Publications

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.

Articles

• 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 (2023), rnac039; 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.

Monographs

• 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.

Surveys

• 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.

Ph.D. Thesis

• M. De Renzi, Construction of Extended Topological Quantum Field Theories, Geometric Topology [math.GT], Université Sorbonne Paris Cité, 2017, English, NNT:2017USPCC114, tel-02003025.