Reza Mafi, Untitled, c. 1972, calligraphy on canvas
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I am a mathematician with an interest in theoretical computer science.
Since January 2025, I have been a postdoctoral researcher at Institut de Recherche en Informatique Fondamentale (IRIF) under the supervision of Mahsa Shirmohammadi.
I completed my PhD at the Institute de Mathématiques de Jussieu-Paris Rive Gauche (IMJ-PRG), Paris Cité University, under the supervision of Georges Skandalis and Stéphane Vassout.
I am a mathematician with an interest in theoretical computer science.
Since January 2025, I have been a postdoctoral researcher at Institut de Recherche en Informatique Fondamentale (IRIF) under the supervision of Mahsa Shirmohammadi.
I completed my PhD at the Institute de Mathématiques de Jussieu-Paris Rive Gauche (IMJ-PRG), Paris Cité University, under the supervision of Georges Skandalis and Stéphane Vassout.
Research
Research
My current research focuses on matrix semigroups in the analysis of weighted automata and context-free languages. In our recent work, we prove the computability of the Zariski closure for 1-VASS reachability and coverability languages, and the undecidability of computing such a closure for indexed languages. This result is part of an ongoing attempt to understand the open problem of computing the Zariski closure of context-free languages.
My doctoral research focuses on the study of pseudo-differential calculus, which is closely connected to Lie groupoids and their C*-algebras. The notion of a groupoid interpolates between groups and spaces, providing a natural framework for encoding deformations from spaces to groups. This becomes particularly relevant in constructing the tangent groupoid of a manifold, as introduced by Alain Connes, which was later recognized as an instance of the general notion of deformation to the normal cone. We advanced the theory of pseudo-differential operators using the built-in geometry of deformation to the normal cone space in two settings: when the space is endowed with a manifold structure and when, moreover, it is endowed with a Lie groupoid structure. This space provides distinct viewpoints, allowing us to examine the theory from different angles and adapt it to new contexts.
My current research focuses on matrix semigroups in the analysis of weighted automata and context-free languages. In our recent work, we prove the computability of the Zariski closure for 1-VASS reachability and coverability languages, and the undecidability of computing such a closure for indexed languages. This result is part of an ongoing attempt to understand the open problem of computing the Zariski closure of context-free languages.
My doctoral research focuses on the study of pseudo-differential calculus, which is closely connected to Lie groupoids and their C*-algebras. The notion of a groupoid interpolates between groups and spaces, providing a natural framework for encoding deformations from spaces to groups. This becomes particularly relevant in constructing the tangent groupoid of a manifold, as introduced by Alain Connes, which was later recognized as an instance of the general notion of deformation to the normal cone. We advanced the theory of pseudo-differential operators using the built-in geometry of deformation to the normal cone space in two settings: when the space is endowed with a manifold structure and when, moreover, it is endowed with a Lie groupoid structure. This space provides distinct viewpoints, allowing us to examine the theory from different angles and adapt it to new contexts.
Publication
Publication
Algebraic Closure of Matrix Sets Recognized by 1-VASS (with Rida Ait El Manssour, Mahsa Shirmohammadi, and James Worrell), SODA 2026
The Calculus of Pseudo-differential Operators: A Geometric Approach (with Georges Skandalis and Stéphane Vassout), working paper
A Result on Bounded Pseudo-differential Operators, working paper
Thesis
Thesis
The Calculus of Pseudo-differential Operators: A Geometric Approach, PhD Thesis
Connection on Lie Algebroids and on Derivation-based Noncommutative Geometry (in Persian), Master Thesis
Teaching
Teaching
My teaching experience includes leading exercise sessions (TD) and laboratory sessions (TP), taught in French, at the Department of Mathematics, Université Paris Cité, for the following courses:
2023/2024 Probabilités, TD, L2 (Course content: probability space, random variables, simple random walk)
2023/2024 Mathématiques en CUPGE, TD, L2 (Course content: topology of normed vector space, Hilbert Space, Fourier series)
2023/2024 Outils bureautiques et internet, TP, L1
2022/2023 Raisonment Mathématiques II, TD, L1 (Course content: topology of the real line)
2022/2023 Interactions Mathématiques - Physique I, TD, L1
2020/2021 Interactions Mathématiques - Physique I, TD, L1 (Course content: complex numbers, system of linear equations, revisions on usual functions and trigonometric functions)
2020/2021 Outils bureautiques et internet, TP, L1
Talks
Talks
Sept. 2025, On the Algebraic Closure of Context-Free Matrix Languages, Highlights 2025, Saarland University, Germany (slides)
Sept. 2025, Polynomial All Around Us, IFIP Working Group 2.2, Aachen, Germany (slides)
July. 2025, Algebraic Closure of Matrix Sets Recognized by 1-VASS, ICALP 2025 Workshop: LIAR, Aarhus University, Denmark (slides)
Dec. 2023, The C*-algebras of 0-order Pseudo-differential Operators on a Lie Groupoid, GDR Franco-German of Noncommutative Geometry, Institute Élie Cartan of Lorraine, France (slides)
May 2023, Deformation to the Normal Cone and Pseudo-differential Calculus, Functional Analysis Seminar, University of Oxford, England (slides)
May 2023, Deformation to the Normal Cone and Pseudo-differential Calculus, Noncommutative Geometry and Operator Algebras Conference, Hausdorff Center of Mathematics, Bonn, Germany (video)
Oct. 2022, Don't worry! We can always find a commutative space there.*, Master-PhD Meeting, IMJ-PRG, France
Jun. 2022, Deformation to the Normal Cone; a Geometric Approach to Pseudo-differential Calculus, GDR of Noncommutative Geometry, University of Caen Normandy, France
May 2022, Convolution Algebra of Pseudo-differential Operators on a Lie Groupoids, Seminar of Thésards, Sorbonne University, France
May 2022, An Introduction to K-theory and C*-algebras, The Bourbakette: PhD seminar, Paris Cité University, France
*This talk is not dedicated to Platonists!
Contact: mnaraghi at irif dot fr
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