András Cristian Lőrincz

Humboldt-Universität zu Berlin
Institut für Mathematik

I am a Dirichlet Postdoctoral Fellow of the Berlin Mathematical School, working in the Algebraic Geometry group at Humboldt University of Berlin.
I received my Ph.D. from the University of Connecticut under the supervision of Prof. Jerzy Weyman.

Curriculum Vitae

Research Interests:

Algebraic Geometry, Representation Theory, Commutative Algebra, D-modules.

Published & accepted papers:

  1. Minimal free resolutions of ideals of minors associated to pairs of matrices, arXiv 2001.08709, Proceedings of the American Mathematical Society, accepted (15 pages).
  2. Iterated local cohomology and Lyubeznik numbers for determinantal rings (with C. Raicu), Algebra & Number Theory 14: 2533-2569 (2020).
  3. Algebraic analysis on rotation data (with M. F. Adamer, A.-L. Sattelberger, B. Sturmfels), Algebraic Statistics 11: 189–211 (2020).
  4. Equivariant D-modules on alternating senary 3-tensors (with M. Perlman), arXiv:1809.08955, Nagoya Mathematical Journal, accepted (19 pages).
  5. On categories of equivariant D-modules (with U. Walther), Advances in Mathematics 351: 429-478 (2019).
  6. Decompositions of Bernstein-Sato polynomials and slices, Transformation Groups 25: 577-607 (2020).
  7. Free resolutions of orbit closures of Dynkin quivers (with J. Weyman), Transactions of the American Mathematical Society 372: 2715-2734 (2019).
  8. Equivariant D-modules on binary cubic forms (with C. Raicu and J. Weyman), Communications in Algebra 47: 2457-2487 (issue in honor of G. Lyubeznik) (2019).
  9. Singularities of zero sets of semi-invariants for quivers, arXiv:1509.04170, Journal of Commutative Algebra, accepted (19 pages).
  10. The b-functions of semi-invariants of quivers, Journal of Algebra 482: 346-364 (2017).
  11. Bernstein-Sato polynomials for maximal minors and sub-maximal Pfaffians (with C. Raicu, U. Walther and J. Weyman), Advances in Mathematics 307: 224-252 (2017).

Preprints:

  1. Holonomic functions and prehomogeneous spaces, arXiv:2102.00766, submitted (35 pages).
  2. On the collapsing of homogeneous bundles in arbitrary characteristic, arXiv:2008.08270, submitted (20 pages).
  3. Local cohomology on a subexceptional series of representations (with J. Weyman), arXiv:1910.13820, submitted (21 pages).
  4. Representation varieties of algebras with nodes (with R. Kinser), arXiv:1810.10997, submitted (25 pages).
  5. De Rham cohomology of local cohomology groups with determinantal support (with C. Raicu), available upon request.

In preparation:

  1. Equivariant perverse sheaves on toric varieties (with U. Walther), in progress.
  2. Characters of equivariant D-modules on affine spherical varieties, in progress.

Other:

Ph.D. Thesis: Bernstein-Sato polynomials for quivers
Research Statement

Contact Information:

Office: 1.425
Phone: +49 (0)30-2093-45368
Email: lorincza[at]hu-berlin.de