Curriculum Vitae
Contact Information
Department of Mathematics
Indiana University Bloomington
Bloomington, IN 47405
jvillato (at) iu.edu
Education
Department of Mathematics, University of Illinois
Ph.D. in Mathematics, August 2018
- Dissertation Title: Stacks in Poisson Geometry
- Advisor: Rui Fernandes
University of Oklahoma
B.S. in Mathematics, May 2012
Academic Positions
Lecturer, Indiana University Bloomington
Fall 2024–Present
NSF Postdoc, Washington University in St. Louis
Spring 2022–Spring 2024 (Funded by MPS-Ascend grant, Award No. 2137999)
Guest, Max Planck Institute for Mathematics in Bonn, Germany
Fall 2021
Postdoctoral Fellow, KU Leuven in Belgium
September 2018–August 2021
Honors and Awards
- 2021: Awarded MPS Ascend Fellowship from the NSF
- 2017–2018: NSF AGEP (Alliances for Graduate Education and the Professoriate) Research support
- 2016: On UIUC’s ‘List of Teachers Ranked as Excellent’
- 2014: NSF AGEP Research support
- 2014: UIUC Research Board Award
- 2013: On UIUC’s ‘List of Teachers Ranked as Excellent’
- 2012–2013: UIUC GAAN (Graduate Assistance in Areas of National Need) Research Fellowship
Publications & Preprints
- David Miyamoto, Joel Villatoro, Regular diffeological groups (in preparation)
- Joel Villatoro, Pseudo-effective integrations of PMCTs (in preparation)
- Pooja Joshi, Joel Villatoro, On the holonomy of Lie algebroids, arXiv:2608.19399 (2026) (preprint) link
- Xiang Tang, Joel Villatoro, Simplicial sheaves of modules and Morita invariance of groupoid cohomology, arXiv:2509.07285 (2025) (preprint) link
- Angel Román, Joel Villatoro, Convolution algebras of double groupoids and strict 2-groups, SIGMA 20 (2024), 093, 26 pages link
- Joel Villatoro, On the integrability of Lie algebroids by diffeological spaces, Indagationes Mathematicae 37 (2026), no. 4, 1192–1242. link
- Joel Villatoro, On sheaves of Lie-Rinehart algebras, arXiv:2010.15463 (2020) (preprint) link
- Alfonso Garmendia, Joel Villatoro, Integration of Singular Foliations via Paths, International Mathematics Research Notices, Volume 2022, Issue 23, December 2022, Pages 18401–18445. link
- J. Villatoro. Picard groups of b-symplectic manifolds. Journal of Symplectic Geometry (2021), vol. 19, no. 3, 723–775. https://dx.doi.org/10.4310/JSG.2021.v19.n3.a6. link
- J. Villatoro, Stacks in Poisson Geometry. (2018 PhD Thesis). arXiv:1806.01939. link
- J. Villatoro. Poisson manifolds and their associated stacks. Letters in Mathematical Physics (2018), no. 3, 897–926. https://doi.org/10.1007/s11005-017-1012-5. link
Teaching Experience
Indiana University Bloomington
- Spring 2025–Spring 2026: Brief Calculus (Instructor, 4 sections) Introductory calculus course for non-STEM majors.
- Spring 2026: Math of Decision and Beauty (Instructor, 2 sections) Gen Ed topics course exploring mathematical ideas in decision-making and aesthetics.
- Fall 2025: First Year Seminar (Instructor) Seminar for first-year students on the transition to college.
- Fall 2024–Spring 2025: Calculus II (Instructor, 3 sections) Standard undergraduate calculus for STEM majors.
- Fall 2024: Calculus I (Instructor) Standard undergraduate calculus for STEM majors.
Washington University in St. Louis
- Fall 2022: Differential Equations (Instructor) Undergraduate course in differential equations.
- Spring 2022: Calculus of Several Variables (Instructor) Junior (300 level) course in multivariable calculus.
KU Leuven
- Spring 2021: Student Seminar Grader: Evaluate and provide feedback on individual bachelor student presentations
- Fall 2020: Differential Equations(TA): Monitor and advise students as they work individually on assigned exercises.
- Spring 2020: Symplectic Geometry(Instructor): Graduate level course. Design a curriculum based on a syllabus of required topics. Give lectures, write and grade exams and homework. Switched to synchronous lectures after COVID.
- Fall 2019: Wiskunde 1(TA): Single variable calculus for non-mathematics majors. Monitor and advise students as they work individually on assigned exercises.
University of Illinois at Urbana-Champaign
- 2012–2017: Teaching Assistant / Tutor: Calculus I, Calculus III, Linear Algebra.
Supervision
- Spring 2021: Bachelor project supervisor: Mentor a group of 6 Bachelor students in studying a new topic and preparing a presentation.
- Spring 2018: Illinois Geometry Lab: graduate student assistant. Graduate student supervisor for a team of students working on computation based research project about Poisson structures on Euclidean space.
- Fall 2017: Illinois Geometry Lab: graduate student assistant. Graduate student supervisor for a team of students working on computation based research project about modeling a partial differential equation.
Diversity Equity and Inclusion
- Fall 2023: Puertas College Prep: Organizer and mentor for Junior and Senior level highschool students from disadvantaged backgrounds.
- Spring 2023: WashU Mathematics DEI Committee: Served on the math department’s committee.
- Fall 2022: WashU Mathematics DEI Committee: Served on the math department’s committee.
- Fall 2022: Puertas College Prep Mentor and Organizer: Organizer and mentor for Junior and Senior level highschool students from disadvantaged backgrounds.
- 2015–2017: SLOAN Peer Mentor: Work with an assigned junior graduate student from underrepresented background. Provide mentorship, advise to mentee as they adapt to life as a new graduate student.
- Summer 2012: Project Transformation Camp Counselor: Worked at an educational summer camp for low income children in the OKC metro area.
Organizational Experience
- Summer 2025: Poisson Geometry, Lie Theory and Symmetry: Co-organizer of an international research conference held at Instituto Superior Técnico, Lisbon; co-PI on the NSF grant supporting U.S. participants. Contributed to scientific planning, speaker selection, and coordination of the event. https://sites.google.com/view/ipgls2025/
- Fall 2023: UIUC–WUSTL Joint Seminar Organizer: Co-organized a joint research seminar between the University of Illinois and Washington University in St. Louis.
- Spring 2022: WashU Geometry Seminar Organizer: Organized weekly research seminars in geometry.
- Fall 2022: WashU Geometry Seminar Organizer: Organized weekly research seminars in geometry.
- Spring 2021: AGEP-GRS Conference Steering Committee: Served on the steering committee for a graduate research symposium, contributing to planning and organization.
- Fall 2020: Junior Seminar Organizer: Organized and led a seminar for junior graduate students.
- Fall–Spring 2019–2020: KU Leuven Weekly Poisson Meetings Organizer: Organized regular research meetings in Poisson geometry.
- Fall–Spring 2018–2019: KU Leuven Weekly Poisson Meetings Organizer: Organized regular research meetings in Poisson geometry.
Service
- Spring 2026: IU First Year Seminar Advisory Team: Volunteer member. Gave feedback on the coordination of the First Year Seminar program and made recommendations on learning outcomes, resources and curriculum for future cohorts.
- Spring 2023: WashU Mathematics DEI Committee: Served on the math department’s committee.
- Fall 2022: WashU Mathematics DEI Committee: Served on the math department’s committee.
- Spring 2022: Washington University Math Club: Organized meetings for the undergraduate mathematics club.
- Spring 2022: Glenridge Elementary School Math Club: Mathematics outreach and lessons at local elementary school.
Selected Talks
- A (slightly different) way to integrate Lie algebroids, University of Illinois at Urbana-Champaign, Urbana, Illinois USA. (September 2026)
- The flow product and integrating algebroids, Geometry & Topology Seminar. Washington University in St. Louis, St. Louis, MO (March 2026).
- Singular spaces in Poisson and symplectic geometry, University of Toledo Department of Mathematics and Statistics Colloquium, Toledo, OH (October 2025).
- Haar systems and convolution algebras for double groupoids, Gone Fishing 2024. Northwestern University, Evanston, IL (April 2024).
- A diffeological approach to integrating infinite dimensional Lie algebras, Mathematics Colloquium. Central Michigan University, Mount Pleasant, MI (April 2023).
- Integration and differentiation for diffeological groupoids, 5-day workshop on Poisson Geometry, Lie Groupoids and Differentiable Stacks. BIRS, Banff (June 2022).
Recording: https://www.birs.ca/events/2022/5-day-workshops/22w5035/videos/watch/202206101030-Villatoro.html - Diffeological Solutions to the Integration Problem Gone Fishing (2020-2022). Savannah, GA (April 2022).
- A diffeological approach to solving the integration problem, Symplectic and Poisson Geometry Seminar. University of Illinois at Urbana-Champaign (April 2022).
- A diffeological approach to solving the integration problem, Geometry and Topology Seminar. Washington University in St. Louis, St. Louis, MO (February 2022).
- Diffeological vector bundles vs sheaves of modules, Western University. London, Ontario CA. (October 2020).
- On the homotopy theory and algebraic geometry of sheaves of Lie-Rinehart algebras, Junior Global Poisson Workshop 2020. Online, (September 2020).
Recording: https://www.youtube.com/watch?v=VFVr4xPkDRw&feature=emb_title - A path approach to holonomy for singular foliations, University of Illinois at Urbana-Champaign. Urbana, Illinois USA. (December 2019).
- Holonomy for Singular Foliations, University of Antwerp. Antwerp, Belgium. (November 2019).
- Symplectic Morita Equivalence and Stacks, Max Planck Institute for Mathematics. Bonn, Germany (February 2019).
- On the singularities of the Weinstein groupoid, Higher Geometric Structures along the Lower Rhine XII. Radboud University, Nijmegen, NL (January 2019).
- Transversely Integrable Lie Algebroids and Asymmetric Orbispaces, Utrecht University. Utrecht, Netherlands (October 2018).
- Geometric stacks for groupoids with geometry, Poisson 2018. University of Toronto, Toronto Canada (August 2018).
- Picard groups of b-symplectic manifolds, 3rd Pacific Rim Mathematical Association (PRIMA) congress. Instituto Tecnológico de Oaxaca, Oaxaca Mexico (August 2017).
- Morita type equivalences for non-integrable algebroids, Conference on Poisson Geometry and Stacks. The Fields Institute, University of Toronto (July 2017).
- Poisson manifolds and their associated stacks, 5-day workshop on Geometric Structures on Lie Groupoids. BIRS, Banff (April 2017).
Recording: https://www.youtube.com/watch?v=rEzlq8118CQ - Poisson manifolds and their stacks, Symplectic and Poisson Geometry Seminar. University of Illinois at Urbana-Champaign (March 2017).
- Picard Groups of b-Symplectic Manifolds Symplectic and Poisson Geometry Seminar. University of Illinois at Urbana-Champaign (October 2016).