Dr. Kh. Kozhasov

I am a substitute professor in the Applied algebra and data analysis working group at the University of Osnabrück and a postdoctoral researcher (on leave) in the Applied algebra group of Timo de Wolff at TU Braunschweig. Before that I was a postdoctoral researcher in the Nonlinear algebra group of Bernd Stufmfels 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 and statistical properties of real polynomials and varieties.

• On eigenvalues of symmetric matrices with PSD principal submatrices

• Nodes on quintic spectrahedra, with Taylor Brysiewicz and Mario Kummer, accepted to Le Matematiche
• Minimality of tensors of fixed multilinear rank, with Alexander Heaton and Lorenzo Venturello, submitted

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

• 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, to appear in the 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

• Facets of Real Algebraic Geometry (dedicated to Viatcheslav Kharlamov on the occasion of his 70-th birthday), June 21-25, 2021, Université de Nantes (in-person, participant)
• Seminar in Real and Complex Geometry, July 15, 2021, Tel-Aviv University (online, speaker)
• Real Algebraic and Convex Geometry, July 30-31, 2021, TU Braunschweig (hybrid, organizer)

• SIAM Conference on Applied Algebraic Geometry, August 16-20, 2021, Texas A&M University (online, speaker in a mini-symposium)

• El Congreso Latinoamericano de Matemáticos, September 13-17, 2021, Montevideo (online, speaker in a session)

• Real Polynomials: Counting and Stability, October 17-22, 2021, Casa Matemática Oaxaca (online, speaker)

• Analytic combinatorics in several variables, April 4-8, 2022, American Institute of Mathematics