Dr. Kh. Kozhasov

I am a substitute professor in Mathematical Optimization at the University of Jena and a postdoctoral researcher (on leave) in the Applied Algebra group of Timo de Wolff at the TU Braunschweig. Summer and Winter semesters of 2021/22 I spent as a substitute professor in the Applied Algebra and Data Analysis group at the University of Osnabrück. From April 2018 till March 2019 I was a postdoctoral researcher in the Nonlinear algebra group of Bernd Sturmfels at MPI MiS. I have obtained PhD in May 2018 at SISSA where my advisors were Andrei Agrachev and Antonio Lerario.Here is my CV.

• Real, computational, convex and random (algebraic) geometry
• Polynomial and tensor optimization
• Multi-linear algebra

I am particularly interested in non-negative polynomials and their applications as well as in ranks, low-rank approximations and eigenvectors of tensors.

• Non-negative forms, volumes of sublevel sets, complete monotonicity and moment matrices, with Jean-Bernard Lasserre

• Probabilistic bounds on best rank-one approximation ratio, with Josué Tonelli-Cueto

• Rational functions with only real periodic points, with Mario Kummer

• On eigenvalues of symmetric matrices with PSD principal submatrices, Journal of Symbolic Computation, http://dx.doi.org/10.2139/ssrn.4290288

• Minimality of tensors of fixed multilinear rank, with Alexander Heaton and Lorenzo Venturello, Linear and Multilinear Algebra, 10.1080/03081087.2022.2062274

• Nodes on quintic spectrahedra, with Taylor Brysiewicz and Mario Kummer, Le Matematiche (2021), 76(2), 415–430

• On minimality of determinantal varieties, Linear Algebra and its Applications (2021), 626, 56-78

• Positivity Certificates via Integral Representations, with Mateusz Michałek and Bernd Sturmfels, LMS volume "Facets of Algebraic Geometry" dedicated to Fulton's 80th birthday

• Nonnegative forms with sublevel sets of minimal volume, with Jean-Bernard Lasserre, Math. Program. (2020), https://doi.org/10.1007/s10107-020-01584-0

• Chebyshev polynomials and best rank-one approximation ratio, with Andrei Agrachev and André Uschmajew,
  SIAM J. Matrix Anal. Appl., 41(1), 308–331

• Random Spectrahedra, with Paul Breiding and Antonio Lerario, SIAM J. Optim., 29(4), 2608–2624

• The Real Polynomial Eigenvalue Problem is Well Conditioned on the Average, with Carlos Beltrán,
  Found Comput Math (2019), https://doi.org/10.1007/s10208-019-09414-2

• On the number of flats tangent to convex hypersurfaces in random position, with Antonio Lerario,
  Discrete Comput Geom (2019), doi.org/10.1007/s00454-019-00067-0
• On the Geometry of the Set of Symmetric Matrices with Repeated Eigenvalues,
  with Paul Breiding and Antonio Lerario, Arnold Math J. (2018), 4:423, doi.org/10.1007/s40598-018-0095-0

• On Fully Real Eigenconfigurations of Tensors, SIAM J. Appl. Algebra Geometry (2018), 2(2), 339-3478

• A geometric flow in the space of G2-structures on the cone over S3×S3,
  Siberian Mathematical Journal (2015), Volume 56, Issue 6, 1093-1100

• Geometry and Control in Cortona (in honor of Andrei Agrachev's 70th birthday), 27 - 31 March 2023, Cortona

• Foundations of Computational Mathematics, 12 - 21 June 2023, Paris (talk at the workshop "Real Number Complexity")

• SIAM Conference on Applied Algebraic Geometry (AG 23), 10 - 14 July 2023, Eindhoven (talk at the minisymposium "Data and certificates in algebra and geometry")