This is a list of third-party funded projects in which I am principal investigator. More information on the projects is below.

  1. Towards unipotent character sheaves associated to Coxeter groups (2020–2024, DFG)
  2. Conjectures and new examples in birational geometry (2020–2024, DFG)
  3. Gröbner techniques for PBW deformations: parametrization, representations, applications (2020–2024, DFG)
  4. Representation theory: studies of symmetry shadows (2019–2022, ARC)

4. Towards unipotent character sheaves associated to Coxeter groups (2020–2024, DFG)

This project is part of DFG SFB-TRR 195. See here for project details.

Positions

  1. Liam Rogel (PhD, University of Kaiserslautern, Since 04/2021)

Publications

  1. Rogel, L. & Thiel, U. (2023). The center of the asymptotic Hecke category and unipotent character sheaves. [arXiv]

Software

  1. Mäurer, F. TensorCategories.jl
  2. Thiel, U. CoxeterGroups.jl (with contributions by C. Braunstein, J. Gibson, and T. Schmit)
  3. Thiel, U. HeckeAlgebras.jl (with contributions by M. Albert)
  4. Thiel, U. JuLie.jl (with contributions by T. Schmit)

3. Conjectures and new examples in birational geometry (2020–2024, DFG)

With V. Lazić and F.O. Schreyer (Saarland University). This project is part of DFG SFB-TRR 195. See here for project details.

Positions

  1. Michael Hoff (Postdoc, Saarland University, 04/2021−04/2022)
  2. Isabel Stenger (Postdoc, Saarland University, 01/2021−12/2023)

Publications

  1. Bellamy, G., Schmitt, J., & Thiel, U. (2022). Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution. Math. Z., 300(1), 661–681. [arXiv], [Journal]
  2. Bellamy, G., Schmitt, J., & Thiel, U. (2023). On Parabolic Subgroups of Symplectic Reflection Groups. Glasg. Math. J. [arXiv], [Journal]
  3. Bonnafé, C. & Thiel, U. (2023). Computational aspects of Calogero-Moser spaces. Selecta Math. (N.S.) (to appear).  [arXiv]
  4. Hang, N. T. A., Hoff, M., & Truong, H. L. (2022). On cylindrical smooth rational Fano fourfolds. J. Korean Math. Soc., 59(1), 87–103. [arXiv], [Journal]
  5. Hoff, M. & Staglianò, G. (2022). Explicit constructions of K3 surfaces and unirational Noether-Lefschetz divisors. J. Algebra, 611, 630–650. [arXiv], [Journal]
  6. Hoff, M. & Stenger, I. (2022). On the Numerical Dimension of Calabi–Yau 3-Folds of Picard Number 2. Int. Math. Res. Not. [arXiv], [Journal]
  7. Lazić, V. & Tsakanikas, N. (2022). Special MMP for log canonical generalised pairs. Selecta Math. (To appear. With an appendix joint with Xiaowei Jiang) [arXiv], [Journal]

Preprints

  1. Hoff, M. (2021). A note on syzygies and normal generation for trigonal curves. arXiv:2108.06106, [arXiv]
  2. Hoff, M., Stenger, I., & Yáñez, J. I. (2022). Movable cones of complete intersections of multidegree one on products of projective spaces. arXiv:2207.11150, [arXiv]
  3. Schmitt, J. (2023). The class group of a minimal model of a quotient singularity. arXiv:2309.05402

Theses

  1. Schmitt, J. (2023). On Q-factorial terminalizations of symplectic linear quotient singularities. University of Kaiserslautern–Landau. [Kluedo]

Software

  1. Schmitt, J. Contributions to OSCAR [Github]
  2. Schmitt, J. Computing the Cox ring of a Q-factorial terminalization of a linear quotient [OSCAR]
  3. Schmitt, J. Matrix models of certain symplectic reflection groups

2. Gröbner techniques for PBW deformations: parametrization, representations, applications (2020–2024, DFG)

With G. Fourier and E. Zerz (RWTH Aachen). This project is part of the DFG SFB-TRR 195. See here for project details.

Positions

  1. Johannes Flake (Postdoc, RWTH Aachen, 02/2021–09/2022)

Publications

  1. Flake, J., Fourier, G., & Levandovskyy, V. (2020). Gröbner bases for fusion products. Algebr. Represent. Theory (To appear). [arXiv]

Preprints

  1. Bellamy, G. & Thiel, U. (2023). The rank one property for free Frobenius extensions. arXiv:2301.03265, [arXiv]
  2. Flake, J. & Mackscheidt, V. (2022). Interpolating PBW Deformations for the Orthosymplectic Groups. arXiv:2206.08226, [arXiv]

Software

  1. Flake, J. PBWDeformations.jl

1. Representation theory: studies of symmetry shadows (2019–2022, ARC)

See here for project details. Terminated early because I took up a professorship at the University of Kaiserslautern.