Dr. Kh. Kozhasov

I am a postdoctoral researcher in the Applied Algebra group of Timo de Wolff at 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 you can find my thesis. Here is my CV.

Geometric, topological, analytic and statistical properties of real polynomials, tensors and varieties.

• 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

• On eigenvalues of symmetric matrices with PSD principal submatrices

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

• 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

• POEMA Final Workshop, 5 - 9 September 2022, Paris (contributed talk)

• AGATES kickoff workshop, 19 - 23 September 2022, Warsaw (invited talk)

• Real Algebraic Geometry, 24 - 28 October 2022, CIRM, Luminy (invited talk)

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