

Contact

roi@ou.edu

University of Oklahoma
Department of Mathematics
601 Elm Avenue, Room 423
Norman, OK 73019

Office: PHSC 1121