Boris Shapiro

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All published works

Action	Title	Year	Authors
+ PDF Chat	An inverse problem in P\'olya--Schur theory. II. Exactly solvable operators and complex dynamics	2024	Per Alexandersson Nils Hemmingsson Boris Shapiro
+	In search of a higher Bochner theorem	2024	Emil Horozov Boris Shapiro Miloš Tater
+ PDF Chat	Bizonotopal Graphical Algebras	2024	Anatol Kirillov Gleb Nenashev Boris Shapiro Arkady Vaintrob
+ PDF Chat	On boundary points of minimal continuously Hutchinson invariant sets	2024	Per Alexandersson Nils Hemmingsson Dmitry A. Novikov Boris Shapiro Guillaume Tahar
+ PDF Chat	An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators	2024	Per Alexandersson Petter Brändén Boris Shapiro
+ PDF Chat	In search of Newton-type inequalities	2024	Olga Katkova Boris Shapiro Anna Vishnyakova
+ PDF Chat	In search of Newton-type inequalities	2024	Olga Katkova Boris Shapiro Anna Vishnyakova
+ PDF Chat	Semiclassical expansion for exactly solvable differential operators	2024	J. Borrego-Morell Boris Shapiro
+	Linear first order differential operators and their Hutchinson invariant sets	2024	Per Alexandersson Nils Hemmingsson Dmitry Novikov Boris Shapiro Guillaume Tahar
+ PDF Chat	Real polynomials with constrained real divisors. I. Fundamental groups	2023	Gabriel Katz Boris Shapiro Volkmar Welker
+ PDF Chat	Meromorphic functions without real critical values and related braids	2023	Anatoly Libgober Boris Shapiro
+ PDF Chat	Rodrigues’ Descendants of a Polynomial and Boutroux Curves	2023	Rikard Bøgvad Christian Hägg Boris Shapiro
+ PDF Chat	Correction: Non-Self-Adjoint Toeplitz Matrices Whose Principal Submatrices Have Real Spectrum	2023	Boris Shapiro František Štampach
+ PDF Chat	Finiteness of rank for Grassmann convexity	2023	Nicolau C. Saldanha Boris Shapiro Michael Shapiro
+ PDF Chat	Introducing isodynamic points for binary forms and their ratios	2023	Christian Hägg Boris Shapiro Michael Shapiro
+ PDF Chat	Fluctuational electrodynamics in and out of equilibrium	2022	Iver Brevik Boris Shapiro Mário G. Silveirinha
+	Corrigendum to “On two conjectures concerning convex curves”, by V. Sedykh and B. Shapiro	2022	Boris Shapiro Michael Shapiro
+	Linear first order differential operators and their Hutchinson-invariant sets	2022	Per Alexandersson Nils Hemmingsson Dmitry Novikov Boris Shapiro Guillaume Tahar
+	Introducing isodynamic points for binary forms and their ratios	2022	Christian Hägg Boris Shapiro Michael Shapiro
+	Deformed graphical zonotopal algebras	2022	Boris Shapiro Ilya Smirnov Arkady Vaintrob
+	Stationary Charge Radiation in Anisotropic Photonic Time Crystals	2022	Huanan Li Shixiong Yin Huan He Jingjun Xu Andrea Alù Boris Shapiro
+ PDF Chat	On Limit Sets for Geodesics of Meromorphic Connections	2021	Dmitry Novikov Boris Shapiro Guillaume Tahar
+ PDF Chat	On spectral asymptotic of quasi-exactly solvable quartic potential	2021	Boris Shapiro Miloš Tater
+	Return of the plane evolute	2021	Ragni Piene Cordian Riener Boris Shapiro
+ PDF Chat	On existence of quasi-Strebel structures for meromorphic $k$-differentials	2021	Boris Shapiro Guillaume Tahar
+	Adjoints and Canonical Forms of Polypols	2021	Kathlén Kohn Ragni Piene Kristian Ranestad Felix Rydell Boris Shapiro Rainer Sinn Miruna‐Ştefana Sorea Simon Telen
+	Quadratic differentials and signed measures	2021	Yuliy Baryshnikov Boris Shapiro
+ PDF Chat	Grassmann Convexity and Multiplicative Sturm Theory, Revisited	2021	Nicolau C. Saldanha Boris Shapiro Michael Shapiro
+ PDF Chat	On the number of intersection points of the contour of an amoeba with a line	2021	Lionel Lang Boris Shapiro Eugeniĭ Shustin
+	Spaces of polynomials with constrained real divisors, II. (Co)homology & stabilization	2021	Gabriel Katz Boris Shapiro Volkmar Welker
+	A critical discussion of different methods and models in Casimir effect	2021	Iver Brevik Boris Shapiro
+	Adjoints and Canonical Forms of Polypols	2021	Kathlén Kohn Ragni Piene Kristian Ranestad Felix Rydell Boris Shapiro Rainer Sinn Miruna‐Ştefana Sorea Simon Telen
+	Return of the plane evolute	2021	Ragni Piene Cordian Riener Boris Shapiro
+	Finiteness of rank for Grassmann convexity	2021	Nicolau C. Saldanha Boris Shapiro Michael Shapiro
+	Rodrigues' descendants of a polynomial and Boutroux curves	2021	Rikard Bøgvad Christian Hägg Boris Shapiro
+	On limit sets for geodesics of meromorphic connections	2020	Dmitry Novikov Boris Shapiro Guillaume Tahar
+	On existence of quasi-Strebel structures for meromorphic k-differentials	2020	Boris Shapiro Guillaume Tahar
+	Algebraic Relations between Harmonic and Anti-harmonic Moments of Plane Polygons	2020	Yurii Burman Ralf Fröberg Boris Shapiro
+	Generalizing Tran's Conjecture	2020	Rikard Bøgvad Innocent Ndikubwayo Boris Shapiro
+	On algebras and matroids associated to undirected graphs	2020	Boris Shapiro Arkady Vaintrob
+	On existence of quasi-Strebel structures for meromorphic k-differentials	2020	Boris Shapiro Guillaume Tahar
+ PDF Chat	On the number of intersection points of the contour of an amoeba with a line	2019	Lionel Lang Boris Shapiro Eugeniĭ Shustin
+ PDF Chat	Moment varieties of measures on polytopes	2019	Kathlén Kohn Boris Shapiro Bernd Sturmfels
+	Level crossing in random matrices. II. Random perturbation of a random matrix	2019	Tobias Grøsfjeld Boris Shapiro Konstantin Zarembo
+	Grassmann convexity and multiplicative Sturm theory, revisited.	2019	Nicolau C. Saldanha Boris Shapiro Michael Shapiro
+	On Hurwitz--Severi numbers	2019	Yuri Burman Boris Shapiro
+ PDF Chat	New Aspects of Descartes’ Rule of Signs	2019	Vladimir Petrov Kostov Boris Shapiro
+	On the number of intersection points of the contour of an amoeba with a line	2019	Lionel Lang Boris Shapiro Eugeniĭ Shustin
+	Algebraic relations between moments of plane polygons	2019	Yurii Burman Ralf Fröberg Boris Shapiro
+	Real polynomials with constrained real divisors. I. Fundamental groups	2019	Gabriel Katz Boris Shapiro Volkmar Welker
+	Grassmann convexity and multiplicative Sturm theory, revisited	2019	Nicolau C. Saldanha Boris Shapiro Michael Shapiro
+ PDF Chat	Electrostatic Problems with a Rational Constraint and Degenerate Lamé Equations	2018	Dimitar K. Dimitrov Boris Shapiro
+ PDF Chat	On generic and maximal k-ranks of binary forms	2018	Samuel Lundqvist Alessandro Oneto Bruce Reznick Boris Shapiro
+ PDF Chat	Algebraic Stories from One and from the Other Pockets	2018	Ralf Fröberg Samuel Lundqvist Alessandro Oneto Boris Shapiro
+	Moment Varieties of Measures on Polytopes	2018	Kathlén Kohn Boris Shapiro Bernd Sturmfels
+	Electrostatic problems with a rational constraint and degenerate Lame equations	2018	Dimitar K. Dimitrov Boris Shapiro
+ PDF Chat	On moments of a polytope	2018	Nick Gravin Dmitrii V. Ṗasechnik Boris Shapiro Michael Shapiro
+	Topological classification of generic real meromorphic functions from compact surfaces	2018	Antonio F. Costa S. M. Natanzon Boris Shapiro
+ PDF Chat	Corrigendum: “Could René Descrates have known this?”	2018	Jens Forsgård Vladimir Petrov Kostov Boris Shapiro
+	In search of higher Bochner theorem	2018	Emil Horozov Boris Shapiro Miloš Tater
+	Moment Varieties of Measures on Polytopes	2018	Kathlén Kohn Boris Shapiro Bernd Sturmfels
+	Electrostatic problems with a rational constraint and degenerate Lame equations	2018	Dimitar K. Dimitrov Boris Shapiro
+ PDF Chat	Non-Self-Adjoint Toeplitz Matrices Whose Principal Submatrices Have Real Spectrum	2017	Boris Shapiro František Štampach
+ PDF Chat	Secant Degeneracy Index of the Standard Strata in The Space of Binary Forms	2017	Gleb Nenashev Boris Shapiro Michael Shapiro
+ PDF Chat	On generic and maximal $k$-ranks of binary forms	2017	Samuel Lundqvist Alessandro Oneto Bruce Reznick Boris Shapiro
+	Comment on arXiv:1705.01165 by V. N. Premakumar, M. G. Vavilov and R. Joynt	2017	Rémi Carminati Boris Shapiro
+ PDF Chat	Asymptotics and Monodromy of the Algebraic Spectrum of Quasi-Exactly Solvable Sextic Oscillator	2017	Boris Shapiro Miloš Tater
+	Something You Always Wanted to Know About Real Polynomials (But Were Afraid to Ask)	2017	Vladimir Petrov Kostov Boris Shapiro
+	Non-self-adjoint Toeplitz matrices whose principal submatrices have real spectrum	2017	Boris Shapiro František Štampach
+	On real banded Toeplitz matrices whose limiting eigenvalue distribution has real support	2017	Boris Shapiro František Štampach
+	“K-theoretic” analog of Postnikov–Shapiro algebra distinguishes graphs	2017	Gleb Nenashev Boris Shapiro
+ PDF Chat	On mother body measures with algebraic Cauchy transform	2017	Rikard Bøgvad Boris Shapiro
+ PDF Chat	Root-counting Measures of Jacobi Polynomials and Topological Types and Critical Geodesics of Related Quadratic Differentials	2017	Boris Shapiro Alexander Yu. Solynin
+	Something You Always Wanted to Know About Real Polynomials (But Were Afraid to Ask)	2017	Vladimir Petrov Kostov Boris Shapiro
+	Non-self-adjoint Toeplitz matrices whose principal submatrices have real spectrum	2017	Boris Shapiro František Štampach
+	Comment on arXiv:1705.01165 by V. N. Premakumar, M. G. Vavilov and R. Joynt	2017	Rémi Carminati Boris Shapiro
+ PDF Chat	Level crossing in random matrices: I. Random perturbation of a fixed matrix	2016	Boris Shapiro Konstantin Zarembo
+	Some remarks on the super Fermat problem for binary forms	2016	Gleb Nenashev Boris Shapiro Michael Shapiro
+	Asymptotics and monodromy of the algebraic spectrum of quasi-exactly solvable sextic oscillator	2016	Boris Shapiro Miloš Tater
+	Topological classification of generic real meromorphic functions	2016	Antonio F. Costa S. M. Natanzon Boris Shapiro
+	On Vandermonde Varieties	2016	Ralf Fröberg Boris Shapiro
+ PDF Chat	A Tropical Analog of Descartes’ Rule of Signs	2016	Jens Forsgård Dmitry Novikov Boris Shapiro
+	On global non-oscillation of linear ordinary differential equations with polynomial coefficients	2016	Dmitry Novikov Boris Shapiro
+	On plane Hurwitz numbers of Severi varieties	2016	Yurii Burman Boris Shapiro
+	Elements of Pólya-Schur theory in the finite difference setting	2016	Petter Brändén Ilia Krasikov Boris Shapiro
+	"K-theoretic" analog of Postnikov-Shapiro algebra distinguishes graphs	2016	Gleb Nenashev Boris Shapiro
+	On Hurwitz--Severi numbers	2016	Yurii Burman Boris Shapiro
+	Level functions of quadratic differentials, signed measures, and the Strebel property	2016	Yuliy Baryshnikov Boris Shapiro
+	Topological classification of generic real meromorphic functions	2016	Antonio F. Costa S. M. Natanzon Boris Shapiro
+	Asymptotics and monodromy of the algebraic spectrum of quasi-exactly solvable sextic oscillator	2016	Boris Shapiro Miloš Tater
+ PDF Chat	Could René Descartes Have Known This?	2015	Jens Forsgård Vladimir P. Kostov Boris Shapiro
+	On global non-oscillation of linear ordinary differential equations with polynomial coefficients	2015	Dmitry Novikov Boris Shapiro
+ PDF Chat	Problems Around Polynomials: The Good, The Bad and The Ugly...	2015	Boris Shapiro
+ PDF Chat	A Note on Planarity Stratification of Hurwitz Spaces	2015	Jared Ongaro Boris Shapiro
+	On Evgrafov–Fedoryuk’s theory and quadratic differentials	2015	Boris Shapiro
+	A tropical analog of Descartes' rule of signs	2015	Jens Forsgård Dmitry Novikov Boris Shapiro
+	On asymptotic Gauss-Lucas theorem	2015	R. Boegvad Dmitry Khavinson Boris Shapiro
+	A Note on Planarity Stratification of	2015	Jared Ongaroand Boris Shapiro
+	Problems around polynomials - the good, the bad and the ugly ...	2015	Boris Shapiro
+ PDF Chat	Could Ren\'e Descartes have known this?	2015	Jens Forsgård Vladimir Petrov Kostov Boris Shapiro
+	Could René Descartes have known this?	2015	Jens Forsgaard Vladimir Petrov Kostov Boris Shapiro
+	On global non-oscillation of linear ordinary differential equations with polynomial coefficients	2015	Dmitry Novikov Boris Shapiro
+	Root-counting measures of Jacobi polynomials and topological types and critical geodesics of related quadratic differentials	2015	Boris Shapiro Alexander Yu. Solynin
+	On spectral asymptotic of quasi-exactly solvable quartic and Yablonskii-Vorob'ev polynomials	2014	Boris Shapiro Miloš Tater
+	A note on planarity stratification of Hurwitz spaces	2014	Jared Ongaro Boris Shapiro
+ PDF Chat	On polygonal measures with vanishing harmonic moments	2014	Dmitrii V. Ṗasechnik Boris Shapiro
+	On mother body measures with algebraic Cauchy transform	2014	Rikard Bœgvad Boris Shapiro
+	Around a multivariate Schmidt–Spitzer theorem	2014	Per Alexandersson Boris Shapiro
+	Planarity stratification of Hurwitz spaces	2014	Jared Ongaro Boris Shapiro
+	On spectral asymptotic of quasi-exactly solvable quartic	2014	Boris Shapiro Miloš Tater
+	On mother body measures with algebraic Cauchy transform	2014	Rikard Bœgvad Boris Shapiro
+ PDF Chat	Hardy–Petrovitch–Hutchinson’s problem and partial theta function	2013	Vladimir Petrov Kostov Boris Shapiro
+	Vandermonde varieties and relations among Schur polynomials	2013	Ralf Fröberg Boris Shapiro
+ PDF Chat	Discriminants, Symmetrized Graph Monomials, and Sums Of Squares	2012	Per Alexandersson Boris Shapiro
+ PDF Chat	On the Waring problem for polynomial rings	2012	Ralf Fröberg Giorgio Ottaviani Boris Shapiro
+ PDF Chat	On Spectral Polynomials of the Heun Equation. II	2012	Boris Shapiro Kouichi Takemura Miloš Tater
+ PDF Chat	Corrigendum: “Homogenized Spectral Problems for Exactly Solvable Operators: Asymptotics of Polynomial Eigenfunctions”	2012	Julius Borcea Rikard Bøgvad Boris Shapiro
+ PDF Chat	A Few Riddles Behind Rolle’s Theorem	2012	Boris Shapiro Michael Shapiro
+ PDF Chat	Spaces of Locally Convex Curves in S^n and Combinatorics of the Group B_(n+1)^+	2012	Nicolau Saladanha Boris Shapiro
+	Elements of Polya-Schur theory in finite difference setting	2012	Petter Brändén Ilia Krasikov Boris Shapiro
+ PDF Chat	Spaces of Locally Convex Curves in S^n and Combinatorics of the Group B_(n+1)^+	2012	Nicolau Saladanha Boris Shapiro
+ PDF Chat	Spaces of Locally Convex Curves in S^n and Combinatorics of the Group B_(n+1)^+	2012	Nicolau Saladanha Boris Shapiro
+ PDF Chat	On higher heine-stieltjes polynomials	2011	Thomas Holst Boris Shapiro
+ PDF Chat	Using Homological Duality in Consecutive Pattern Avoidance	2011	Anton Khoroshkin Boris Shapiro
+ PDF Chat	Parametric Poincaré-Perron theorem with applications	2011	Julius Borcea Shmuel Friedland Boris Shapiro
+	LINEAR ORDINARY DIFFERENTIAL EQUATIONS AND SCHUBERT CALCULUS	2011	Boris Shapiro Michael Shapiro
+ PDF Chat	Maximal univalent disks of real rational functions and Hermite-Biehler polynomials	2010	Vladimir Petrov Kostov Boris Shapiro Mikhail Tyaglov
+ PDF Chat	Multiplier sequences and logarithmic mesh	2010	Olga Katkova Boris Shapiro Anna Vishnyakova
+ PDF Chat	Algebro-geometric aspects of Heine-Stieltjes theory	2010	Boris Shapiro
+	Multiplier sequences and logarithmic mesh	2010	Olga Katkova Boris Shapiro Anna Vishnyakova
+	Using homological duality in consecutive pattern avoidance	2010	Anton Khoroshkin Boris Shapiro
+	New Multiplier Sequences via Discriminant Amoebae	2010	Mikael Passare Boris Shapiro J. Maurice Rojas
+ PDF Chat	Root Asymptotics for the Eigenfunctions of Univariate Differential Operators	2010	Boris Shapiro
+	A Note on EVgrafov-Fedoryuk's theory and quadratic differentials	2010	Boris Shapiro
+	LINEAR RECURRENCES AND VANDERMONDE VARIETIES. I.	2010	Boris Shapiro
+	New Multiplier Sequences via Discriminant Amoebae	2010	Boris Shapiro
+	Multiplier sequences and logarithmic mesh	2010	Olga Katkova Boris Shapiro Anna Vishnyakova
+	Using homological duality in consecutive pattern avoidance	2010	Anton Khoroshkin Boris Shapiro
+ PDF Chat	On eigenvalues of rectangular matrices	2009	Boris Shapiro Michael Shapiro
+	Parrametric Poincare-Perron theorem with applications	2009	Julius Borcea Shmuel Friedland Boris Shapiro
+ PDF Chat	Homogenized Spectral Problems for Exactly Solvable Operators: Asymptotics of Polynomial Eigenfunctions	2009	Julius Borcea Rikard Bøgvad Boris Shapiro
+	On spectral polynomials of the Heun equation. II	2009	Boris Shapiro Kouichi Takemura Miloš Tater
+	On higher Heine-Stieltjes polynomials	2009	Thomas Holst Boris Shapiro
+	Parrametric Poincare-Perron theorem with applications	2009	Julius Borcea Shmuel Friedland Boris Shapiro
+	Narayana numbers and Schur–Szegő composition	2008	Vladimir P. Kostov Andrei Martı́nez-Finkelshtein Boris Shapiro
+ PDF Chat	On linear operators preserving the set of positive polynomials	2008	Alexander Guterman Boris Shapiro
+ PDF Chat	Root Asymptotics of Spectral Polynomials for the Lamé Operator	2008	Julius Borcea Boris Shapiro
+	Preserving positive polynomials and beyond	2008	Julius Borcea Alexander Guterman Boris Shapiro
+ PDF Chat	Zeros of eigenfunctions of some anharmonic oscillators	2008	Alexandre Erëmenko Andrei Gabrielov Boris Shapiro
+	Narayana numbers and Schur-Szego composition	2008	Vladimir Petrov Kostov Boris Shapiro
+	On spectral polynomials of the Heun equation	2008	Boris Shapiro Miloš Tater
+	High Energy Eigenfunctions of One-Dimensional Schrödinger Operators with Polynomial Potentials	2007	Alexandre Erëmenko Andrei Gabrielov Boris Shapiro
+	Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions	2007	Julius Borcea Rikard Bøgvad Boris Shapiro
+	Classification of spaces of locally convex curves in S^n and combinatorics of the Weyl group D_{n+1}	2007	Nicolau C. Saldanha Boris Shapiro
+ PDF Chat	A Giambelli-type formula for subbundles of the tangent bundle	2007	Boris Shapiro Maxim Kazarian
+ PDF Chat	Root Asymptotics of Spectral Polynomials	2007	Boris Shapiro Miloš Tater
+ PDF Chat	On total reality of meromorphic functions	2007	Alex Degtyarev Torsten Ekedahl Ilia Itenberg Boris Shapiro Michael Shapiro
+	On eigenvalues of rectangular matrices	2007	Julius Borcea Boris Shapiro Michael Shapiro
+	High energy eigenfunctions of one-dimensional Schrodinger operators with polynomial potentials	2007	Alexandre Erëmenko Andrei Gabrielov Boris Shapiro
+	Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions	2007	Julius Borcea Rikard Bøgvad Boris Shapiro
+	Spaces of locally convex curves in S^n and combinatorics of the group B_{n+1}	2007	Nicolau C. Saldanha Boris Shapiro
+	Asymptotics of spectral polynomials	2007	Boris Shapiro Miloš Tater
+ PDF Chat	On the Schur–Szegö composition of polynomials	2006	Vladimir P. Kostov Boris Shapiro
+	Classification of hyperbolicity and stability preservers: the multivariate Weyl algebra case	2006	Julius Borcea Petter Brändén Boris Shapiro
+	On Schur-Szego composition of polynomials	2006	Vladimir Petrov Kostov Boris Shapiro
+ PDF Chat	On total reality of meromorphic functions	2006	Alex Degtyarev Torsten Ekedahl Ilia Itenberg Boris Shapiro Michael Shapiro
+ PDF Chat	First Steps towards Total Reality of Meromorphic Functions	2006	Torsten Ekedahl Boris Shapiro Michael Shapiro
+ PDF Chat	Around matrix-tree theorem	2006	Yuri Burman Boris Shapiro
+	First steps towards total reality of meromorphic functions	2006	Torsten Ekedahl Boris Shapiro Michael Shapiro
+	Zeros of eigenfunctions of some anharmonic oscillators	2006	Alexandre Erëmenko Andrei Gabrielov Boris Shapiro
+	On Schur-Szego composition of polynomials	2006	Vladimir Petrov Kostov Boris Shapiro
+ PDF Chat	ON TWO CONJECTURES CONCERNING CONVEX CURVES	2005	V. D. Sedykh Boris Shapiro
+ PDF Chat	On rational approximation of algebraic functions	2005	Julius Borcea Rikard Bøgvad Boris Shapiro
+ PDF Chat	Periodic de Bruijn triangles: exact and asymptotic results	2005	Boris Shapiro Michael Shapiro Alek Vainshtein
+	Around matrix-tree theorem	2005	Yurii Burman Boris Shapiro
+	Mystery of point charges	2004	Andrei Gabrielov Dmitry Novikov Boris Shapiro
+	Trees, parking functions, syzygies, and deformations of monomial ideals	2004	Alexander Postnikov Boris Shapiro
+ PDF Chat	On Bochner-Krall orthogonal polynomial systems	2004	Tanja Bergkvist Hans Rullgård Boris Shapiro
+	None	2004	Julius Borcea Boris Shapiro
+	Classifying real polynomial pencils	2004	Julius Borcea Boris Shapiro
+	Mystery of point charges	2004	Andrei Gabrielov Dmitry Novikov Boris Shapiro
+ PDF Chat	Hyperbolic polynomials and spectral order	2003	Julius Borcea Boris Shapiro
+	On the number of connected components in the space of M-polynomials in hyperbolic functions	2003	Boris Shapiro Alek Vainshtein
+	Trees, parking functions, syzygies, and deformations of monomial ideals	2003	Alexander Postnikov Boris Shapiro
+	Hyperbolic polynomials and spectral order	2003	Julius Borcea Boris Shapiro
+	A few riddles behind Rolle's theorem	2003	Boris Shapiro Michael Shapiro
+	Periodic de Bruijn triangles: exact and asymptotic results	2003	Boris Shapiro Michael Shapiro Alek Vainshtein
+ PDF Chat	TOPOLOGICAL CLASSIFICATION OF GENERIC REAL RATIONAL FUNCTIONS	2002	Sergei Natanzon Boris Shapiro Alek Vainshtein
+	Two conjectures on convex curves	2002	V. D. Sedykh Boris Shapiro
+	Counting real rational functions with all real critical values	2002	Boris Shapiro Alek Vainshtein
+	On arrangements of roots for a real hyperbolic polynomial and its derivatives	2002	Vladimir Petrov Kostov Boris Shapiro
+	On Bochner-Krall orthogonal polynomial systems	2002	Tanja Bergkvist Hans Rullgård Boris Shapiro
+	On two conjectures concerning convex curves	2002	V. D. Sedykh Boris Shapiro
+	Topological classification of generic real rational functions	2001	Sergei Natanzon Boris Shapiro Alek Vainshtein
+ PDF Chat	On Polynomial Eigenfunctions of a Hypergeometric-Type Operator	2001	Gisli Màsson Boris Shapiro
+	Topological classification of generic real rational functions	2001	Sergei Natanzon Boris Shapiro Alek Vainshtein
+	PROJECTIVE CONVEXITY IN ℙ<sup>3</sup> IMPLIES GRASSMANN CONVEXITY	2000	Boris Shapiro Michael Shapiro
+ PDF Chat	Simply laced Coxeter groups and groups generated by symplectic transvections.	2000	Boris Shapiro Michael Shapiro Alek Vainshtein Andrei Zelevinsky
+ PDF Chat	Algebras of curvature forms on homogeneous manifolds	1999	Alexander Postnikov Boris Shapiro Michael Shapiro
+	Tree-like curves and their number of inflection points	1999	Boris Shapiro
+	Tree-like curves and their number of inflection points. Differential and symplectic topology of knots and curves	1999	Boris Shapiro
+	Simply-laced Coxeter groups and groups generated by symplectic transvections	1999	Boris Shapiro Michael Shapiro Alek Vainshtein Andrei Zelevinsky
+	Algebras of curvature forms on homogeneous manifolds	1999	Alexander Postnikov Boris Shapiro Michael Shapiro
+	Homotopy classification of nondegenerate quasiperiodic curves on the 2-sphere	1999	Boris Shapiro Boris Khesin
+	On Young hulls of convex curves in ?2n	1998	V. D. Sedykh Boris Shapiro
+	Combinatorics & Topology of Stratifications of The Space of Monic Polynomials With Real Coefficients	1998	Boris Shapiro Volkmar Welker
+	\̄t6-Free maps satisfy the homotopy principle	1998	Boris Shapiro
+	Kazhdan-Lusztig polynomials for certain varieties of incomplete flags	1998	Boris Shapiro Michael Shapiro Alek Vainshtein
+	On associated discriminants for polynomials in one variable	1998	Boris Shapiro A. L. Gorodentsev
+ PDF Chat	Discriminants of convex curves are homeomorphic	1998	Boris Shapiro
+	None	1998	Boris Shapiro Michael Shapiro Alek Vainshtein
+	On ring generated by Chern 2-forms on %plane1D;54A;%plane1D;543;n/B	1998	Boris Shapiro Michael Shapiro
+	On ring generated by Chern 2-forms on SLn/B	1998	Boris Shapiro Michael Shapiro
+	Skew-symmetric Vanishing Lattices and Intersections of Schubert Cells	1998	Boris Shapiro Michael Shapiro Alek Vainshtein
+	On ring generated by Chern 2-forms on SL_n/B	1998	Boris Shapiro Michael Shapiro
+	d-free maps satisfy the homotopy principle	1998	Boris Shapiro
+	On the number of connected components of the space of trigonometric polynomials of degreen with2n different critical values	1997	Boris Shapiro
+	Tree-like curves and their inflection points	1997	Boris Shapiro
+ PDF Chat	Characteristic classes for the degenerations of two-plane fields in four dimensions	1997	Maxim Kazarian Richard Montgomery Boris Shapiro
+	Characteristic Classes for the Degenerations of Two-Plane Fields in Four Dimensions	1997	Maxim Kazarian Richard Montgomery Boris Shapiro
+	On Combinatorics and Topology of Pairwise Intersections of Schubert Cells in SL n /B	1997	Boris Shapiro Michael Shapiro Alek Vainshtein
+	Ramified coverings of S^2 with one degenerate branching point and enumeration of edge-ordered graphs	1997	Boris Shapiro Michael Shapiro A. D. Vainshtein
+	Connected components in the intersection of two open opposite Schubert cells in real complete flag manifold	1997	Boris Shapiro Michael Shapiro Alek Vainshtein
+	Tree-like curves and their inflection points	1997	Boris Shapiro
+	On algebra generated by Chern-Bott forms on SL_n/B	1997	Boris Shapiro Michael Shapiro
+ PDF Chat	О числе компонент пространства тригонометрических многочленов степени $n$ с $2n$ различными критическими значениями	1997	Boris Shapiro Boris Shapiro
+	Characteristic Classes for the Degenerations of Two-Plane Fields in Four Dimensions	1997	Maxim Kazarian Richard Montgomery Boris Shapiro
+	Normal forms of the Whitney umbrella with respect to a cone-preserving contact group	1997	Boris Shapiro
+	Topology of intersections of Schubert cells and Hecke algebra	1996	Boris Shapiro Michael Shapiro Alek Vainshtein
+	Discriminants of convex curves are homeomorphic	1996	Boris Shapiro
+	On Young hulls of convex curves in R^{2n}	1996	V. D. Sedykh Boris Shapiro
+	Giambelli-type formula for subbundles of the tangent bundle	1996	Maxim Kazarian Boris Shapiro
+	Combinatorics and topology of stratifications of the space of monic polynomials with real coefficients	1996	Volkmar Welker Boris Shapiro
+	On the boundary of totally positive upper triangular matrices	1995	Boris Shapiro Michael Shapiro
+	On the Boundary of Totally Positive Upper Triangular Matrices	1995	Boris Shapiro
+ PDF Chat	On Singularities of Smooth Maps to a Space with a Fixed Cone.	1995	Boris Shapiro
+	On the complements of affine subspace arrangements	1994	Ken Jewell Peter Orlik Boris Shapiro
+ PDF Chat	The mixed Hodge structure of the complement to an arbitrary arrangement of affine complex hyperplanes is pure	1993	Boris Shapiro
+ PDF Chat	The Mixed Hodge Structure of the Complement to an Arbitrary Arrangement of Affine Complex Hyperplanes is Pure	1993	Boris Shapiro
+	Nondegenerate curves onS 2 and orbit classification of the Zamolodchikov algebra	1992	Boris Khesin Boris Shapiro
+	Swallowtails and Whitney umbrellas are homeomorphic	1992	Boris Shapiro Boris Khesin
+	The M-property of flag varieties	1992	Boris Shapiro Michael Shapiro
+	SPACES OF LINEAR DIFFERENTIAL EQUATIONS, AND FLAG MANIFOLDS	1991	Boris Shapiro
+ PDF Chat	On the number of connected components in the space of closed nondegenerate curves on 𝑆_{𝑛}	1991	Boris Shapiro Michael Shapiro
+ PDF Chat	Euler characteristics for links of Schubert cells in the space of complete flags	1990	Boris Shapiro Alek Vainshtein
+	Singularities on the boundary of the hyperbolicity region	1990	A. D. Vainshtein Boris Shapiro
+	Disconjugate linear ordinary differential equations, flag varieties and classification of symplectic leaves in several Kac-Moody and Gelfand-Dikii algebras	1990	Boris Shapiro
+	Higher-dimensional analogs of the theorems of Newton and Ivory	1985	A. D. Vainshtein Boris Shapiro

Common Coauthors

Coauthor	Papers Together
Michael Shapiro	40
Julius Borcea	16
Alek Vainshtein	16
Miloš Tater	13
Vladimir Petrov Kostov	11
Dmitry Novikov	11
Rikard Bøgvad	9
Guillaume Tahar	8
Nicolau C. Saldanha	7
Per Alexandersson	7
Andrei Gabrielov	6
Ralf Fröberg	6
V. D. Sedykh	5
Kathlén Kohn	5
Maxim Kazarian	5
Anna Vishnyakova	5
Gleb Nenashev	5
Yurii Burman	5
Jens Forsgård	5
Volkmar Welker	5
Olga Katkova	5
František Štampach	5
Nils Hemmingsson	4
Alexandre Erëmenko	4
Torsten Ekedahl	4
Alexander Postnikov	4
Petter Brändén	4
Christian Hägg	4
Ragni Piene	4
A. D. Vainshtein	3
Sergei Natanzon	3
Boris Khesin	3
Vladimir P. Kostov	3
Nicolau Saladanha	3
Bernd Sturmfels	3
Antonio F. Costa	3
Anton Khoroshkin	3
S. M. Natanzon	3
Dimitar K. Dimitrov	3
Arkady Vaintrob	3
Gabriel Katz	3
Alessandro Oneto	3
Eugeniĭ Shustin	3
Richard Montgomery	3
Samuel Lundqvist	3
Jared Ongaro	3
Shmuel Friedland	3
Lionel Lang	3
Tanja Bergkvist	2
Dmitrii V. Ṗasechnik	2

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Rational Functions with Real Critical Points and the B. and M. Shapiro Conjecture in Real Enumerative Geometry	2002	Alexandre Erëmenko Andrei Gabrielov	14
+ PDF Chat	Algebro-geometric aspects of Heine-Stieltjes theory	2010	Boris Shapiro	13
+ PDF Chat	Analytic Capacity and Measure	1972	John B. Garnett	11
+ PDF Chat	Orthogonal Polynomials	1971		10
+ PDF Chat	On polynomial eigenfunctions for a class of differential operators	2002	Tanja Bergkvist Hans Rullgård	10
+	TOPOLOGY OF THE SPACE OF NONDEGENERATE CURVES	1994	Michael Shapiro	9
+ PDF Chat	Sur certains polynômes: Qui vérifient une équation différentielle linéaire du second ordre et sur la theorie des fonctions de Lamé	1885	T. J. Stieltjes	9
+ PDF Chat	Nondegenerate homotopies of curves on the unit 2-sphere	1970	John A. Little	9
+	The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis	1983	Lars Hörmander Lars Hörmander	9
+	Über zwei Arten von Faktorenfolgen in der Theorie der algebraischen Gleichungen.	1914	J. Schur G. PɃlya	9
+	Enumerative Combinatorics	1997	Richard P. Stanley Gian‐Carlo Rota	9
+	The Asymptotic Zero Distribution of Orthogonal Polynomials with Varying Recurrence Coefficients	1999	Arno B. J. Kuijlaars Walter Van Assche	9
+	PROBLEMS AND THEOREMS IN THE THEORY OF MULTIPLIER SEQUENCES	1996	Thomas C. Craven George Csordás	8
+	Parametrizations of Canonical Bases and Totally Positive Matrices	1996	Arkady Berenstein Sergey Fomin Andrei Zelevinsky	8
+	Asymptotic Analysis : Linear Ordinary Differential Equations	2012	M. V. Fedoriuk Andrew Rodick	7
+	Composition Theorems, Multiplier Sequences and Complex Zero Decreasing Sequences	2006	Thomas C. Craven George Csordás	7
+	Analytic Theory of Polynomials	2002	Q I Rahman Gerhard Schmeißer	7
+	SPACES OF LINEAR DIFFERENTIAL EQUATIONS, AND FLAG MANIFOLDS	1991	Boris Shapiro	7
+ PDF Chat	Real Schubert Calculus: Polynomial Systems and a Conjecture of Shapiro and Shapiro	2000	Frank Sottile	7
+	On the Uniqueness of the Inverse Logarithmic Potential Problem	1986	В. Н. Страхов M. A. Brodsky	7
+	Principles of Algebraic Geometry	1978	Phillip Griffiths Joseph Harris	7
+	Descartes' Rule of Signs: Another Construction	1999	David J. Grabiner	6
+ PDF Chat	On polygonal measures with vanishing harmonic moments	2014	Dmitrii V. Ṗasechnik Boris Shapiro	6
+ PDF Chat	Pólya-Schur master theorems for circular domains and their boundaries	2009	Julius Borcea Petter Brändén	6
+ PDF Chat	On rational approximation of algebraic functions	2005	Julius Borcea Rikard Bøgvad Boris Shapiro	6
+ PDF Chat	On Spectral Polynomials of the Heun Equation. II	2012	Boris Shapiro Kouichi Takemura Miloš Tater	6
+	Swallowtails and Whitney umbrellas are homeomorphic	1992	Boris Shapiro Boris Khesin	6
+	The special Schubert calculus is real	1999	Frank Sottile	6
+ PDF Chat	Asymptotic zero distribution for a class of multiple orthogonal polynomials	2008	Els Coussement J. Coussement Walter Van Assche	6
+ PDF Chat	Conjugate points and simple zeros for ordinary linear differential equations	1969	Thomas L. Sherman	6
+	Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics	1991	Vladimir I. Arnold	6
+	PROJECTIVE CONVEXITY IN ℙ<sup>3</sup> IMPLIES GRASSMANN CONVEXITY	2000	Boris Shapiro Michael Shapiro	6
+	Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient	1975		5
+ PDF Chat	Hurwitz numbers and intersections on moduli spaces of curves	2001	Torsten Ekedahl S. K. Lando Michael Shapiro Alek Vainshtein	5
+ PDF Chat	Conjecture on the interlacing of zeros in complex Sturm–Liouville problems	2000	Carl M. Bender Stefan Boettcher Van M. Savage	5
+	Flags, Schubert polynomials, degeneracy loci, and determinantal formulas	1992	William Fulton	5
+	Remarks on eigenvalues and eigenvectors of Hermitian matrices, berry phase, adiabatic connections and quantum Hall effect	1995	Vladimir I. Arnold	5
+ PDF Chat	Genus 0 characteristic numbers of the tropical projective plane	2013	Benoît Bertrand Erwan Brugallé Grigory Mikhalkin	5
+ PDF Chat	The zero multiplicity of linear recurrence sequences	1999	Wolfgang M. Schmidt	5
+ PDF Chat	Sur quelques points de la théorie des équations numériques	1884	Eric Laguerre	5
+	Families of Plane Curves and Their Limits: Enriques' Conjecture and Beyond	1989	Ziv Ran	5
+	Asymptotic Properties of Heine–Stieltjes and Van Vleck Polynomials	2002	Andrei Martı́nez-Finkelshtein Edward B. Saff	5
+ PDF Chat	Critical Measures, Quadratic Differentials, and Weak Limits of Zeros of Stieltjes Polynomials	2011	Andrei Martínez–Finkelshtein Евгений Андреевич Рахманов	5
+ PDF Chat	On higher heine-stieltjes polynomials	2011	Thomas Holst Boris Shapiro	5
+ PDF Chat	Multiplier sequences for fields	1977	Thomas C. Craven George Csordás	5
+ PDF Chat	ON TWO CONJECTURES CONCERNING CONVEX CURVES	2005	V. D. Sedykh Boris Shapiro	5
+	Polynomials, roots, and interlacing	2006	Steve Fisk	5
+ PDF Chat	Locally homogeneous complex manifolds	1969	Phillip Griffiths Wilfried Schmid	5
+ PDF Chat	Homogenized Spectral Problems for Exactly Solvable Operators: Asymptotics of Polynomial Eigenfunctions	2009	Julius Borcea Rikard Bøgvad Boris Shapiro	5
+ PDF Chat	Linear Turning Point Theory	1985	Wolfgang Wasow	4