I am mainly interested in representation theory, quantum groups, tensor categories, categorification, and exploring applications of these areas to low-dimensional topology and mathematical physics. Some of my research focuses on non-commutative generalizations of symmetric functions.
My research can best be classified with in the areas of Representation Theory (for example, of braided bialgebras, monoidal categories or 2-categories), Quantum Algebra (Hopf algebras, Nichols algebras, etc), Diagrammatic Tensor Categories, and further work in Noncommutative Algebra (Koszul algebras, noncommutative symmetric functions).
Part of my recent work relates to categorification (joint work with Vanessa Miemietz and You Qi). My work with Vladimir Retakh falls into the area of noncommutative geometry.
My preprints are also available on the arXiv.
List of Publications and Preprints
[1] Johannes Flake, Robert Laugwitz, and Sebastian Posur. Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers. arXiv preprint arXiv:2410.08702, 2024. doi: 10.48550/arXiv.2410.08702.
[2] Cameron Kemp, Robert Laugwitz, and Alexander Schenkel. Infinitesimal 2-braidings from 2-shifted Poisson structures. arXiv preprint arXiv:2408.00391, 2024. doi: 10.48550/arXiv.2408.00391.
[3] Johannes Flake, Robert Laugwitz, and Sebastian Posur. Projection formulas and induced functors on centers of monoidal categories. arXiv preprint arXiv:2402.10094, 2024. doi: 10.48550/arXiv.2402.10094.
[4] Michelle Cheng and Robert Laugwitz. The braids on your blanket. Journal of Humanistic Mathematics, 14(2):286–337, 2024. ISSN 2159-8118. doi: 10.5642/jhummath.YMZO2460.
[5] Robert Laugwitz, Chelsea Walton, and Milen Yakimov. Reflective centers of module categories and quantum K-matrices. arXiv preprint arXiv:2307.14764, 2023. doi: 10.48550/arXiv.2307.14764.
[6] Samuel Hannah, Robert Laugwitz, and Ana Ros Camacho. Frobenius monoidal functors of Dijkgraaf-Witten categories and rigid Frobenius algebras. SIGMA Symmetry Integrability Geom. Methods Appl., 19:Paper No. 075, 42, 2023. doi: 10.3842/SIGMA.2023.075.
[7] Robert Laugwitz and Guillermo Sanmarco. Finite-dimensional quantum groups of type Super a and non-semisimple modular categories. arXiv preprint arXiv:2301.10685, 2023. doi: 10.48550/arXiv.2301.10685.
[8] Robert Laugwitz and Vanessa Miemietz. Differential graded cell 2-representations. arXiv preprint arXiv:2212.07753, 2022. doi: 10.48550/arXiv.2212.07753.
[9] Robert Laugwitz and Vanessa Miemietz. Pretriangulated 2-representations via dg algebra 1-morphisms. arXiv preprint arXiv:2205.09999, 2022. doi: 10.48550/arXiv.2205.09999.
[10] Robert Laugwitz and Chelsea Walton. Constructing non-semisimple modular categories with local modules. Comm. Math. Phys., 403(3): 1363–1409, 2023. ISSN 0010-3616. doi: 10.1007/s00220-023-04824-4.
[11] Johannes Flake, Robert Laugwitz, and Sebastian Posur. Indecomposable objects in Khovanov-Sazdanovic’s generalizations of Deligne’s interpolation categories. Adv. Math., 415:Paper No. 108892, 70, 2023. ISSN 0001-8708. doi: 10.1016/j.aim.2023.108892.
[12] Johannes Flake, Nate Harman, and Robert Laugwitz. The indecomposable objects in the center of Deligne’s category . Proc. Lond. Math. Soc. (3), 126(4):1134–1181, 2023. ISSN 0024-6115. doi: 10.1112/plms.12509.
[13] Mikhail Khovanov and Robert Laugwitz. Planar diagrammatics of self-adjoint functors and recognizable tree series. Pure Appl. Math. Q., 19(5):2409–2499, 2023. ISSN 1558-8599.
[14] Robert Laugwitz and Chelsea Walton. Constructing non-semisimple modular categories with relative monoidal centers. Int. Math. Res. Not. IMRN, 2022(20):15826–15868, 2022. ISSN 1073-7928. doi: 10.1093/imrn/rnab097.
[15] Robert Laugwitz and Chelsea Walton. Braided commutative algebras over quantized enveloping algebras. Transform. Groups, 26(3): 957–993, 2021. ISSN 1083-4362. doi: 10.1007/s00031-020-09599-9.
[16] Johannes Flake and Robert Laugwitz. On the monoidal center of Deligne’s category . J. Lond. Math. Soc. (2), 103(3):1153–1185, 2021. ISSN 0024-6107. doi: 10.1112/jlms.12403.
[17] Robert Laugwitz and Vladimir Retakh. Noncommutative shifted symmetric functions. Mosc. Math. J., 20(1):93–126, 2020. ISSN 1609-3321. doi: 10.17323/1609-4514-2020-20-1-93-126.
[18] Robert Laugwitz and You Qi. A categorification of cyclotomic rings. Quantum Topol., 13(3):539–578, 2022. ISSN 1663-487X. doi: 10.4171/qt/172.
[19] Robert Laugwitz. The relative monoidal center and tensor products of monoidal categories. Commun. Contemp. Math., 22(8):1950068, 53, 2020. ISSN 0219-1997. doi: 10.1142/S0219199719500688.
[20] Robert Laugwitz and Vanessa Miemietz. Cell 2-representations and categorification at prime roots of unity. Adv. Math., 361:106937, 66, 2020. ISSN 0001-8708. doi: 10.1016/j.aim.2019.106937.
[21] Robert Laugwitz. Comodule algebras and 2-cocycles over the (braided) Drinfeld double. Commun. Contemp. Math., 21(4):1850045, 46, 2019. ISSN 0219-1997. doi: 10.1142/S0219199718500451.
[22] Robert Laugwitz and Vladimir Retakh. Algebras of quasi-Plücker coordinates are Koszul. J. Pure Appl. Algebra, 222(9):2810–2822, 2018. ISSN 0022-4049. doi: 10.1016/j.jpaa.2017.11.001.
[23] Robert Laugwitz. On Fomin-Kirillov algebras for complex reflection groups. Comm. Algebra, 45(8):3653–3666, 2017. ISSN 0092-7872. doi: 10.1080/00927872.2016.1243698.
[24] Robert Laugwitz. Pointed Hopf algebras with triangular decomposition. Algebr. Represent. Theory, 19(3):547–578, 2016. ISSN 1386-923X. doi: 10.1007/s10468-015-9588-x.
[25] Robert Laugwitz. Koszulness of enveloping algebras associated to generalized Yang–Baxter equations. arXiv preprint arXiv:1410.4528, 2014. doi: 10.48550/arXiv.1410.4528.
[26] Robert Laugwitz. Braided Drinfeld and Heisenberg doubles. J. Pure Appl. Algebra, 219(10):4541–4596, 2015. ISSN 0022-4049. doi: 10.1016/j.jpaa.2015.02.031.