Rainer Sinn - Institute of Mathematics

Research Interests: Geometry (algebraic, convex, discrete, real)

• Positive polynomials and sums of squares
• Convex, semi-algebraic sets
• Positive Geometry

PhD students

• Joris Köfler (IMPRS, MPI MiS)
• Jannik Wesner (jointly supervised with Daniel Plaumann)

Postdocs

• Lorenzo Baldi (Humboldt Postdoctoral Fellowship, June 2024 to May 2026)

Graduated students

• Marie-Charlotte Brandenburg
• Chiara Meroni (jointly supervised with Bernd Sturmfels)
• Laith Rastanawi (jointly supervised with Günter Rote)
• Hannah Sjöberg (jointly supervised with Günter Ziegler) at Freie Universität Berlin

Affiliations

Grants

• Co-Spokesperson of MaRDI for TA6 (Data Culture and Community Integration), funding period 2021 - 2026
  Mathematik in der Nationalen Forschungsdateninfrastruktur, with Christiane Görgen, Mitteilungen der DMV, 29(3), 2021
• DFG project Geometry of Hyperbolic Polynomials (with Daniel Plaumann), funding period 2019 - 2022
  "At the heart of this project are hyperbolic polynomials and their hyperbolicity cones. These are real polynomials in several variables bounding a convex cone, with a particular reality condition on the roots. They originate in complex analysis and the theory of partial differential equations, but have more recently arisen in optimization, combinatorics, and probability theory. [..]"
• SAXAG: Saxonian Algebraic Geometry (incubator grant of the Saxonian Ministry of Science and Art), funding period 2022

SIAM Journal on Applied Algbera and Geometry

Publications

Book

Articles

• Adjoints and Canonical Forms of Tree Amplituhedra with Kristian Ranestad & Simon Telen
  Preprint (2024)
• Convex hulls of surfaces in fourspace with Chiara Meroni & Kristian Ranestad
  Preprint (2022)
• Weak and Strong Extremal Biquadratics
  with Grigoriy Blekherman, Bogdan Raiță & Isabelle Shankar
  Preprint (2022)
• Moments, Sums of Squares, and Tropicalization
  with Grigoriy Blekherman, Felipe Rincon, Cynthia Vinzant & Josephine Yu
  Preprint (2022)
• Adjoints and Canonical Forms of Polypols
  with Kathlén Kohn, Ragni Piene, Kristian Ranestad, Felix Rydell, Boris Shapiro, Miruna-Stefana Sorea & Simon Telen
  Preprint (2021)
• Do Alcoved Lattice Polytopes Have Unimodal h*-Vector?
  with Hannah Sjöberg
  Preprint (2021)
• [S2] Landau on Chess Tournaments and Google's PageRank
  with Günter M. Ziegler
  to appear in Edmund Landau: Collected Works, Volume 10, edited by A. Hüntelmann, A. Kreuzer, H. Wefelscheid and U. Wefelscheid
• [Z23] Tropical Positivity and Determinantal Varieties with Marie Brandenburg & Georg Loho
  Algebraic Combinatorics, 6(4), 999-1040 (2023)
• [Z22] Families of Faces and the Normal Cycle of a Convex Semi-algebraic Set
  with Daniel Plaumann & Jannik Lennart Wesner
  Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 64, 851-875 (2023)
• [Z21] The Chiral Domain of a Camera Arrangement
  with Sameer Agarwal, Andrew Pryhuber & Rekha Thomas
  Journal of Mathematical Imaging and Vision, 64, 948-967 (2022)
• [Z20] On the Existence of Two View Chiral Reconstructions
  with Andrew Pryhuber & Rekha Thomas
  SIAM Journal on Applied Algebra and Geometry, 6, No. 1, 41-76 (2022)
• [Z19] Hyperbolic Secant Varieties of M-Curves
  with Mario Kummer
  Journal für die Reine und Angewandte Mathematik, 787, 125-162 (2022)
• [Z18] Sums of Squares and Quadratic Persistence on Real Projective Varieties
  with Grigoriy Blekherman, Gregory G. Smith & Mauricio Velasco
  Journal of the EMS, 24, No. 3, 925-965 (2022)
• [Z17] Maximum Likelihood Estimation for Nets of Conics
  with Stefan Dye, Kathlén Kohn & Felix Rydell
  Le Matematiche, 76, No. 2, 399-414 (2021)
• [S1] Sums of Squares: A real projective story
  with Grigoriy Blekherman, Gregory G. Smith & Mauricio Velasco
  Notices of the AMS, 68, No. 5, 734-747 (2021)
• [Z16] On the Dimensions of the Realization Spaces of Polytopes
  with Laith Rastanawi & Günter M. Ziegler
  Mathematika, 67, No. 2, 342-365 (2021)
• [Z15] Conic Programming: Infeasibility Certificates and Projective Geometry
  with Simone Naldi
  Journal of Pure and Applied Algebra, 225, No. 7, 22 pages (2021)
• [Z14] Kippenhahn's Theorem for Joint Numerical Ranges and Quantum States
  with Daniel Plaumann & Stephan Weis
  SIAM Journal on Applied Algebra and Geometry, 5, No. 1, 86-113 (2021)
• [Z13] Combinatorial inscribability obstructions for higher-dimensional polytopes
  with Joseph Doolittle, Jean-Philippe Labbé, Carsten Lange, Jonathan Spreer & Günter M. Ziegler
  Mathematika, 66, No. 4, 927-953 (2020)
• [Z12] Typical and Generic Ranks in Matrix Completion
  with Daniel Bernstein & Grigoriy Blekherman
  Linear Algebra and Applications, 585, 71-104 (2020)
• [Z11] Positive Semidefinite Univariate Matrix Polynomials
  with Christoph Hanselka
  Mathematische Zeitschrift, 292, No. 1-2, 83-101 (2019)
  Read-only link
• [Z10] Maximum Likelihood Threshold and Generic Completion Rank of Graphs
  with Grigoriy Blekherman
  Discrete and Computational Geometry, 61, No. 2, 303-324 (2019)
• [Z9] Gram Spectrahedra
  with Lynn Chua, Daniel Plaumann & Cynthia Vinzant
  in Ordered Algebraic Structures and Related Topics, vol. 697 of Contemporary Mathematics, 81-105. American Mathematical Society, Providence, RI (2017)
• [Z8] Low-Rank Sum-of-Squares Representations on Varieties of Minimal Degree
  with Grigoriy Blekherman, Daniel Plaumann & Cynthia Vinzant
  International Mathematical Research Notices, 2019, No. 1, 33-54 (2019)
• [Z7] Do Sums of Squares Dream of Free Resolutions?
  with Grigoriy Blekherman & Mauricio Velasco
  SIAM Journal on Applied Algebra and Geometry, 1, No. 1, 175-199 (2017)
• [Z6] Extreme Rays of the Hankel Spectrahedra for Ternary Forms
  with Grigoriy Blekherman
  Journal of Symbolic Computation, 79, Part 1, 23-42 (2017)
• [Z5] Real Rank with Respect to Varieties
  with Grigoriy Blekherman
  Linear Algebra and its Applications, 505, 344-360 (2016)
• [Z4] Computing hermitian determinantal representations of hyperbolic curves
  with Daniel Plaumann, David E Speyer & Cynthia Vinzant
  Our implementation of the algorithm in Mathematica is available here.
  International Journal on Algebra and Computation, 25, No. 8, 1327-1336 (2015)
• [Z3] Generic Spectrahedral Shadows
  with Bernd Sturmfels
  SIAM Journal on Optimization, 25, No. 2, 1209-1220 (2015)
• [Z2] Algebraic Boundaries of Convex Semi-algebraic Sets
  Research in the Mathematical Sciences, 2, No. 1 (2015)
  
• [T] Algebraic Boundaries of Convex Semi-algebraic Sets
  PhD thesis (Universität Konstanz, 2014)
• [Z1] Algebraic Boundaries of SO(2)-Orbitopes
  Discrete and Computational Geometry, 50, No. 1, 219-235 (2013)
• [A1] A Note on the Convex Hull of Finitely Many Projections of Spectrahedra
  Tim Netzer
  Appendix of [Z15]