Mario Denis Kummer
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Inselstr. 22
04103 Leipzig
Germany

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Mario Denis Kummer

Research interests

I am interested in real algebraic geometry and connections to combinatorics and optimization.

Personal homepage

Curriculum vitae

  • Since August 2016: Postdoctoral Research Assistant at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
  • July 2016: Finished my dissertation titled "From Hyperbolic Polynomials to Real Fibered Morphisms" under the supervision of Claus Scheiderer at Universitat Konstanz, Konstanz, Germany
  • August-December 2014: Visiting Graduate Student at the Simons Institute for the Theory of Computing, Berkeley, USA

Publications

Journal Articles

Kummer, Mario and Eli Shamovich: Real fibered morphisms and Ulrich sheaves
In: Journal of algebraic geometry, 29 (2020) 1, p. 167-198
Bibtex DOI: 10.1090/jag/735 ARXIV: https://arxiv.org/abs/1507.06760

Kummer, Mario and Kristin Shaw: The separating semigroup of a real curve
In: Annales de la Faculté des Sciences de Toulouse, 29 (2020) 1, p. 79-96
Bibtex MIS-Preprint: 48/2017 DOI: 10.5802/afst.1624 ARXIV: https://arxiv.org/abs/1707.08227

Chua, Lynn ; Kummer, Mario and Bernd Sturmfels: Schottky algorithms : classical meets tropical
In: Mathematics of computation, 88 (2019) 319, p. 2541-2558
Bibtex MIS-Preprint: 42/2017 DOI: 10.1090/mcom/3406 ARXIV: https://arxiv.org/abs/1707.08520

Kaihnsa, Nidhi ; Kummer, Mario ; Plaumann, Daniel ; Sayyary Namin, Mahsa and Bernd Sturmfels: Sixty-four curves of degree six
In: Experimental mathematics, 28 (2019) 2, p. 132-150
Bibtex MIS-Preprint: 23/2017 DOI: 10.1080/10586458.2017.1360808 ARXIV: https://arxiv.org/abs/1703.01660 CODE: https://mathrepo.mis.mpg.de/planeSexticCurves

Kummer, Mario: On the connectivity of the hyperbolicity region of irreducible polynomials
In: Advances in geometry, 19 (2019) 2, p. 231-233
Bibtex MIS-Preprint: 28/2017 DOI: 10.1515/advgeom-2017-0055 ARXIV: https://arxiv.org/abs/1704.04388

Kummer, Mario: Totally real theta characteristics
In: Annali di matematica pura ed applicata, 198 (2019) 6, p. 2141-2150
Bibtex DOI: 10.1007/s10231-019-00858-5 ARXIV: https://arxiv.org/abs/1802.05297

Kummer, Mario and Cynthia Vinzant: The Chow form of a reciprocal linear space
In: The Michigan mathematical journal, 68 (2019) 4, p. 831-858
Bibtex DOI: 10.1307/mmj/1571731287 ARXIV: https://arxiv.org/abs/1610.04584

Carlini, Enrico ; Kummer, Mario ; Oneto, Alessandro and Emanuele Ventura: On the real rank of monomials
In: Mathematische Zeitschrift, 286 (2017) 1-2, p. 571-577
Bibtex DOI: 10.1007/s00209-016-1774-y ARXIV: https://arxiv.org/abs/1602.01151

Higashitani, Akihiro ; Kummer, Mario and Mateusz Michałek: Interlacing Ehrhart polynomials of reflexive polytopes
In: Selecta mathematica, 23 (2017) 4, p. 2977-2998
Bibtex MIS-Preprint: 7/2017 DOI: 10.1007/s00029-017-0350-6 ARXIV: https://arxiv.org/abs/1612.07538

Kahle, Thomas ; Kubjas, Kaie ; Kummer, Mario and Zvi Rosen: The geometry of rank-one tensor completion
In: SIAM journal on applied algebra and geometry, 1 (2017) 1, p. 200-221
Bibtex DOI: 10.1137/16M1074102 ARXIV: https://arxiv.org/abs/1605.01678

Kummer, Mario: Determinantal representations and Bézoutians
In: Mathematische Zeitschrift, 285 (2017) 1, p. 445-459
Bibtex DOI: 10.1007/s00209-016-1715-9 ARXIV: https://arxiv.org/abs/1308.5560

Kummer, Mario: Eigenvalues of symmetric matrices over integral domains
In: Journal of algebra, 466 (2016), p. 195-203
Bibtex DOI: 10.1016/j.jalgebra.2016.07.024 ARXIV: https://arxiv.org/abs/1511.01048

Kummer, Mario: Two results on the size of spectrahedral descriptions
In: SIAM journal on optimization, 26 (2016) 1, p. 589-601
Bibtex DOI: 10.1137/15M1030789 ARXIV: https://arxiv.org/abs/1506.07699

Kummer, Mario: A note on the hyperbolicity cone of the specialized Vámos polynomial
In: Acta applicandae mathematicae, 144 (2016) 1, p. 11-15
Bibtex DOI: 10.1007/s10440-015-0036-z ARXIV: https://arxiv.org/abs/1306.4483

Kummer, Mario ; Plaumann, Daniel and Cynthia Vinzant: Hyperbolic polynomials, interlacers, and sums of squares
In: Mathematical programming, 153 (2015) 1, p. 223-245
Bibtex DOI: 10.1007/s10107-013-0736-y ARXIV: https://arxiv.org/abs/1212.6696

Preprints

Al Ahmadieh, Abeer ; Sorea, Miruna-Ştefana and Mario Kummer: A generalization of the space of complete quadrics

Brysiewicz, Taylor ; Kozhasov, Khazhgali and Mario Kummer: Nodes on quintic spectrahedra

di Dio, Philipp J. and Mario Kummer: The multidimensional truncated moment problem : Carathéodory numbers from Hilbert functions and shape reconstruction from derivatives of moments

Kummer, Mario and Eli Shamovich: On deformations of hyperbolic varities

Academic Theses

Kummer, Mario: From hyperbolic polynomials to real fibered morphisms
Dissertation, Universität Konstanz, 2016
Bibtex LINK: http://nbn-resolving.de/urn:nbn:de:bsz:352-0-348808
19.01.2021, 05:45