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

- Towards unipotent character sheaves associated to Coxeter groups (2020–2024, DFG)
- Conjectures and new examples in birational geometry (2020–2024, DFG)
- Gröbner techniques for PBW deformations: parametrization, representations, applications (2020–2024, DFG)
- 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

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

### Software

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

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

### Publications

- 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] - Bellamy, G., Schmitt, J., & Thiel, U. (2023). On Parabolic Subgroups of Symplectic Reflection Groups.
*Glasg. Math. J.*[arXiv], [Journal] - 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] - Hoff, M. & Staglianò, G. (2022). Explicit constructions of K3 surfaces and unirational Noether-Lefschetz divisors.
*J. Algebra, 611*, 630–650. [arXiv], [Journal] - Hoff, M. & Stenger, I. (2022). On the Numerical Dimension of Calabi–Yau 3-Folds of Picard Number 2.
*Int. Math. Res. Not.*[arXiv], [Journal] - 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

- Bonnafé, C. & Thiel, U. (2021). Computational aspects of Calogero-Moser spaces. arXiv:2112.15495, [arXiv]
- Hoff, M. (2021). A note on syzygies and normal generation for trigonal curves. arXiv:2108.06106, [arXiv]
- 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]

### Software

- Schmitt, J. Contributions to OSCAR (Invariant theory)
- 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

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

### Publications

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

### Preprints

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

### Software

- 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.