Robert Laugwitz

Contact

• workRoom C45a Mathematical Sciences Building
  University Park
  Nottingham
  NG7 2RD
  UK
• Robert.Laugwitz@nottingham.ac.uk

Biography

2015 DPhil Pure Mathematics (Oxford)

2015-16 EPSRC Doctoral Prize Fellowship (University of East Anglia)

2016-2019 Triennial Assistant Professor (Rutgers University)

2019 Senior Research Associate (UEA)

2019-2022 Nottingham Research Fellow

Since 2022 Assistant Professor in Mathematics

Research Summary

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.… read more

Recent Publications

• JOHANNES FLAKE, NATE HARMAN and ROBERT LAUGWITZ, 2023. The indecomposable objects in the center of Deligne's category Rep(St) Proceedings of the London Mathematical Society.
• JOHANNES FLAKE, ROBERT LAUGWITZ and SEBASTIAN POSUR, 2023. Indecomposable objects in Khovanov-Sazdanovic's generalizations of Deligne's interpolation categories Advances in Mathematics. (In Press.)
• LAUGWITZ, ROBERT and WALTON, CHELSEA, 2022. Constructing Non-Semisimple Modular Categories With Relative Monoidal Centers International Mathematics Research Notices. 2022(20), 15826-15868
• MIKHAIL KHOVANOV and ROBERT LAUGWITZ, 2021. Planar Diagrammatics of Self-Adjoint Functors and Recognizable Tree Series Pure and Applied Mathematics Quarterly. (In Press.)

• View all publications

Current Research

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 available on the Arxiv.

• JOHANNES FLAKE, NATE HARMAN and ROBERT LAUGWITZ, 2023. The indecomposable objects in the center of Deligne's category Rep(St) Proceedings of the London Mathematical Society.
• JOHANNES FLAKE, ROBERT LAUGWITZ and SEBASTIAN POSUR, 2023. Indecomposable objects in Khovanov-Sazdanovic's generalizations of Deligne's interpolation categories Advances in Mathematics. (In Press.)
• LAUGWITZ, ROBERT and WALTON, CHELSEA, 2022. Constructing Non-Semisimple Modular Categories With Relative Monoidal Centers International Mathematics Research Notices. 2022(20), 15826-15868
• MIKHAIL KHOVANOV and ROBERT LAUGWITZ, 2021. Planar Diagrammatics of Self-Adjoint Functors and Recognizable Tree Series Pure and Applied Mathematics Quarterly. (In Press.)
• FLAKE, JOHANNES and LAUGWITZ, ROBERT, 2021. On the monoidal center of Deligne's category Rep(St) Journal of the London Mathematical Society. 103(3), 1153-1185
• ROBERT LAUGWITZ and YOU QI, 2021. A categorification of cyclotomic rings Quantum Topology. (In Press.)
• ROBERT LAUGWITZ, 2020. The relative monoidal center and tensor products of monoidal categories Communications in Contemporary Mathematics. 22(9), 1950068
• ROBERT LAUGWITZ and VLADIMIR RETAKH, 2020. Noncommutative Shifted Symmetric Functions Moscow Math. Journal. 20(1), 93–126
• LAUGWITZ, ROBERT and WALTON, CHELSEA, 2020. Braided commutative algebras over quantized enveloping algebras Transformation Groups. 26(3), 957-993
• ROBERT LAUGWITZ and MIEMIETZ, VANESSA, 2020. Cell 2-representations and categorification at prime roots of unity Advances in Mathematics. 361, 106937
• ROBERT LAUGWITZ, 2019. Comodule algebras and 2-cocycles over the (Braided) Drinfeld double Communications in Contemporary Mathematics. 21(4), 1850045
• ROBERT LAUGWITZ and VLADIMIR RETAKH, 2018. Algebras of quasi-Plücker coordinates are Koszul J. Pure Appl. Algebra. 222(9), 2810-2822
• ROBERT LAUGWITZ, 2017. On Fomin–Kirillov algebras for complex reflection groups Comm. Algebra. 45(8), 3653-3666
• ROBERT LAUGWITZ, 2016. Pointed Hopf algebras with triangular decomposition Algebr. Represent. Theory. 19(3), 547-578
• ROBERT LAUGWITZ, 2015. Braided Drinfeld and Heisenberg doubles J. Pure Appl. Algebra. 219(10), 4541--4596