publications.html

[1] A. Parusiński, A. Rainer, Perturbation theory of polynomials and linear operators, a chapter of Handbook of Geometry and Topology of Singularities VII, eds. José Luis Cisneros-Molina, Dũng Tráng Lê, José Seade, Springer-Verlag, 2025, pp. 121-202

[2] A. Parusiński, Algebro-geometric equisingularity of Zariski, a chapter of Handbook of Geometry and Topology of Singularities II, eds. José Luis Cisneros-Molina, Dũng Tráng Lê, José Seade, Springer-Verlag, 2021, pp. 177–222

[3] S. Guillermou, G. Lebeau, A. Parusiński, P. Schapira, J.-P. Schneiders, Subanalytic sheaves and Sobolev spaces, SMF, Astérisque 383, 2016

[4] M. Coste, T. Fukui, K. Kurdyka, A. Parusiński, L. Paunescu, Arc Spaces and Additive Invariants in Real Algebraic Geometry, SMF, Panoramas et Synthèses 24, Société Mathématique de France, Paris 2007

[5] A. Belotto da Silva, A. Parusiński, L. Rifford, Abnormal Singular Foliations and the Sard Conjecture for generic co-rank one distributions, arXiv :2310.20284, Revista Matemática Iberoamericana to appear

[6] A. Parusiński, G. Rond, Płoski Approximation Theorem, Annales Polon. Math. (volume in honor of A. Płoski), .pdf

[7] A. Parusiński, L. Pǎunescu, On Teissier’s example of an equisingularity class that cannot be defined over the rationals, Annales Polon. Math. (volume in honor of A. Płoski), .pdf

[8] L. Baldi, B. Mourrain, A. Parusiński, On Łojasiewicz Inequalities and the Effective Putinar’s Positivstellensatz, Journal of Algebra 662 (2025) 741–767, https ://doi.org/10.1016/j.jalgebra.2024.08.02, .pdf

[9] J.-B. Campesato, G. Fichou, A. Parusiński, Motivic, logarithmic, and topological Milnor fibrations, arXiv :2111.14881, Adv. Math. (2024), https ://doi.org/10.1016/j.aim.2024.110075, .pdf

[10] A. Parusiński, A. Rainer, Definable Lipschitz selections for affine-set valued maps, Israel. J. Math., 2025, doi : 10.1007/s11856-025-2795-1, .pdf

[11] A. Parusiński, A. Rainer, Uniform extension of definable C^m,ω-Whitney jets, Pacific J. Math. , 2024, https ://doi.org/10.2140/pjm.2024.330.317, .pdf

[12] A. Parusiński, L. Pǎunescu, Zariski’s dimensionality type of singularities. Case of dimensionality type 2, J. Algebraic Geom. 33.1 (2024), pp. 117–142. issn : 1056–3911,1534–7486.,https ://doi.org/10.1090/jag/815, .pdf

[13] A. Parusiński, L. Pǎunescu, Lipschitz stratification of complex hypersurfaces in codimension 2, J. Eur. Math. Soc. (JEMS) 25, No. 5 (2023), pp. 1743–1781. .pdf

[14] A. Belotto da Silva, A. Figalli, A. Parusiński, L. Rifford, Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3, Invent. math. 229 (2022), pp. 395–448, https ://doi.org/10.1007/s00222-022-01111-2, .pdf

[15] B. Gryszka, J. Gwoździewicz, A. Parusiński, Initial Newton polynomial of the discriminant, Bull. London Math. Soc. 2022; 54 :1584–1594, http ://doi.org/10.1112/blms.12644, .pdf

[16] A. Parusiński, A. Rainer, Sobolev lifting over invariants, SIGMA Symmetry, Integrability and Geometry : Methods and Applications 17 (2021), 037, 31 pages. doi :10.3842/SIGMA.2021.037. .pdf

[17] A. Parusiński, G. Rond, Algebraic varieties are homeomorphic to varieties defined over number fields, Commentari Math. Helvetici, Volume 95, Issue 2, 2020, pp. 339-359, .pdf

[18] C. McCrory, A. Parusiński, Real intersection homology II : A local duality obstruction,Topology and its Applications, 271 (2020), .pdf

[19] A. Parusiński, A. Rainer, Selections of bounded variation for roots of smooth polynomials, Sel. Math. New Ser. 26, 13 (2020). .pdf

[20] A. Parusiński, G. Rond, Multiparameter perturbation theory of matrices and linear operators, Trans. Amer. Math. Soc. 373 (2020) 2933-2948. .pdf

[21] J.-B. Campesato, T. Fukui, K. Kurdyka, A. Parusiński, Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets, Mathematische Annalen (2019) 374, 211–251. .pdf

[22] S. McCallum, A. Parusiński, L. Paunescu, Validity proof of Lazard’s method for CAD construction, J. of Symbolic Computation, 92 (2019) 52–69, .pdf

[23] C. McCrory, A. Parusiński, L. Paunescu, Algebraic Stratified General Position and Transversality, J. Algebraic Geom. 28 139–152 (2019). .pdf

[24] A. Parusiński, A. Rainer, Optimal Sobolev regularity of roots of polynomials, Ann. Scient. Éc. Norm. Sup. 4 e série, t. 51, 2018, p. 1343–1387. .pdf

[25] E. Bierstone, A. Parusiński, Global smoothing of a subanalytic set, Duke Math. J. 167, 3115–3128, (2018). .pdf

[26] M. Bruveris, P. W. Michor, A. Parusiński, A. Rainer, Moser’s theorem on manifolds with corners, Proc. Amer. Math. Soc. 140„ 4889–4897 (2018). .pdf

[27] M. Bilski, K. Kurdyka, A. Parusiński, G. Rond, Higher order approximation of analytic sets by topologically equivalent algebraic sets. Math. Zeitschrift, 288 (2018), 1361–1375, .pdf

[28] C. McCrory, A. Parusiński, Real intersection homology, in Real and Complex Singularities and their applications in Geometry and Topology, Topology and its Applications, Volume 234, 1 February 2018, Pages 108-129. .pdf

[29] A. Parusiński, L. Pǎunescu, Arcwise analytic stratification, Whitney fibering conjecture and Zariski equisingularity, Advances in Math. 309 (2017), 254–305. .pdf

[30] M. Bilski, A. Parusiński, G. Rond, Local topological algebraicity of analytic function germs. J. Algebraic Geom. 26 (2017), 177-197, .pdf

[31] A. Parusiński, A. Rainer, Lifting differentiable curves from orbit spaces. Transformation Groups, Vol. 21, No. 1, 2016, pp. 153-179, .pdf

[32] A. Parusiński, A. Rainer, Regularity of roots of polynomials. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XVI (2016), 481-517, .pdf

[33] A. Parusiński, A. Rainer, A new proof of Bronshtein’s theorem, J. Hyperbolic Differ. Equation., Vol. 12, No. 4 (2015) 1-18, .pdf

[34] M. Bilski, A. Parusiński, Approximation of holomorphic maps from Runge domains to affine algebraic varieties, J. London Math. Soc. (2014) 90 (3), 807–826

[35] A. Parusiński, J.-P. Rolin, A Note on the Weierstrass Preparation Theorem in Quasianalytic Local Rings, Canad. Math. Bull. 57 (2014), no. 3, 614–620. .pdf

[36] C. McCrory, A. Parusiński, The weight filtration for real algebraic varieties II : Classical homology, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. (volume in honor of H. Hironaka), (2014) 108, 63–94, .pdf

[37] S. Koike, A. Parusiński, Equivalence relations for two variable real analytic function germs, J. Math. Soc. Japan Volume 65, Number 1 (2013), 237-276. .pdf

[38] A. Parusiński, G. Rond, The Abhyankar-Jung Theorem, Journal of Algebra 365 (2012) 29-41, .pdf

[39] K. Kurdyka, A. Parusiński, On the non-analyticity locus of an arc-analytic function, J. Algebraic Geom. 21 (2012), 61-75, .pdf

[40] C. McCrory, A. Parusiński, The weight filtration for real algebraic varieties, MSRI Publications, 18 "Topology of Stratified Spaces" (2011), 121–160, .pdf

[41] S. Koike, A. Parusiński, Some questions on the Fukui numerical set for complex analytic function germs, Demonstratio Mathematica, 43, 2 (2010), 285–302

[42] S. Koike, A. Parusiński, Blow-analytic equivalence of two variable real analytic function germs, J. Algebraic Geometry, 19, 3 (2010), 439–472, .pdf

[43] A. Parusiński, A criterion for topological equivalence of two variable complex analytic function germs, Proc. Japan Acad. Ser. A Math. Sci. Volume 84, Number 8 (2008), 147-150. .pdf

[44] A. Parusiński, C. McCrory, Algebraically constructible functions: real algebra and topology, Panor. Synthèses, 24, Société Mathématique de France, Paris, 2007, 69–85.

[45] A. Parusiński, Characteristic Classes of Singular Varieties, Proceedings of 12th MSJ-IRI symposium "Singularity theory and its applications". Advanced Studies in Pure Mathematics 43, 2006, 347–368

[46] K. Kurdyka, A. Parusiński, Quasi-convex Decomposition in o-Minimal Structures. Application to the Gradient Conjecture, Proceedings of 12th MSJ-IRI symposium "Singularity theory and its applications". Advanced Studies in Pure Mathematics 43, 2006, 137–178, .pdf

[47] A. Parusiński, Bi-Lipschitz trivialization of the distance function to a stratum of a stratification, Dans le numéro special de Annales Mathematici Polonici dédié à la mémoire de Professor Stanisław Łojasiewicz, 87 (2005), 213–218

[48] A. Parusiński, Integrabitlity of some functions on semi-analytic sets in Singularités franco-japonaises, Brasselet, Suwa eds., Seminaires et Congrès 10, SMF 2005, 243–254

[49] T.-C. Kuo, A. Parusiński, Newton-Puiseux Roots of Jacobian Determinants, Journal of Alg. Geom., 13 (2004), 570–601. .pdf

[50] A. Parusiński, Topology of injective endomorphisms of real algebraic sets, Math. Annalen, 328 (2004), 353–372.

[51] J.-P. Henry, A. Parusiński, Invariants of bi-Lipschitz equivalence of real analytic functions, in Geometric Singularity Theory, Banach Center Publications 65, PWN, Warszawa 2004, 67–75. .pdf

[52] S. Koike, A. Parusiński, Motivic-type Invariants of Blow-analytic Equivalence, Annales Institut Fourier 53, 7 (2003), 2061–2104.

[53] J.-P. Henry, A. Parusiński, Existence of Moduli for bi-Lipschitz equivalence of analytic functions, Compositio Math. 136 (2003), 217–235.

[54] C. McCrory, A. Parusiński, Virtual Betti numbers of real algebraic varieties, C.R.A.S. Ser. I 336 (2003), 763–768.

[55] T.-C. Kuo, A. Parusiński, On Puiseux Roots of Jacobians, Proc. Japan Acad., 78, Ser. A (2002), 55–59.

[56] A. Parusiński, On the preparation theorem for subanalytic functions , in New Developments in Singularity Theory, Cambridge 2000, eds. Siersma, Wall, Zakalyukin, Kluwer Academic Publishers (2001), 193–215

[57] A. Parusiński, P. Pragacz, Characteristic Classes of Hypersurfaces and Characteristic Cycles, Journal of Alg. Geom. 10 (2001), 63–79

[58] K. Kurdyka, T. Mostowski, A. Parusiński, Proof of Gradient Conjecture of R. Thom, Annals of Math. 152, 3 (2000), 763–792

[59] C.McCrory, A. Parusiński, Topology of real algebraic sets of dimension 4 : necessary conditions, Topology 39 (2000), 495–523

[60] T.-C. Kuo, A. Parusiński, Newton Polygon relative to an arc, in Real and Complex Singularities (São Carlos, 1998), Chapman & Hall Res. Notes Math., 412, Chapman & Hall/CRC 2000, 76–93, .pdf

[61] J. Gwoździewicz, K. Kurdyka et A. Parusiński, On the number of solution of an algebraic equation on the curve y = e^x +sinx, x > 0 and a consequence for O-minimal structures, Proc. Amer. Math. Soc. 127, 4 (1999), 1057-1064, .pdf

[62] A. Parusiński, Topological Triviality of μ-constant Deformations of Type f(x) + tg(x), Bull. Lond. Math. Soc. 31 (1999), 686–692

[63] A. Parusiński, Blow-Analytic Retraction onto the Central Fibre, in Real analytic and algebraic singularities, Proceedings of the Kuo Symposium, eds. Fukuda et al. Pitman Research Notes in Mathematics 381, Longman 1998, 43–61, .pdf

[64] A. Parusiński, Z. Szafraniec, On the Euler Charcteristic of Fibres of Real Polynomial Maps, in Singularities Symposium - Łojasiewicz 70, Banach Center Publications 44, PWN, Warszawa 1998, 175-182

[65] A. Parusiński, Z. Szafraniec, Algebraically Constructible Functions and Signs of Polynomials, Manuscripta Math. 93 (1997),443–456

[66] C. McCrory, A. Parusiński, Algebraically Constructible Functions, Annales Sci. Éc. Norm. Sup. 30, 4 (1997), 527–552

[67] C. McCrory, A. Parusiński, Complex monodromy and the topology of real algebraic sets, Compositio Math. 106 (1997), 211–233.

[68] A. Parusiński, A note on singularities at infinity of complex polynomials, in Symplectic singularities and geometry of gauge fields, Banach Center Publications 39, PWN, Warszawa 1997, 131–141. .pdf

[69] A. Parusiński, P. Pragacz, Chern-Schwartz-MacPherson classes and the Euler characteristic of degeneracy loci and special divisors, Journal Amer. Math. Soc. 8, 4 (1995), 793–817, .pdf

[70] A. Parusiński, P. Pragacz, A formula for the Euler characteristic of singular hypersufaces, Journal of Alg. Geom. 4,2 (1995), 337–352.

[71] A. Parusiński, On the bifurcation set of a complex polynomial with isolated singularities at infinity, Compositio Math. 97, 3 (1995), 369–384

[72] A. Parusiński, Lipschitz stratification of subanalytic sets, Annales Sci. Éc. Norm. Sup. 27, 6 (1994), 661–696

[73] A. Parusiński, Subanalytic functions, Trans. Amer. Math. Soc. 344, 2 (1994), 583–595, .pdf

[74] K. Kurdyka, A. Parusiński, W_f-stratification of subanalytic functions and Łojasiewicz Inequality, Compt. Rend. Acad. Sci. Paris, Série I 318, 2 (1994), 129–134

[75] A. Parusiński, Limits of tangent spaces to fibres and the w_f condition, Duke Math. Jour. 72, 1 (1993), 99-109

[76] A. Parusiński, Lipschitz stratification a review of results, in Global Analysis in Modern Mathematics, Proceedings Of A Symposium In Honor Of Richard Palais’ Sixtieth Birthday, K. Uhlenbeck ed., Publish or Perish, Houston 1993, 73–91

[77] A. Parusiński, Constructibility of the set of points where complex analytic morphism is open, Proc. Amer. Math. Soc. 117, 1 (1993), 205–211

[78] A. Parusiński, P. Pragacz, Characteristic numbers of degeneracy loci, in Enumerative Algebraic Geometry (S. L. Kleiman, A. Thorup eds), Proceedings of the 1989 Zeuthen Symposium, Contemporary Mathematics 123, Amer. Math. Soc., Providence 1991, 189–198

[79] E. Bierstone, P. Milman & A. Parusiński, A function which is arc analytic but not continuous, Proc. Amer. Math. Soc. 113, 2 (1991), 419–424.

[80] A. Parusiński, Multiplicity of the dual variety, Bull. Lond. Math. Soc. 23 (1991), 429–436.

[81] A. Parusiński, Gradient Homotopies of gradient vector fields , Studia Math. XCVI (1990), 73–80

[82] A. Parusiński, A generalization of the Milnor number, Math. Ann. 281 (1988), 247–254, .pdf

[83] A. Parusiński, Regular projection for sub-analytic sets, C. R. Acad. Sci. Paris, Série I 307, (1988), 343–347, .pdf

[84] A. Parusiński, Lipschitz properties of semi-analytic sets, Ann. Inst. Fourier (Grenoble) 38, (1988), 189–213, .pdf

[85] A. Parusiński, Lipschitz stratification of real analytic sets, in Singularities (S. Łojasiewicz ed.), Banach Center Publications XX, PWN, Warszawa 1988, 323–333.

[86] W. Marzantowicz, A. Parusiński, Periodic Solutions Near an Equilibrium of a Differential Equation with a First Integral, Rend. Sem. Mat. Univ. Padova 77, 1987, 193–206.

[87] A. Parusiński, Algebraic equisingularity and Whitney’s conditions, Bull. Pol. Acad. Sc. 33 (5–6), 1985, 247–253, .pdf

[88] A. Belotto da Silva, A. Parusiński, L. Rifford, The Analytic Minimal Rank Sard Conjecture, arXiv :2208.01392

[89] A. Parusiński, A. Rainer, Continuity of the solution map for hyperbolic polynomials, arXiv :2410.01321

[90] A. Parusiński, A. Rainer, On the continuity of the solution map for polynomials, arXiv :2410.01326