Relation between bicrossed products and crossed extensions of fusion categories
Revista de la Unión Matemática Argentina (2025)
Mathematician · Bloomington, Indiana
Héctor Martín Peña Pollastri
I work in quantum algebra and representation theory, with particular interests in Hopf algebras, quantum groups, and tensor and fusion categories. I received my Ph.D. in Mathematics from Universidad Nacional de Córdoba in 2021, under the supervision of Nicolás Andruskiewitsch.
RESEARCH INTERESTS
Hopf algebras · Quantum groups · Tensor & fusion categories · Representation theory
Curriculum vitae (PDF)
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Research
My research concerns Hopf algebras and their representations, including Nichols algebras and Drinfeld doubles. I also study tensor and fusion categories, their bicrossed products, and exact factorizations.
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Publications
Articles & proceedings
On the finite-dimensional representations of the double of the Jordan plane
Contemporary Mathematics 814 (2025)
On the double of the Jordan plane
Arkiv för Matematik 60(2), 213–229 (2022)
On the double of the (restricted) super Jordan plane
New York Journal of Mathematics 28, 1596–1622 (2022)
On the restricted Jordan plane in odd characteristic
Journal of Algebra and Its Applications 20(01), 2140012 (2021)
Preprints
On bicrossed product of fusion categories and exact factorizations
Preprint (2024)
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Teaching
Indiana University Fall 2025 · M301: Linear Algebra and Applications Spring 2025 · M502: Commutative Algebra (graduate course) Fall 2024 · M119: Survey in Calculus II Fall 2023 · M301: Linear Algebra and Applications Universidad Nacional de Córdoba Teaching in analysis, algebra, electromagnetism, and mathematical methods in physics. A complete teaching history is included in my CV.
Mentoring
I have mentored high school research through MIT PRIMES and undergraduate research at Indiana University, often jointly with Julia Plavnik and other collaborators.
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Curriculum vitae
Download CV (PDF)
Appointments
2022–2026 · Zorn Postdoctoral Fellow, Indiana University. Funded by the Simons Foundation. 2021–2022 · Postdoctoral Fellow, Universidad Nacional de Córdoba. Funded by CONICET. 2016–2021 · Doctoral Fellow, Universidad Nacional de Córdoba. Funded by CONICET.
Education
2021 · Ph.D. in Mathematics, Universidad Nacional de Córdoba. Advisor: Nicolás Andruskiewitsch. 2015 · Licenciatura in Physics, Universidad Nacional de Córdoba.
Service
Organizer, Quantum Algebra Seminar, Indiana University (2024–2025). Doctoral student representative, CIEM board of directors (2018–2021). Organizer, Training Camp Argentina competitive programming workshop (2019).
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Contact
For research, collaboration, and academic correspondence:
hmppollastri@gmail.com