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Former Research Group

Combinatorial Algebraic Geometry

The main topics examined by the group were:

  1. toric geometry and its relations to phylogenetics and tensors
  2. secant varieties with a view towards tensor decompositions and tensor rank
  3. geometric approach to fast matrix multiplication
  4. combinatorial aspects of polytopes and relations to algebra
  5. application of local algebraic methods in topological problems

Mateusz Michałek

Nonlinear Algebra
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Publications

inJournal
2024
Laurent Manivel et al.

Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming

In: Journal of the European Mathematical Society
BibTex DOI: 10.4171/JEMS/1330 ArXiv: 2011.08791 MiS Preprint Code: mathrepo.mis.mpg.de
inJournal
2023
Alessio Borzì et al.

The leading coefficient of Lascoux polynomials

In: Discrete mathematics
BibTex DOI: 10.1016/j.disc.2022.113217 ArXiv: 2106.13104
inJournal
2023
Adam Czapliński et al.

Uniform matrix product states from an algebraic geometer's point of view

In: Advances in applied mathematics
BibTex DOI: 10.1016/j.aam.2022.102417 ArXiv: 1904.07563 MiS Preprint
inJournal
2022
Laura Colmenarejo et al.

A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula

In: European journal of combinatorics
BibTex DOI: 10.1016/j.ejc.2021.103406 ArXiv: 2003.01574
inJournal
2022
Lek-Heng Lim et al.

Best \(k\)-layer neural network approximations

In: Constructive approximation
BibTex DOI: 10.1007/s00365-021-09545-2 ArXiv: 1907.01507 MiS Preprint
inJournal
2022
Muhammad Azeem Khadam et al.

Cohen-Macaulay and Gorenstein tangential varieties of the Segre-Veronese varieties

In: The bulletin of the London Mathematical Society
BibTex DOI: 10.1112/blms.12652 ArXiv: 2012.14476
Academic
2022
Martin Vodička

Combinatorial methods in algebraic geometry

Dissertation, Universität Konstanz
BibTex Link: nbn-resolving.de
inJournal
2022
Paul Görlach et al.

Computing zero-dimensional tropical varieties via projections

In: Computational complexity
BibTex DOI: 10.1007/s00037-022-00222-9 ArXiv: 1908.03486 MiS Preprint Code: mathrepo.mis.mpg.de
inJournal
2022
Kathryn Heal et al.

Deep learning Gauss-Manin connections

In: Advances in applied Clifford algebras
BibTex DOI: 10.1007/s00006-022-01207-1 ArXiv: 2007.13786
inJournal
2022
Paul Breiding et al.

Equations for GL invariant families of polynomials

In: Vietnam journal of mathematics
BibTex DOI: 10.1007/s10013-022-00549-4 ArXiv: 2110.06608
inBook
2022
Amanda Cameron et al.

Flag matroids : algebra and geometry

In: Interactions with lattice polytopes : Magdeburg, Germany, September 2017
BibTex DOI: 10.1007/978-3-030-98327-7_4 ArXiv: 1811.00272 MiS Preprint
inJournal
2022
Alessio D'Alì et al.

Many faces of symmetric edge polytopes

In: The electronic journal of combinatorics
BibTex DOI: 10.37236/10387 ArXiv: 1910.05193
inBook
2022
Khazhgali Kozhasov et al.

Positivity certificates via integral representations

In: Facets of algebraic geometry : a collection in honor of William Fulton's 80th birthday ; Volume 2
BibTex DOI: 10.1017/9781108877855.004 ArXiv: 1908.04191 MiS Preprint
inJournal
2022
Austin Conner et al.

Rank and border rank of Kronecker powers of tensors and Strassen's laser method

In: Computational complexity
BibTex DOI: 10.1007/s00037-021-00217-y ArXiv: 1909.04785
inJournal
2021
Paul Görlach et al.

Algebraic analysis of the hypergeometric function \(\,{_1F_{\!\!\;1}}\,\) of a matrix argument

In: Beiträge zur Algebra und Geometrie
BibTex DOI: 10.1007/s13366-020-00546-z ArXiv: 2005.06162
inJournal
2021
Matthias Christandl et al.

Border rank non-additivity for higher order tensors

In: SIAM journal on matrix analysis and applications
BibTex DOI: 10.1137/20M1357366 ArXiv: 2007.05458
inJournal
2021
Paul Görlach et al.

Detecting tropical defects of polynomial equations

In: Journal of algebraic combinatorics
BibTex DOI: 10.1007/s10801-019-00916-4 ArXiv: 1809.03350 Code: mathrepo.mis.mpg.de
inBook
2021
Edgar Costa et al.

Effective obstruction to lifting Tate classes from positive characteristic

In: Arithmetic geometry, number theory, and computation
BibTex DOI: 10.1007/978-3-030-80914-0_9 ArXiv: 2003.11037 MiS Preprint
Preprint
2021
Rodica Dinu et al.

Geometry of the Gaussian graphical model of the cycle

BibTex ArXiv: 2111.02937
inJournal
2021
Takayuki Hibi et al.

Gorenstein graphic matroids

In: Israel journal of mathematics
BibTex DOI: 10.1007/s11856-021-2136-y ArXiv: 1905.05418 MiS Preprint
All Group Publications
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