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

  1. SymbTools – Symbolic Tools in Mathematics and their Application (2024–2028, FI Rheinland-Pfalz)
  2. Towards unipotent character sheaves associated to Coxeter groups (2020–2024, DFG)
  3. Conjectures and new examples in birational geometry (2020–2024, DFG)
  4. Gröbner techniques for PBW deformations: parametrization, representations, applications (2020–2024, DFG)
  5. Representation theory: studies of symmetry shadows (2019–2022, ARC)

5. SymbTools – Symbolic Tools in Mathematics and their Application (2024–2028, FI Rheinland-Pfalz)

With J. Böhm, C. Fieker, A. Gathmann, M. Horn, C. Lassueur, G. Malle, M. Rahn, J. Roth, M. Schulze. See here for details.

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. L. Rogel (PhD student, University of Kaiserslautern, Since 04/2021)

Affiliates

  1. F. Mäurer (PhD student, University of Kaiserslautern, Since 06/2022)

Preprints

  1. F. Mäurer & U. Thiel. Computing the center of a fusion category. arXiv:2406.13438 (2024)
  2. L. Rogel & U. Thiel. The center of the asymptotic Hecke category and unipotent character sheaves. arXiv:2307.07276 (2023)

Software

  1. F. Mäurer. TensorCategories.jl
  2. U. Thiel. CoxeterGroups.jl (with contributions by C. Braunstein, J. Gibson, and T. Schmit)
  3. U. Thiel. HeckeAlgebras.jl (with contributions by M. Albert)
  4. U. Thiel. 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. M. Hoff (Postdoc, Saarland University, 04/2021−04/2022)
  2. I. Stenger (Postdoc, Saarland University, 01/2021−12/2023)
  3. T. Metzlaff (Postdoc, University of Kaiserslautern–Landau, since 01/24)

Affiliates

  1. J. Schmitt (PhD student, University of Kaiserslautern, 11/2019–07/2023)

Publications

  1. G. Bellamy, J. Schmitt, & U. Thiel. Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution. Math. Z., 300(1) (2022), 661–681. [arXiv], [Journal]
  2. G. Bellamy, J. Schmitt, & U. Thiel. On Parabolic Subgroups of Symplectic Reflection Groups. Glasg. Math. J. 65 (2023), no. 2, 401–413. [arXiv], [Journal]
  3. M. Belotti, M. Joswig, C. Meroni, V. Schleis & J. Schmitt. Algebraic and geometric computations in OSCAR. SIAM News 56 (2023), no. 7, 9–10. [Journal]
  4. C. Bonnafé & U. Thiel. Computational aspects of Calogero-Moser spaces. Selecta Math. (N.S.) 29 (2023), no.5, Paper No. 79.  [arXiv]
  5. N.T.A. Hang, M. Hoff & H.L. Truong. On cylindrical smooth rational Fano fourfolds. J. Korean Math. Soc. 59(1) (2022), 87–103. [arXiv], [Journal]
  6. M. Hoff & G. Staglianò. Explicit constructions of K3 surfaces and unirational Noether-Lefschetz divisors. J. Algebra 611 (2022), 630–650. [arXiv], [Journal]
  7. M. Hoff & I. Stenger. On the Numerical Dimension of Calabi–Yau 3-Folds of Picard Number 2. Int. Math. Res. Not. (2022), no.12, 10736–10758, [arXiv], [Journal]
  8. V. Lazić. Programming the Minimal Model Program: a proposal. Beitr. Algebra Geom. (2024) [DOI] [arXiv]
  9. V. Lazić, S. Matsumura, Th. Peternell, N. Tsakanikas & Z. Xie. The Nonvanishing Problem for varieties with nef anticanonical bundle. Doc. Math. 28 (2023), no. 6, 1393–1440. [arXiv]
  10. V. Lazić & N. Tsakanikas. Special MMP for log canonical generalised pairs (with an appendix joint with Xiaowei Jiang). Selecta Math. (N.S.) 28 (2022), no. 5, Paper No. 89 [arXiv], [Journal]
  11. T. Metzlaff. On symmetry adapted bases in trigonometric optimization. J. Symbolic Comput. (to appear). [arXiv]
  12. J. Schmitt. The class group of a minimal model of a quotient singularity. Bull. Lond. Math. Soc. (2024, to appear) [arXiv]
  13. F.-O. Schreyer & I. Stenger. An 8-dimensional family of simply connected Godeaux surfaces. Trans. Amer. Math. Soc. 376 (2023), 3419–3443. [arXiv]

Preprints

  1. D. Eisenbud & F.-O. Schreyer. Hyperelliptic curves and Ulrich sheaves on the complete intersection of two quadrics. arXiv:2212.07227
  2. M. Hoff. A note on syzygies and normal generation for trigonal curves. arXiv:2108.06106
  3. M. Hoff, I. Stenger & J.I. Yáñez. Movable cones of complete intersections of multidegree one on products of projective spaces. arXiv:2207.11150
  4. V. Lazić. A few remarks on effectivity and good minimal models. arXiv:2401.14190
  5. V. Lazić, Z. Xie. Nakayama-Zariski decomposition and the termination of flips. arXiv:2305.01752
  6. V. Lazić & Z. Xie. Rigid currents in birational geometry. arXiv:2402.05807
  7. F.-O. Schreyer & I. Stenger. Marked Godeaux surfaces with special bicanonical fibers. arXiv:2201.12065
  8. I. Stenger & Z. Xie. Cones of divisors on P3 blown up at eight very general points. arXiv:2303.12005

Theses

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

Software

  1. J. Schmitt. Contributions to OSCAR [Github]
  2. J. Schmitt. Computing the Cox ring of a Q-factorial terminalization of a linear quotient [OSCAR]
  3. J. Schmitt. 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. J. Flake (Postdoc, RWTH Aachen, 02/2021–09/2022)

Affiliates

  1. V. Mackscheidt (PhD student, RWTH Aachen)
  2. D. Mathiä (PhD student, University of Kaiserslautern, 10/2019–12/2022)

Publications

  1. G. Bellamy & U. Thiel. Cellularity of endomorphism algebras of tilting objects. Adv. Math. 404 (2022), Paper No. 108387.
  2. G. Bellamy & U. Thiel. The rank one property for free Frobenius extensions. C. R. Math. Acad. Sci. Paris 361 (2023), 1341–1348.
  3. J. Flake, G. Fourier & V. Levandovskyy. Gröbner bases for fusion products. Algebr. Represent. Theory 26 (2023), no. 5, 2235–2253. [arXiv]
  4. G. Fourier & L. van Eß. A minimal Gröbner basis for simple sln or spn-modules. arXiv:2401.01634
  5. M. Harms, S. Bamberger, E. Zerz, and M. Herty. On d-Collision-Free Dynamical Systems. IFAC-PapersOnLine 55.34 (2022), 25–30. [DOI]
  6. M. Harms, C. Schilli, and E. Zerz. Invariant sets for a class of nonlinear control systems tractable by symbolic computation. IFAC-PapersOnLine 56.2 (2023), 3899–3903. [DOI]
  7. D. Mathiä & U. Thiel. Wreath Macdonald polynomials at q=t as characters of rational Cherednik algebras. Trans. Amer. Math. Soc. 375 (2022), 8945–8968.

Preprints

  1. J. Flake & V. Mackscheidt. Interpolating PBW Deformations for the Orthosymplectic Groups. arXiv:2206.08226

Theses

  1. V. Mackscheidt. PBW deformations arising from algebraic groups. RWTH Aachen (2023). [DOI]
  2. D. Mathiä. Wreath combinatorics in the context of restricted rational Cherednik algebras. University of Kaiserslautern (2022). [DOI]

Software

  1. J. Flake, L. Göttgens & P. Pützstück. PBWDeformations.jl – an OSCAR package for PBW deformations.
  2. L. van Eß. LieTools.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.