Journal articles and drafts of Boris Shapiro
Notice that below you normally find only initially submitted versions. For the final versions contact the respective journals.
- (with D. Pasechnik)
On polygonal measures with vanishing harmonic moments, draft
- (with R. Froeberg and G.Ottaviani)
On the Waring problem for polynomial rings, PNAS, 109(15) (2012), 5600--5602.
- (with N. Saldanha)
Spaces of locally convex curves in S^n and combinatorics of the group B^+_{n+1}, J. of Singularities, vol. 4, (2012) 1--22
- (with M.Shapiro)
A few riddles behind Rolles's theorem, to appear in Amer. Math. Monthly
- (with M.Tater) Polynomial solutions of the Heun equation, Acta Polytechnica, vol. 51(4), (2011) 90--94
- (with V.Kostov) Hardy-Petrovich-Hutchinson's problem and partial theta function, to appear in Duke Math. J
- (with P.Alexandersson) Discriminants, symmetrized graph monomials, and sums of squares, to appear in Experimental Mathematics
- (with R.Froeberg) Linear recurrences and Vandermonde varieties. I, draft
- (with Y.Baryshnikov) How to run a roach, draft
- (with P.Braenden and I. Krasikov) Elements of Polya-Schur theory in finite difference setting, submitted.
- (with M.Shapiro) Linear ordinary differential equations and Schubert calculus, Proc. of 17th Goekova Geometry-Topology conference, (2011) 79--87.
- On Evgrafov-Fedoryuk's theory and quadratic differentials, submitted
- (with J.Borcea and R.Boegvad)
Corrigendum: "Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions", Publ. RIMS. vol. 48 (2012), 229--233.
- (with A.Vishnyakova and O.Katkova) Multiplier sequences and logarithmic mesh, Comptes Rendus Mathematique vol. 349 (1-2) (2011), 35--38.
- (with A.Khoroshkin) Using homological duality in consecutive pattern avoidance, Electr. J. Comb. vol 18(2) (2011) #P9.
- (with V.Kostov, and M.Tyaglov) Maximal univalent disks of real rational functions and Hermite-Biehler polynomials, Proc. Amer. Math. Soc. vol 139(5), (2011), 1625--1635.
- (with M.Passare, and M.Rojas)
New multiplier sequences and discriminant amoebae, Moscow Math. J vol 11(3) (2011), 547--560.
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Root asymptotics for the eigenfunctions of univariate differential operators, Acta Polytechnica, vol. 50(5) (2010), 77--83.
- (with J.Borcea, and S.Friedland)
Parametric Poincare-Perron theorem with applications, J. d'Analyse Mathematique, vol. 113(1) (2011), 197--225.
- (with K. Takemura, and M.Tater)
On spectral polynomial of the Heun equation.II, Comm. Math. Phys. 311(2) (2012), 277--300
- (with T.Holst)
On higher Heine-Stieltjes polynomials, Isr. J. Math. vol. 183 (2011), 321--347.
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Algebro-geometric aspects of Heine-Stieltjes theory, J. London Math. Soc. vol. 83(1) (2011), 36--56.
- (with M.Tater)
On spectral polynomial of the Heun equation.I, JAT, vol. 162 (2010), 766--781.
- (with A.Guterman)
On linear operators preserving the set of positive polynomials, JFPTA, vol. 3 (2) (2008), 411--429.
- (with V.Kostov, and A.Martinez-Finkelshtein)
Narayana numbers and Schur-Szego composition, JAT, vol. 161 (2) (2009), 464--476.
- (with M.Shapiro)
On eigenvalues of rectangular matrices, Proc. Steklov Math. Inst, vol. 267 (2009), 248--255.
- (with J.Borcea and R.Boegvad)
Homogenized spectral pencils for exactly solvable operators: asymptotics of polynomial eigenfunctions, Publ. RIMS. vol. 45 (2009), 525--568.
- (with M.Tater)
Asymptotics of spectral polynomials, Acta Polytechnica, vol. 47 (2-3) (2007), 32--35.
- (with J.Borcea)
Root asymptotics of spectral polynomials for the Lame operator, Commun. Math. Phys. vol. 282 (2008), 323--337.
- (with A.Eremenko and A.Gabrielov )
High energy eigenfunctions of one-dimensional Schroedinger operators with polynomial potentials, Comput. Methods Funct Theory vol. 8(2) (2008), 513--529.
- (with A.Eremenko and A.Gabrielov)
Zeros of eigenfunctions of some anharmonic oscillators, Annales de l'institut Fourier, vol. 58(2) (2008), 603--624.
- (with V.Kostov)
On Schur-Szegoe composition of polynomials, CRAS, vol. 343 (2006), 81--86.
- (with A.Degtyarev, I.Itenberg, T.Ekedahl, and M.Shapiro)
On total reality of meromorphic functions, Annales de l'institut Fourier, vol. 57(6) (2007), 2015--2030.
- (with T.Ekedahl and M.Shapiro)
First steps towards total reality for meromorphic functions, Moscow Math. J, vol. 6 (2006), 95--106.
- (with Y.Burman)
Around matrix theorem, MRL vol. 13(5) (2006), 761--774.
- (with J.Borcea and R.Boegvad)
On rational approximation of algebraic functions, Adv. Math. vol. 204 (2006), 448--480.
- (with A.Gabrielov and D.Novikov)
Mystery of point charges, Proc. London Math. Soc. vol 95(2), (2007), 443--472.
- (with M.Kazarian)
Giambelli-type formula for subbundles of the tangent bundle, Pacific J. Math. vol 230 (1) (2007), 233--255.
- (with J.Borcea)
Classifying real polynomial pencils, IMRN, vol. 69 (2004), 3689--3708.
- (with J.Borcea)
Hyperbolic polynomials and spectral order, C. R. Math. Acad. Sci. Paris vol. 337(11) (2003), 693--698.
- (with M.Shapiro and A.Vainshtein)
Periodic de Bruijn triangles: exact and asymptotic results,
Discr.Math. vol. 298 (2005), 321--333.
- (with A.Postnikov)
Trees, parking functions, syzygies, and deformations of monomial ideals,
Trans. AMS, vol. 356 (2004), 3109--3142.
- (with V.Sedykh)
On two conjectures related to convex curves, Intern.J.Math., vol. 16(10) (2005), 1157--1174.
- (with A.Vainshtein)
Counting real rational functions with all real critical values, Moscow Math. J., vol.3(2) (2003), 647--659.
- (with T.Bergkvist and H.Rullgaard)
On Bochner-Krall orthogonal polynomial systems, Math. Scand. vol. 94(1) (2004), 148--154.
- (with S.Natanzon and A.Vainshtein)
Topological classification of generic real rational functions, J. Knot Theory Ramifications vol. 11(7) (2002), 1063--1075.
- (with V.Kostov)
On arrangements of roots for a real hyperbolic polynomial and its derivatives, Bull. Sci. Math. vol. 126(1) (2002), 45--60.
- (with G.Mason)
On polynomial eigenfunctions of d^k/dx^kQ(x), Experiment. Math. vol. 10(4) (2001), 609--618.
- (with A.Vainshtein)
On the number of connected components in the space of M-polynomials in hyperbolic functions, Adv. in Appl. Math. vol. 30(1-2) (2003), 273--282.
- (with M.Shapiro, A.Vainshtein and A.Zelevinsky)
Simply-laced Coxeter groups and groups generated by symplectic transvections, Michigan J. of Maths, vol. 48 (2000), 531--552.
- (with A.Postnikov and M.Shapiro)
Algebra of Chern forms on homogeneous manifolds, AMS Trans. Ser 2, vol. 194, 227--235.
- (with M.Shapiro)
Projective convexity in P^3 implies Grassmann convexity, Int. J. Math, vol. 11(4) (2000), 579--588.
- (with M.Shapiro and A. Vainshtein)
Skew-symmetric vanishing lattices and intersection of Schubert cells, IMRN (11) (1998), 563--588.
- (with M.Shapiro)
On ring generated by Chern curvature forms on SL_n/B, Comptes Rendus, vol. 326 (1998), 75--80.
- (with M.Kazarian and R.Montgomery)
Characteristic classes for the degeneration of 2-plane fields in four dimensions, Pacific J. Math, vol. 179(2) (1997), 355--370.
- (with M.Shapiro and A.Vainshtein)
On combinatorics and topology of pairwise intersections of Schubert cells in SL_n/B, Arnold-Gelfand Math. Seminars,
(1997), 397--437.
- d-free maps satisfy the homotopy principle, Indag. Math., vol. 7(1) (1998), 107--111.
- (with M. Shapiro and A. Vainshtein)
On the number of connected components in the intersection of 2 open Schubert cells in SL_n/B, Int. Math. Res. Not, (10) (1997), 469--493.
-
Discriminants of convex curves are homeomorphic, Proc. of the AMS, vol. 128(8) (1998), 1923--1930.
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On the number of connected components in the space of trigonometric polynomials of degree n with 2n different critical
values (in Russian), Mat. Zametki, vol. 62 (1997) 635--640.
- (with V.Welker)
Combinatorics and topology of stratifications of the space of monic polynomials with real coefficients, Result. Math. vol. 33 (1998), 338--355.
- (with V.Sedykh)
On Young hulls of convex curves in R^{2n}, J. of Geometry, vol. 63(1/2) (1998), 168--182.
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Tree-like curves and their number of inflection points, AMS Transl. ser.2 (Advances in Math. Sciences), vol. 190 (1999)
113--130.
- (with A.~L.~Gorodentsev)
On associated discriminants for polynomials of one variable, Beitrage zur Algebra und Geometrie, vol. 39(1) (1998), 53--74.
- (with M.Shapiro and A.Vainshtein)
Generalized Lyashko--Looijenga map, ramified coverings of the sphere, and enumeration of edge-labeled $k$-trees Proc. 8th Intl. Conf. on Formal Power Series and Algebr. Combinatorics, 1996, 421--426.
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Normal forms of Whitney umbrella in the presence of a cone, Funct. Anal. Applic, vol. 31(2) (1997), 91--94.
- (with M.Shapiro and A.Vainshtein)
Incomplete flag varieties and Kazhdan-Lusztig polynomials, 1995, Proc. 7th Intl.
Conf. on Formal Power series and Algebr. Combinatorics, Disc. Math, vol. 180 (1998), 345--355.
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Singularities of maps to a space with a fixed cone, Math. Scand., vol. 77 (1995) 17--44.
- (with M.Shapiro)
On the totally positive upper triangular matrices, Lin. Alg. and Appl., vol. 273 (1996), 23--29.
- (with M.Shapiro and A.Vainshtein)
Intersections of Schubert cells and structure constants of Hecke algebra, Discr. Math, vol. 153 (1996), 305--318.
- (with B.Khesin)
Homotopy classification of nondegenerate quasiperiodic curves on 2-sphere,
Publications de l'Institut Mathematique, nouvelle serie, vol. 66(80) (1999), 127--156.
- (with K.Jewell, P.Orlik)
On homology of the complement to an arbitrary subspace arrangement, Top. and Appl.,
vol. 56 (1994), 215--233.
-
Mixed Hodge structures of complements to complex hyperplane arrangements are pure, Proc. of the AMS, vol. 117(4) (1993), 931--934.
- (with B.Khesin)
Swallowtails and Whitney umbrellas are homeomorphic, J. of Alg. Geom., vol. 1 (1992) 549--560.
- (with B.Khesin)
Nondegenerate curves on S^2 and orbit classification of the Zamolodchikov algebra, Comm. Math. Phys.,
vol. 145 (1992), 357--362.
- (with M.Shapiro)
On the number of connected components of non-degenerate curves on S^n, Bull. of the AMS, vol. 25(1) (1991),
75--79.
- (with M.Shapiro)
The M-property of flag varieties Top. and Appl., vol. 43)(1) (1992), 65--81.
- (with A.Vainshtein)
Euler characteristics for links of Schubert cells in the space of complete flags, Adv. Sov. Math.,
v.1, AMS, Providence, 1990, pp. 273--286.
-
Space of linear differential operators and flag manifolds, Izv. Acad. Sci. USSR, vol. 54(1) 1990, 183--197 (English and Russian versions) (SHORTENED ENGLISH VERSION, 7 pages).
- Linear differential operators and flag manifolds, Funct. Anal. Apppl, vol. 23(1) (1989), 82--83 (English and Russian versions)
- (with A.Vainshtein) The Maslov index for a quadruple of Lagrangian planes and the index of a two-folded closed trajectory of the Birkhoff billiards in R}^{n+1}. (Russian), Proc. 13th USSR Sem. on Operator Theory in Functional Spaces, Kuibyshev (1988), 39
- (with V.Kostov)
The flags in R^3, transversal to a given set of flags form an M-manifold. (Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh. vol. 44(5) (1989), 26--30.
- (with A.Vainshtein)
Singularities of the boundary of a domain of hyperbolicity. (Russian), Itogi Nauki i Tekhniki, Current problems in mathematics. Newest results, 236, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, vol 33 (1988), 193--214 (English transl. in J. Soviet Math. vol. 52(4) (1990), 3326--3337)
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The boundary of disconjugate domain for linear Hamiltonian systems. (Russian), Uspekhi Mat. Nauk, vol. 43(4) (1988), 170--171
- (with A.Vainshtein)
Singularities of hyperbolic polynomials and the boundary of a domain of hyperbolicity. (Russian), Uspekhi Mat. Nauk vol. 40(5) (1985), 305
- (with A.Vainshtein)
Multi-dimensional analogues of the Newton and Ivory theorems. (Russian), Funktsional. Anal. i Prilozhen. vol. 19(19 (1985), 20--24. (English transl. in Functional Anal. Appl. vol. 19 (1985), 17--20)
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O Newtonovskom prityazhenii ellipsoidov. (Russian), Kvant vol. 3(5) (1985), 18--25.
- (with A.Vainshtein and L.Reitblat)
Asymptotic behavior of the solution of difference equations of two variables. (Russian), Differentsial' nye Uravneniya vol. 20(8) (1984), 1433--1437.
- (with A.Vainshtein)
Structure of a set of $\bar a$-representable numbers. (Russian), Izv. Vyssh. Uchebn. Zaved. Mat. vol. 7(5) (1980) 8--11.
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An algorithm for construction of a chain covering of an undirected graph. (Russian), Moskov. Inst. Inzh. Zheleznodorozh. Transporta Trudy, Prikl. Mat. i Zadachi Zheleznodorozh. Transporta, vol. 640 (1979), 138--142
Miscellaneous publications and texts
-
Ett oeppet brev till matematikdelegationen, in Swedish (in connection with a new school debate, winter 2008)
-
To my former classmates, in Russian
- (with A.Guterman)
A note on positivity preservers, unpublished note
-
About 'Jewish' University and Misha Marinov (Russian and English versions), 3 p. Multiple facets of quantization and supersymmetry, 36--39, World Sci. Publishing, River Edge, NJ, 2002,
- Disconjugate linear ordinary differential equations, flag varieties and classification of symplectic leaves in several Kac-Moody and Gelfand-Dikii algebras, my Swedish Ph. D. disservation defended on June 1, 1990 at Stockholm University (rather different from the Soviet dissertation)
- Singularities of the boundaries of the spaces of differential equations, my Soviet Ph. D. disservation which was failed on December 15, 1989 at Moscow State University
- (with A. Ryvlin) o Algorithm formirovaniya i vybora predpochtitel'nyh variantov tekhnologicheskih linii i ego primenenie k proektirovaniyu gidroliznyh proizvodstv. (Russian), Biotekhnologiya, vol. 4(1), 1988, 119--124.
- (with V. Danilov and A.Vainshtein), Metody formirovaniya i optimizacii general'nyh planov promyshlennyh proizvodstv i komponovki proizvodstvennyh pomeshenii. (Russian), Ekonomika mikrobiologicheskih proizvodstv, obzornaya informaciya, 1987, 1--48.