# Andreas Kretschmer

Welcome! I am a member of the Nonlinear Algebra group at the MPI MiS Leipzig. Just recently I submitted my PhD thesis at OvGU Magdeburg under the supervision of Benjamin Nill and Thomas Kahle where I was part of the research training group MathCoRe. Earlier, I did my master's degree at Bonn University with Georg Oberdieck and my bachelor's degree at FAU Erlangen.

My interests lie in algebraic geometry, commutative algebra and connections to combinatorics and applications. For instance, I have worked on the characteristic numbers problem in enumerative geometry in the case of cubic hypersurfaces, on the Chow rings of certain hyperkähler fourfolds, on invariant Hilbert schemes of affine space for the permutation action of the symmetric group, on determinantal ideals for sparse generic symmetric matrices, on the local h*-polynomial of lattice polytopes and on generalizations of graphical models in algebraic statistics.

Contact:

E-mail: firstname dot lastname [at] mis dot mpg dot de

Papers:

Symmetric Ideals and Invariant Hilbert Schemes, with Sebastian Debus

Ideals of submaximal minors of sparse symmetric matrices, with Jiahe Deng, J. Pure Appl. Algebra (2024)

Thin polytopes: Lattice polytopes with vanishing local h*-polynomial, with Christopher Borger and Benjamin Nill, IMRN (2023)

See here for the supplementing code.The enumerative geometry of cubic hypersurfaces: point and line conditions, with Mara Belotti, Alessandro Danelon and Claudia Fevola, Collect. Math. (2023)

When are symmetric ideals monomial?, J. Commut. Algebra (2023)

The geometry of Gaussian double Markovian distributions, with Tobias Boege, Thomas Kahle and Frank Röttger, Scand. J. Stat. (2022)

The Chow ring of hyperkähler varieties of K3^[2]-type via Lefschetz actions, Math. Z. (2022)

Activities:

Talk at MEGA 2024, Symmetric Ideals and Invariant Hilbert Schemes (MPI MiS Leipzig, 30th July 2024)

Talk at MPI MiS Leipzig in the Nonlinear Algebra Seminar, Characteristic Numbers for Cubics and Sparse Quadrics (28th May 2024)

Workshop on Combinatorial Algebraic Geometry from Physics (MPI MiS Leipzig, 13th - 15th May 2024)

Talk at TU Chemnitz in the seminar on Algebra and Theoretical Mathematics, Characteristic Numbers for Cubic Hypersurfaces (23rd April 2024)

Combinatorial Coworkspace 2024 (18th - 23rd March 2024)

Workshop on Positive Geometry in Particle Physics and Cosmology (MPI MiS Leipzig, 12th - 16th February 2024)

Talk at HU Berlin in the Algebraic Geometry Seminar, Characteristic Numbers for Cubic Hypersurfaces (11th January 2024)

Hodge and K-Theory meet Combinatorics (Bernoulli Center, Lausanne, 4th - 8th September 2023)

Talk at SIAM Conference on Applied Algebraic Geometry, Symmetric ideals, Radicals and Deformations (Eindhoven University, 14th July 2023)

Workshop on Commutative Algebra TOwards Applications (Politecnico and Università di Torino, 22nd - 24th May 2023)

Talk at Regional Workshop in Algebraic Geometry, How many cubic surfaces are tangent to 19 general lines? (Jena University, 29th - 31st March 2023)

Workshop on Research Data in Discrete Mathematics (MPI MiS Leipzig, 13th - 14th March 2023)

Oberwolfach Workshop on Resolutions in Local Algebra and Singularity Theory (5th - 11th February 2023)

Contributed talk at AGATES Algebraic Geometry and Complexity Theory, When are (radicals of) symmetric ideals monomial? (14th November 2022)

AGATES Algebraic Geometry and Complexity Theory (IMPAN, Warsaw, 14th - 18th November 2022)

Talk at FU Berlin in the Discrete Geometry Seminar, Thin polytopes: lattice polytopes with vanishing local h*-polynomial (10th November 2022)

Talk at MathCoRe Fellows Seminar, When are (radicals of) symmetric ideals monomial? (9th November 2022)

AGATES Geometry of Secants Workshop (IMPAN, Warsaw, 24th-28th October 2022)

Talk at the DMV Annual Meeting, Thin polytopes: lattice polytopes with vanishing local h*-polynomial (FU Berlin, 15th September 2022)

Geometry meets Combinatorics in Bielefeld (5th - 9th September 2022)

CIME School on "Hyperkähler manifolds and related geometries" (CIME, Cetraro, 29th August - 2nd September 2022)

Leipzig-Magdeburg seminar day (MPI MiS Leipzig, 9th August 2022)

Supervision of a research intern within the RISE Germany program of the DAAD (May - August 2022)

75+80=155 years of commutative algebra school and conference (Universität Osnabrück, 13th - 17th June 2022)

CIRM School on "Moduli Spaces and Stability Conditions" (CIRM, Levico Terme, 6th - 10th June 2022)

Talk at MathCoRe Fellows Seminar, How many cubic surfaces are tangent to 19 general lines? (25th May 2022)

MathCoRe Annual Colloquium in Thale (18th - 20th May 2022)

Talk at the Oberseminar Reelle Geometrie und Algebra in Konstanz, How many cubic surfaces are tangent to 19 general lines? (6th May 2022)

Talk at the Oberseminar Algebra in Osnabrück, When are symmetric ideals monomial? (12th April 2022)

Talk at Convex and Discrete Day, The geometry of Gaussian double Markovian distributions (FU Berlin, 11th March 2022)

Mini-Symposium on Lattice Polytopes (3rd - 4th March, 2022)

MathCoRe Annual Colloquium in Potsdam (3rd - 5th October 2021)

SIAM Conference on Applied Algebraic Geometry (16th - 20th August 2021)

Minicourse on Convex Geometry (MPI MiS Leipzig, 5th - 16th July 2021)

GAeL XXVIII (Loughborough University, 5th - 9th July 2021)

GO60 (21st - 25th June 2021)

MEGA 2021 (UiT The Arctiv University of Norway, 7th - 11th June 2021)

Workshop on Software and Applications of Numerical Nonlinear Algebra (MPI MiS Leipzig, 31st May - 2nd June 2021)

Talk at MathCoRe Fellows Seminar, The geometry of Gaussian double Markovian distributions (5th May 2021)

Graduate Student Meeting on Applied Algebra and Combinatorics (University of Copenhagen, 21st - 23rd April 2021)

(Polytop)ics: Recent advances on polytopes (MPI MiS Leipzig, 6th - 9th April 2021)

MathCoRe: The Algebra of Tensors (Eliana Duarte and Thomas Kahle, 29th March - 9th April 2021)

Talk at Ghent Toric Geometry Reading Seminar, Toric varieties, products and blowing up (22nd March 2021)

REACT [Research Encounters in Algebraic and Combinatorial Topics] (15th February - 5th March 2021)

Toric Fano varieties and beyond (4th December 2020)

Short talk at WISST Seminar Magdeburg, What is... a sheaf? (10th November 2020)

3CinG Workshop 2020 on algebraic and tropical geometry (16th - 18th September 2020)

DMV Annual Meeting 2020 (14th - 17th September 2020)

Talk at IAG Seminar Magdeburg, A Lie algebra action on the Chow ring of the Fano variety of lines of a smooth cubic fourfold (28th April 2020)