Algebra, Geometry and Computer Algebra Group

Prof. Dr. Ulrich Thiel


Address

Gottlieb-Daimler-Straße
Building 48, Office 416
67663 Kaiserslautern

 

Mailing Address

Postfach 3049
67653 Kaiserslautern

Contact

Tel.: +49 631 205 2258
Fax: +49 631 205 4427
E-Mail: thiel (at) mathematik.uni-kl.de

Research Interest

  • Symplectic algebraic geometry (symplectic singularities, Poisson deformations, symplectic duality, minimal model program; symplectic reflection algebras, rational Cherednik algebras, Calogero–Moser spaces)
  • Coxeter groups, Kazhdan–Lusztig theory, Hecke algebras
  • Complex reflection groups, cyclotomic Hecke algebras
  • Highest weight categories, cellular algebras
  • Soergel bimodules
  • Tensor categories
  • Generic representation theory
  • Computer algebra

Publications

  1. Introduction to Soergel bimodules (with B. Elias, S. Makisumi, and G. Williamson).
    In preparation and to appear in Springer RSME (2019).
  2. Calogero–Moser families and cellular characters: computational aspects (with C. Bonnafé).
    In preparation (2019).
  3. Cores of graded algebras with triangular decomposition (with G. Bellamy).
    Preprint (2017).
  1. Highest weight theory for finite-dimensional graded algebras with triangular decomposition
    Adv. Math330 (2018) 361–419. With G. Bellamy. Final, Preprint.
  2. Blocks in flat families of finite-dimensional algebras
    Pac. J. Math. 295 (2018), No. 1, 191–240. Final, Preprint.
  3. Hyperplane arrangements associated to symplectic quotient singularities
    Phenomenological approach to algebraic geometry, 25–45, Banach Center Publ., 116,
    Polish Acad. Sci. Inst. Math., Warsaw, 2018. With G. Bellamy and T. Schedler. FinalPreprint.
  4. Restricted rational Cherednik algebras
    EMS Ser. Congr. Rep., Representation theory – current trends and perspectives (2017), 681–745. Final, Preprint.
  5. Cuspidal Calogero–Moser and Lusztig families for Coxeter groups
    J. Algebra 462 (2016), 197–252. With G. Bellamy. Final, Preprint.
  6. Decomposition matrices are generically trivial
    Int. Math. Res. Not. (2016), no. 7, 2157–2196. Final, Preprint.
  7. CHAMP: A Cherednik Algebra Magma Package
    LMS J. Comput. Math. 18 (2015), no. 1, 266–307. Final, Preprint.
  8. A counter-example to Martino’s conjecture about generic Calogero–Moser families
    Algebr. Represent. Theory 17 (2014), no. 5, 1323–1348. Final, Preprint.

 

 

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