My research focuses on the construction and characterization of non-semisimple Topological Quantum Field Theories (TQFTs), which provide topological invariants of 3-manifolds and representations of mapping class groups of surfaces. I am particularly interested in understanding the underlying categorical formalism, developing alternative combinatorial and homological models, and investigating applications to questions of geometric nature.
M. De Renzi, J. Martel, On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups, arXiv:2407.20644 [math.GT], 28 pages.
M. De Renzi, J. Martel, B. Wang, Hennings TQFTs for Cobordisms Decorated With Cohomology Classes, arXiv:2402.05103 [math.GT], 31 pages.
A. Beliakova, I. Bobtcheva, M. De Renzi, R. Piergallini, On Algebraization in Low-Dimensional Topology, arXiv:2312.15986 [math.GT], 96 pages.
M. De Renzi, J. Martel, Homological Construction of Quantum Representations of Mapping Class Groups, arXiv:2212.10940 [math.GT], 83 pages.
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], 34 pages.
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], 55 pages.
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], 35 pages.
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], 41 pages.
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], 62 pages.
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], 49 pages.
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], 37 pages.
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], 33 pages.
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], 52 pages.
M. De Renzi, Non-Semisimple Extended Topological Quantum Field Theories, Mem. Amer. Math. Soc. 277 (2022), no. 1364; arXiv:1703.07573 [math.GT], 172 pages.
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], 26 pages.
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], 18 pages.
M. De Renzi, Construction of Extended Topological Quantum Field Theories, Geometric Topology [math.GT], Université Sorbonne Paris Cité, 2017, English, NNT:2017USPCC114, tel-02003025.