My research focuses on the construction (and classification) of non-semisimple Topological Quantum Field Theories (TQFTs), which provide topological invariants of low-dimensional manifolds (dimension 3 and 4) and of codimension 2 embeddings (links and surfaces), as well as mapping class group representations. I am particularly interested in characterizing their properties, understanding the underlying categorical formalism, and developing alternative combinatorial and homological models, with the goal of investigating applications to questions of topological and geometric nature.
M. De Renzi, J. Martel, On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups, to appear in Ann. Inst. Fourier (Grenoble); arXiv:2407.20644 [math.GT].
M. De Renzi, J. Martel, B. Wang, Hennings TQFTs for Cobordisms Decorated With Cohomology Classes, to appear in Trans. Amer. Math. Soc.; arXiv:2402.05103 [math.GT].
A. Beliakova, I. Bobtcheva, M. De Renzi, R. Piergallini, Algebraic Presentation of 4-Dimensional 2-Handlebodies and 3-Dimensional Cobordisms, arXiv:2312.15986 [math.GT].
M. De Renzi, J. Martel, Homological Construction of Quantum Representations of Mapping Class Groups, arXiv:2212.10940 [math.GT].
A. Beliakova, M. De Renzi, Refined Bobtcheva–Messia Invariants of 4-Dimensional 2-Handlebodies, Essays in Geometry, 387–432, IRMA Lect. Math. Theor. Phys. 34, Eur. Math. Soc., Zürich, 2023; arXiv:2205.11385 [math.GT].
A. Beliakova, M. De Renzi, Kerler–Lyubashenko Functors on 4-Dimensional 2-Handlebodies, Int. Math. Res. Not. IMRN 2024 (2024), no. 13, 10005–10080; arXiv:2105.02789 [math.GT].
M. De Renzi, Extended TQFTs From Non-Semisimple Modular Categories, Indiana Univ. Math. J. 70 (2021), no. 5, 1769–1811; arXiv:2103.04724 [math.GT].
M. De Renzi, A. Gainutdinov, N. Geer, B. Patureau-Mirand, I. Runkel, Mapping Class Group Representations From Non-Semisimple TQFTs, Commun. Contemp. Math. 25 (2023), no. 1, 2150091; arXiv:2010.14852 [math.GT].
M. De Renzi, J. Murakami, Non-Semisimple 3-Manifold Invariants Derived From the Kauffman Bracket, Quantum Topol. 13 (2022), no. 2, 255–333; arXiv:2007.10831 [math.GT].
M. De Renzi, A. Gainutdinov, N. Geer, B. Patureau-Mirand, I. Runkel, 3-Dimensional TQFTs From Non-Semisimple Modular Categories, Selecta Math. (N.S.) 28 (2022), 42; arXiv:1912.02063 [math.GT].
C. Blanchet, M. De Renzi, J. Murakami, Diagrammatic Construction of Representations of Small Quantum 𝔰𝔩2, Transform. Groups 27 (2022), no. 3, 751–795; arXiv:1910.12427 [math.QA].
M. De Renzi, N. Geer, B. Patureau-Mirand, Non-Semisimple Quantum Invariants and TQFTs From Small and Unrolled Quantum Groups, Algebr. Geom. Topol. 20 (2020), no. 7, 3377–3422; arXiv:1812.10685 [math.GT].
M. De Renzi, N. Geer, B. Patureau-Mirand, Renormalized Hennings Invariants and 2+1-TQFTs, Comm. Math. Phys. 362 (2018), no. 3, 855–907; arXiv:1707.08044 [math.GT].
M. De Renzi, Non-Semisimple Extended Topological Quantum Field Theories, Mem. Amer. Math. Soc. 277 (2022), no. 1364; arXiv:1703.07573 [math.GT].
C. Blanchet, M. De Renzi, Modular Categories and TQFTs Beyond Semisimplicity, Topology and Geometry, 175–208, IRMA Lect. Math. Theor. Phys. 33, Eur. Math. Soc., Berlin, 2021; arXiv:2011.12932 [math.GT].
M. De Renzi, Quantum Invariants of 3-Manifolds Arising From Non-Semisimple Categories, Vestn. Chelyab. Gos. Univ. Mat. Mekh. Inform. 17 (2015), 26–40; arXiv:1703.07319 [math.GT].
M. De Renzi, Construction of Extended Topological Quantum Field Theories, Geometric Topology [math.GT], Université Sorbonne Paris Cité, 2017, English, NNT:2017USPCC114, tel-02003025.