Hristo Sendov

Professor
Office: WSC 205
Phone: 519-661-2111 x86985
Email: hsendov@uwo.ca


Website

 

M.Sc. in Mathematics, Sofia University, 1994
M.Sc. in Mathematics, Michigan Technological University, 1996
Ph.D. in Optimization, University of Waterloo, 2001
M.A. in Mathematical Finance, University of Waterloo, 2002

Research Areas

  • Mathematics

Graduate Students Supervision

 

Publication

  1. H.S. Sendov and A.L. Shen, ‘On Polynomial Covariants, k-Polarity, and the Location of Zeros and Critical Points’, submitted, 19 pages, (2026).
  2. H.S. Sendov and M. Yuan, ‘A Note on the De Bruijn-Springer Inequality Between the Zeros and Critical Points of Polynomials’, submitted, 7 pages, (2026).
  3. H.S. Sendov and M. Yuan, ‘Two absolutely bounded determinantal ratios’, submitted, 14 pages, (2026).
  4. Sh. Fallat, S. Mondal, and H.S. Sendov, ‘Variations on Majorization of Vectors and Connections to Determinantal Inequalities’, submitted, 19 pages, (2026).
  5. Sh. Fallat, S. Mondal, and H.S. Sendov, ‘Determinant Bounds for (n-1)-Locally Positive Semidefinite Matrices’, submitted, 18 pages, (2026).
  6. H.S. Sendov, ‘A Bounded Determinantal Ratio for Positive Definite Matrices’, submitted, 20 pages, (2026).
  7. H.S. Sendov and M. Yuan, ‘Aggregate Bounds on the eigenvalues of the principal submatrices of a Hermitian matrix and majorization relations’, submitted, 18 pages, (2026).
  8. H.S. Sendov, ‘On the  Siebeck-Marden theorem  and geometry in the projective plane’, submitted, 21 pages, (2025).
  9. Poulton and H.S. Sendov, ‘Lesser Known Formulas and Properties of Mobius Transformations’, submitted, 15 pages, (2025).
  10. H.S. Sendov and T. Jiang, ‘Canonical representation of k-tensor isotropic functions’, submitted, 20 pages (2025).
  11. H.S. Sendov, ‘On the geometry of polynomials acting on the unit circle’, 27 pages, accepted in Aequationes Mathematicae, (2026).
  12. Sh. Bhatt and H.S. Sendov, ‘Gauss-Lucas theorems for multivariate polynomials and their Polar Derivatives’, 26 pages, accepted in the Canadian Journal of Mathematics, (2026).
  13. Sh. Bhatt and H.S. Sendov, ‘Stronger Grace's theorem for complex polynomials using polar convexity’, 20 pages, accepted in Mathematica Scandinavica, (2026).
  14. Sh. Bhatt and H.S. Sendov, ‘A Survey on polar convexity and its applications’, Strategies for Handling Applications with Nonconvexity, (H.H. Bauschke, R.I. Bot, R. Burachik, W. Moursi eds.)  Springer Optimization and Its Applications, accepted 25 pages, Springer (2025).
  15. H.S. Sendov, ‘A note on Lidskii's theorem for the directional derivatives of the eigenvalues of symmetric matrices’, Electronic Journal of Linear Algebra, 41, 338–341 (2025).
  16. H.S. Sendov, ‘On two refinements of the Gauss-Lucas Theorem’, Serdica Mathematical Journal, 51(2), 197–202 (2025).
  17. Ph. Braun and H.S. Sendov, ‘On the necessary and sufficient conditions for Hadamard-Fischer-Koteljanskii type inequalities’, Linear Algebra and its Applications, 708, 525–550 (2025).
  18. H.S. Sendov and J. Xiao, ‘On the geometry of multi-affine polynomials: invariant circles and circular solutions’, Computational Methods and Function Theory, 25(4), 913—949 (2025).
  19. Sh. Bhatt and H.S. Sendov, ‘On Polar Convexity in Finite-Dimensional Euclidean Spaces’,  Canadian Journal of Mathematics, 77(6), 2111–2147 (2025).
  20. Jedidi, H.S. Sendov and Sh. Shan, ‘Classes of completely monotone and Bernstein functions defined by convexity properties of their spectral measures’, AIMS Mathematics, 9(5), 11372–11395 (2024).
  21. Bridaa, W. Jedidi, and H.S. Sendov, ‘Generalized unimodality and subordinators with applications to stable laws and to the Mittag-Leffler function’, Journal of Theoretical Probability, 37, 1–42 (2024).
  22. Ph. Braun and H.S. Sendov, ‘On the Hadamard-Fischer's Inequality, the Inclusion-Exclusion Formula, and Bipartite Graphs’, Linear Algebra and its Applications, 668(1), 64–92 (2023).
  23. H.S. Sendov and J. Xiao, ‘Complex multi-affine polynomials and invariant circles’, 29 pages, Journal of Mathematical Analysis and its Applications, 523(2), 127076 (2023).
  24. H.S. Sendov and J. Xiao, ‘Coninvolutory matrices, multi-affine polynomials, and invariant circles’, Journal of Linear and Multilinear Algebra, 71(6), 911–944 (2022).
  25. H.S. Sendov and J. Xiao, ‘On Loci of Complex Polynomials of degree three’, Journal of Mathematical Analysis and Applications, 21 pages, 495(2), 124767 (2021).
  26. H.S. Sendov, ‘Refinements of the Gauss-Lucas theorem using rational lemniscates and polar convexity’, Proceedings of the American Mathematical Society, 149, 5179–5193 (2021).
  27. Bl. Sendov and H.S. Sendov, ‘Sector analogue of the Gauss-Lucas theorem’, Canadian Journal of Mathematics, 73(2), 318–338 (2021).
  28. Bl. Sendov and H.S. Sendov, ‘Sets in the complex plane mapped into convex ones by Mobius transformations’, Journal of Convex Analysis, 27 (3),  3, 791–810 (2020).
  29. Bl. Sendov and H.S. Sendov, ‘Further Strengthening of Rolle’s theorem for complex polynomials’, Constructive Approximation, 52, 341–356 (2020).
  30. Bl. Sendov and H.S. Sendov, ‘Duality between loci of complex polynomials and the zeros of polar derivatives’, Mathematical Proceedings of the Cambridge Philosophical Society, 167(1) 65–87 (2019). 
  31. Jiang, M.S. Mousavi, and H.S. Sendov, ‘On the analyticity of k-isotropic functions’, Linear and Multilinear Algebra, 67(2) 228–247 (2019).
  32. Bl. Sendov, H.S. Sendov and Ch. Wang, ‘Polar convexity and critical points of polynomials’, Journal of Convex Analysis, 26(2) 635–660 (2019).
  33. Jiang and H.S. Sendov, ‘On differentiability of a class of orthogonally invariant functions on several operator variables’, Operators and Matrices, 12(3) 711–721 (2018).
  34. Bl. Sendov and H.S. Sendov, ‘Stronger Rolle’s Theorem for Complex Polynomials’, Proceedings of the American Mathematical Society, 146(8), 3367–3380 (2018).
  35. Jiang and H.S. Sendov, ‘A unified approach to operator monotone functions’, Linear Algebra and its Applications, 541, 185–210 (2018).
  36. M.S. Mousavi and H.S. Sendov, ‘A unified approach to spectral and isotropic functions’, SIAM Journal on Matrix Analysis and Applications, 39(2), 632–663 (2018).
  37. H.S. Sendov and J. Xiao, ‘Tauberian theorems for the mean of Lebegue-Stieltjes integrals’, Serdica Mathematical Journal, 43, 293–320 (2017).
  38. Bl. Sendov and H.S. Sendov, ‘Separation of the critical points of a polynomial’, Proceedings of the Bulgarian Academy of Sciences, 70(5), 607–610 (2017).
  39. Bl. Sendov and H.S. Sendov, ‘On the zeros and critical points of polynomials with non-negative coefficients: a non-convex analogue of the Gauss-Lucas theorem’, Constructive Approximation, 46(2), 305–317 (2017).
  40. Bl. Sendov and H.S. Sendov, ‘Two Walsh-type theorems for the solutions of multi-affine symmetric polynomials’, Progress in Approximation Theory and Applicable Complex Analysis: In Memory of Q.I. Rahman, (Govil, N., Mohapatra, R., Qazi, M., Schmeisser, G. eds.) Springer Optimization and Its Applications, 117, 145–162 (2017).
  41. Daniilidis, J. Malick, and H.S. Sendov, ‘Spectral (isotropic) manifolds and their dimension’, Journal d’Analyse Mathematique, 128(1) 369–397 (2016).
  42. H.S. Sendov and Sh. Shan, ‘Properties of completely monotone and Bernstein functions related to the shape of their measures’, Journal of Convex Analysis, 23(4), 981–1015 (2016). 
  43. B.P.W. Ames and H.S. Sendov, ‘Derivatives of compound matrix-valued functions’, Journal of Mathematical Analysis and Applications, 433(2), 1459–1485 (2016). 
  44. Ch. Planiden and H.S. Sendov, ‘Some Geometric Properties of the Solutions of Complex Multi-Affine Polynomials of Degree Three’, Journal of Mathematical Analysis and Applications, 426(1), 312–329 (2015). 
  45. Bl. Sendov and H.S. Sendov, ‘Loci of complex polynomials, part II: polar derivatives’, Mathematical Proceedings of the Cambridge Philosophical Society, 159(2), 253–273 (2015). 
  46. Daniilidis, J. Malick, and H.S. Sendov, ‘On the structure of locally symmetric manifolds’, Journal of Convex Analysis, 22(2), 399–426 (2015). 
  47. H.S. Sendov and Sh. Shan, ‘New representation theorems for completely monotone and Bernstein functions with convexity properties on their measures’, Journal of Theoretical Probability, 28(4), 1689–1725 (2015). 
  48. Bl. Sendov and H.S. Sendov, ‘Loci of complex polynomials, part I’, Transactions of the American Mathematical Society, 366(10), 5155–5184 (2014). 
  49. H.S. Sendov and R. Zitikis, ‘The Shape of the Borwein-Affleck-Girgensohn Function Generated by Completely Monotone and Bernstein Functions’, Journal of Optimization Theory and Applications, 160, 67–89 (2014). 
  50. L.H. Yue, W. He, D. Murdoch, and H.S. Sendov, ‘Building Cost-efficient Models using BLARS Method’, Journal of Biometrics and Biostatistics, 4(5):177, doi:10.4172/2155-6180.1000177 (2013). 
  51. Bl. Sendov and H.S. Sendov, ‘Extension of apolarity and Grace theorem’, Mathematica Balkanica New Series, 27(1–2), 77–87 (2013).
  52. B.P.W. Ames and H.S. Sendov, ‘A new derivation of a formula by Kato’, Linear Algebra and Its Applications,  436, 722–730 (2012).
  53. Labb ́e, H.S. Sendov, and K.P. Sendova, ‘The Gerber-Shiu function and the generalized Cramer-Lundberg model’, Applied Mathematics and Computation, 218, 3035–3056 (2011).
  54. H.S. Sendov, Y. Wang, and R. Zitikis, ‘Log-supermodularity of weight functions, ordering weighted losses, and the loading monotonicity of weighted premiums', Insurance Mathematics and Economics, 48, 257–264 (2011).
  55. Pen ̃a and H.S. Sendov, ‘Spectral self-concordant functions in the space of two by two symmetric matrices’, Optimization, 60(4), 441–449 (2011).
  56. B.P.W. Ames and H.S. Sendov, ‘Asymptotic expansions of the ordered spectrum of symmetric matrices’,  Nonlinear Analysis, Series A: Theory, Methods & Applications, 72(11), 4288–4297 (2010).
  57. Fischer and H.S. Sendov, ‘On Malamud majorization and the extreme points of its level sets’, Journal of Convex Analysis, 17(2), 485–507 (2010).
  58. Pena and H.S. Sendov, ‘Separable self-concordant spectral functions and a conjecture of Tuncel’, Mathematical Programming, Series A, 125(1), 101–122 (2010).
  59. H.S. Sendov, ‘Pirates of democracy’, (in Bulgarian) Matematika Plus, 1, 70–72 (2010).
  60. Daniilidis, A.S. Lewis, J. Malick, and H.S. Sendov, ‘Prox-regularity of spectral functions and spectral sets’, Journal of Convex Analysis, 15(3), 547–560 (2008).
  61. H.S. Sendov, ‘Nonsmooth analysis of Lorentz invariant functions’, SIAM Journal on Optimization, 18(1), 1106– 1127 (2007). 
  62. H.S. Sendov, ‘The higher-order derivatives of spectral functions’, Linear Algebra and its Applications, 424(1), 240–281 (2007).
  63. Malick and H.S. Sendov, ‘Clarke generalized Jacobian of the projection onto the cone of positive semidefinite matrices’, Set-Valued Analysis, 14(3), 273–293 (2006).
  64. H.H. Bauschke, D.A. McLaren and H.S. Sendov, ‘Fitzpatrick functions: inequalities, examples and remarks on a problem by S. Fitzpatrick’, Journal of Convex Analysis, 13(3/4), 499–523 (2006).
  65. H.S. Sendov, ‘Generalized Hadamard product and the derivatives of spectral functions’, SIAM Journal of Matrix Analysis and Applications, 28(3), 667–681 (2006).
  66. A.S. Lewis and H.S. Sendov, ‘Nonsmooth analysis of singular values. Part II: Applications’, Set-Valued Analysis, 13(3), 243–264 (2005).
  67. A.S. Lewis and H.S. Sendov, ‘Nonsmooth analysis of singular values. Part I: Theory’, Set-Valued Analysis, 13(3), 213–241 (2005).
  68. A.S. Lewis and H.S. Sendov, ‘Quadratic expansions of spectral functions’, Linear Algebra and its Applications, 340, 97–121 (2002).
  69. H.S. Sendov, ‘Variational spectral analysis. Thesis (Ph.D.)’, University of Waterloo (Canada) 298 pp., ISBN: 978-0612-85348-5, (2001).
  70. A.S. Lewis and H.S. Sendov, ‘Twice differentiable spectral functions’, SIAM Journal on Matrix Analysis and Applications, 23, 368–386 (2001).
  71. A.S. Lewis and H.S. Sendov, ‘Self-concordant barriers for hyperbolic means’, Mathematical Programming, Series A, 91, 1–10 (2001).
  72. H.H. Bauschke, O. Guler, A.S. Lewis and H.S. Sendov, ‘Hyperbolic polynomials and convex analysis’, Canadian Journal of Mathematics, 53, 470–488 (2001).