Damir Kinzebulatov's Homepage damir.kinzebulatov@gmail.com Ph.D University of Toronto Mathematics, 2012 M.Sc University of Calgary Mathematics, 2006 B.Sc Izhevsk State Technical University, Russia Mathematics, 2004 I am an NSERC postdoc at The Fields Institute in Toronto My research: §1 [1] "Unique continuation for Schroedinger operators. Towards an optimal result" (with L.Shartser), J. Funct. Anal., 258 (2010), p. 2662-2681 0902.0423v2.pdf We prove the property of unique continuation for solutions of differtial inequality |\Delta u| \leq |Vu| (extending a number of classical results), and apply it (using Kato's result) to the problem of absence of positive eigenvalues of self-adjoint Schroedinger operators with form-bounded potentials V. §2 [2] "Towards Oka-Cartan theory for algebras of fibrewise bounded holomorphic functions on coverings of Stein manifolds I. Cartan theorems A and B" (with A.Brudnyi), Preprint, 36 p (2012) bru_kinz_1.pdf [3] "Towards Oka-Cartan theory for algebras of fibrewise bounded holomorphic functions II. Elements of function theory" (with A.Brudnyi), Preprint, 53 p (2012) bru_kinz_2.pdf [4] "Holomorphic almost periodic functions on coverings of complex manifolds" (with A.Brudnyi) New York J. Math, 17a (2011), p. 267-300 nyjm.pdf We establish the basic results of complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds, including    (1) Bohr's holomorphic almost periodic functions,    (2) algebras of all fibrewise bounded holomorphic functions arising, e.g., in the corona problem. In particular, we obtain results on holomorphic extension from complex submanifolds, properties of divisors, corona type theorems, holomorphic analogues of the Peter-Weyl approximation theorem, Hartogs type theorems, characterizations of uniqueness sets, etc. Our proofs are based on analogues of Cartan theorems A and B for coherent type sheaves on maximal ideal spaces of these algebras. §3 [5] "Holomorphic semi-almost periodic functions" (with A.Brudnyi), Integr. Equ. Operat. Theory, 66 (2010), p.293-325 0911.0954v1.pdf [6] "On algebras of holomorphic functons with semi-almost periodic boundary values" (with A.Brudnyi), C. R. Math. Rep. Acad. Sci. Canada, 32 (2010), p.1-12. [7] "On uniform subalgebras of L\infty on the unit circle generated by almost periodic functions" (with A.Brudnyi), St. Petersburg Math. J., 19 (2008), p.495-518 BK - SPbJMath.pdf We obtain a number of functin-theoretic results on the subalgebra of Hardy algebra of bounded holomorphic functions on the unit disk that have, in a sense, the weakest possible boundary discontinuities (corona-type theorem, approximation property etc). The techniques developed in this paper were used in the subsequent papers [2]-[4]. §4 [8] "A note on Gagliardo-Nirenberg type inequalities on analytic sets", C. R. Math. Rep. Acad. Sci. Canada, 30 (2009), p.97-105. We study a new invariant of singularities of complex analytic sets that arises as a `correcting exponent' in a family of inequalities relating norms of functions on these sets. Long yet productive :-) journey from the 2nd year of my B.Sc, through M.Sc, to the very begining of Ph.D: §5 [9] "Systems with distributions and viability theorem", J. Math. Anal. Appl., 331 (2007), p. 1046-1067 kinz_viab.pdf [10] "Dynamical generalized functions and the multiplication problem" (with V.Derr), Russian Math., 51 (2007), p.32-43 0603351.pdf We introduce two spaces of distributions endowed with continuous operation of multiplication by first-kind discontinuous functions, as needed for some classes of ordinary differential equations with distributions arising, e.g. in singular optimal control problems. §6 [11] "On linear perturbations of Ricker model" (with E.Braverman), Math Biosci., 202,  (2006), p. 323-339 We generalize a classical model of population dynamics.