Daniel Plaumann - Fakultät für Mathematik

Research Interests

• Positive polynomials
• Convex algebraic geometry
• Classical algebraic geometry
• Algebraic foundations of optimization

Advances in Geometry

Publications

• Totally real divisors on curves with Lorenzo Baldi and Mario Kummer. Preprint (2025)
• Plane quartics and heptagons with Daniele Agostini, Rainer Sinn and Jannik Lennart Wesner. Preprint (2024)
• Computing totally real hyperplane sections and linear series on algebraic curves
  with Huu Phuoc Le and Dimitri Manevich. Le Matematiche Vol. 77(1), 119-141 (2022)
• Families of faces and the normal cycle of a convex semi-algebraic set
  with Rainer Sinn and Jannik Lennart Wesner. Beiträge zur Algebra und Geometrie (2022)
• Kippenhahn's Theorem for joint numerical ranges and quantum states
  with Rainer Sinn and Stephan Weis. SIAM Journal on Applied Algebra and Geometry, 5, No. 1, 86-113 (2021)
• Testing hyperbolicity of real polynomials
  with Papri Dey. Mathematics in Computer Science. 14, 111-121 (2020)
• Spectrahedral representations of plane hyperbolic curves
  with Mario Kummer and Simone Naldi. Pacific Journal of Mathematics Vol. 303, No. 1, 243–263 (2019)
• Sixty-Four Curves of Degree Six
  with Nidhi Kaihnsa, Mario Kummer, Mahsa Sayyary Namin, and Bernd Sturmfels. Experimental Mathematics 28(2), 132-150 (2019)
• Symbolic computation in hyperbolic programming
  with Simone Naldi. Journal of Algebra and its Applications 17(10)(2018)
• Gram spectrahedra
  with Lynn Chua, Rainer Sinn, and Cynthia Vinzant. Contemporary Mathematics 697 (2017)
• Low-rank sum-of-squares representations on varieties of minimal degree
  with Grigoriy Blekherman, Rainer Sinn, and Cynthia Vinzant. International Mathematics Research Notices 2019(1), 33-54 (2017)
• Toric completions and bounded functions on real algebraic varieties
  with Claus Scheiderer. Journal of the London Mathematical Society (2) 94, 598-616 (2016)
• Computing hermitian determinantal representations of hyperbolic curves
  with Rainer Sinn, David E Speyer, and Cynthia Vinzant. International Journal of Algebra and Computation 25, No. 8, 1327–1336 (2015)
• A relative Grace theorem for complex polynomials
  with Mihai Putinar. Mathematical Proceedings of the Cambridge Philosophical Society, 161, No. 1, 17-30 (2016)
• Hyperbolic polynomials, interlacers, and sums of squares
  with Mario Kummer and Cynthia Vinzant. Mathematical Programming 153, no.1, Ser. B, 223-245 (2015).
• Determinantal representations of hyperbolic curves via polynomial homotopy continuation
  with Anton Leykin. Mathematics of Computation 86(308), 2877-2888 (2017). (Supplementary material)
• Determinantal representations of hyperbolic plane curves: An elementary approach
  with Cynthia Vinzant. Journal of Symbolic Computation 57, No. 1, 48-60 (2013)
• Determinantal Representations and the Hermite Matrix
  with Tim Netzer and Andreas Thom. Michigan Mathematical Journal 62, 407-420 (2013)
• The ring of bounded polynomials on a semi-algebraic set
  with Claus Scheiderer. Transactions of the American Mathematical Society 364, No. 9, 4663-4682 (2012).
• Positivity of continuous piecewise polynomials
  Bulletin of the London Mathematical Society, 44, No. 4, 749-757 (2012).
• Computing linear matrix representations of Helton-Vinnikov curves
  with Bernd Sturmfels and Cynthia Vinzant. Volume in honor of Bill Helton, Mathematical Methods in Systems, Optimization and Control, (eds. Harry Dym, Mauricio de Oliveira, Mihai Putinar), Operator Theory: Advances and Applications, Birkhäuser, Basel, 2011. (Supplementary material)
• Quartic curves and their bitangents
  with Bernd Sturmfels and Cynthia Vinzant. Journal of Symbolic Computation 46, No. 6, 712-733 (2011). (Supplementary material)
• Exposed faces of semidefinitely representable sets
  with Tim Netzer and Markus Schweighofer. SIAM Journal on Optimization 20, No. 4, 1944-1955 (2010)
• Sums of squares on reducible real curves
  Mathematische Zeitschrift 265, No. 4, 777-797 (2009)
• Bounded polynomials, sums of squares and the moment problem
  PhD thesis (Universität Konstanz). Konstanzer Online-Publikationssystem (2008)

Text books

• Einführung in die Algebraische Geometrie (Springer-Spektrum, 2020)
  
• Algebra (Springer-Spektrum, 2023)
  
• Geometry of Linear Matrix Inequalities (Birkhäuser, 2023)

Lecture Notes

• Real Algebraic Geometry (Short Tutorial at IHP, Paris, 12 October 2023)

Events