Publications
(since 2000)
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Strong Sard Conjecture and regularity of
singular minimizing geodesics for analytic
sub-Riemannian structures in dimension 3,
(with A.
Belotto
da Silva, A. Figalli and L. Rifford), Invent. math. 229 (2022), pp. 395--448.
Zariski's dimensionality type of singularities. Case of dimensionality type 2. (with L. Paunescu), J. Algebraic Geometry, electronically published on November 2, 2022.
Lipschitz stratification of complex hypersurfaces in codimension 2. (with L. Paunescu), Journal of the European Mathematical Society, published online: 2022-03-14 .
Initial Newton polynomial of the discriminant. (with B. Gryszka, J. Gwozdziewicz), Bull. London Math. Soc. 2022; 54:1584--1594.
Sobolev lifting over invariants. (with A. Rainer), SIGMA Symmetry, Integrability and Geometry: Methods and Applications 17 (2021), 037, 31 pages.
Real intersection homology II: A local duality obstruction. (with C. McCrory), Topology and its Applications, {271}, (2020).
Algebraic
varieties are homeomorphic to varieties
defined over number fields, (with
G. Rond), Commentari Math. Helvetici, Volume 95, Issue 2, 2020, pp. 339-359
Arc
spaces, motivic measure and Lipschitz
geometry of real algebraic sets, (with
J.-B. Campesato, T. Fukui and K. Kurdyka), Mathematische Annalen (2019) 374, 211--251.
Multiparameter
perturbation theory of matrices and linear
operators, (with G. Rond), Trans. Amer. Math. Soc. 373 (2020) 2933-2948.
Selections
of bounded variation for roots of smooth
polynomials, (with A. Rainer), Sel. Math. New Ser. 26, 13 (2020).
Global
smoothings of subanalytic sets, (with E.
Bierstone), Duke Math. J. {167}, 3115--3128, (2018).
Moser's
Theorem for manifolds with corners, (with
M. Bruveris, P. Michor and A. Rainer), Proc. Amer. Math. Soc. {140},,
4889--4897 (2018).
Real
Intersection Homology (with C. McCrory ), in Real
and Complex Singularities and their applications in
Geometry and Topology, Topology and its Applications,
Volume 234, 1 February 2018, Pages 108-129.
Algebraic
Stratified
General Position and Transversality, (with C. McCrory
and L. Paunescu), J. Algebraic Geom. \textbf{28} 139--152 (2019).
Higher
Order Approximation of Analytic Sets Topologically
Equivalent Algebraic Ones (with M. Bilski, K. Kurdyka
and G. Rond), Math. Zeitschrift, 288 (2018), 1361–1375
Validity
proof of Lazard’s method for CAD construction (with S.
McCallum and L. Paunescu) J. of Symbolic Computation, \textbf{92} (2019) 52--69.
Optimal
Regularity of Roots of Polynomials. (with A. Rainer)
Ann. Scient. Ec. Norm. Sup.
4 e serie, t. 51, 2018, pp. 1343--1387.
Arc-wise
Analytic Stratification, Whitney Fibering Conjecture and
Zariski Equisingularity . (with L. Paunescu), Advances
in Math. 309 (2017), 254–305..
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Equisingularity
Theory
of Analytic and ALgebraic Set Germs, Proof of Whitney
Fibering Conjecture and Zariski Equisingularity,
Minicourse at Jagiellonian University, Kraków, May 2015
Lifting
Differentiable
Curves from Orbit Spaces. (with A. Rainer)
Transformation Groups, Vol. 21, No. 1, 2016, pp. 153-179
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Regular
Covers
for Open Relatively Compact Subanalytic Sets. in
Astérisque, Subanalytic sheaves and Sobolev spaces. 383 (2016)
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Regularity
of
Roots of Polynomials. (with A. Rainer) Ann. Sc.
Norm. Super. Pisa Cl. Sci. (5) Vol. XVI (2016), 481-517
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A
New Proof of Bronshtein's Theorem. (with A. Rainer)
Journal of Hyperbolic Differential Equations Vol. 12, No. 4
(2015) 671–688
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A
Local Topological Algebraicity of Analytic Function Germs.
(with M. Bilski and G. Rond) J. Algebraic Geom. 26 (2017)
177-197
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Characteristic
Classes
of Singular Varieties via Conormal Geometry, lectures at
the annual meeting of GDR Singularités. Classes
caractéristiques. Porquerolles 22 au 26 octobre 2012
A
Note on the Weierstrass Preparation Theorem in Quasianalytic
Local Rings (with J.-P. Rolin), Canad. Math. Bull. 57
(2014), no. 3, 614–620.
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The
weight
filtration
for real algebraic varieties II: Classical Homology,
(with C. McCrory), Revista de la Real Academia de Ciencias
Exactas, Fisicas y Naturales. Serie A. (volume in honor of H.
Hironaka), (2014) 108, 63–94
Equivalence
relations
for two variable real analytic function germs, (with S.
Koike), J. Math. Soc. Japan Volume 65, Number 1 (2013),
237-276
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The
Abhyankar-Jung Theorem, (with G. Rond), Journal of
Algebra 365 (2012) 29-41
On
the
non-analyticity locus of an arc-analytic function,
(with K. Kurdyka), J. Algebraic Geom. 21 (2012), no.
1,61–75.
The
weight
filtration
for real algebraic varieties, (with C. McCrory), in
"Topology of Stratified Spaces", MSRI Publications
Volume 58, 2011,
Berkeley, California, 121-160. Blow-analytic
equivalence of two variable real analytic function germs,
(with S. Koike), J. Algebraic Geom. 19 (2010), no. 3,
439–472.
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. Arc-symmetric
Sets and Arc-analytic Mappings, (with K. Kurdyka), course at
Winter School Real Algebraic and Analytic Geometry and
Motivic Integration, Aussois, Savoie, in "Arcs Spaces and
Additive Invariants in Real algebraic and Analytic
Geometry", Panoramas et Synthèses, 24 (2008), SMF,
33-67.
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Algebraically
Constructible Functions: Real Algebra and Topology , (with
C. McCrory) , in "Arcs Spaces and Additive Invariants in
Real algebraic and Analytic Geometry", Panoramas et
Synthèses, 24 (2008), SMF, 69-85.
Characteristic
Classes of Singular Varieties, Proceedings of 12th MSJ-IRI
symposium "Singularity theory and its applications".
Advances Studies in Pure Mathematics 43, Mathematical
Society of Japan, 2006, pp. 347--368
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Quasi-convex
Decomposition in o-Minimal Structures. Application to the
Gradient Conjecture, (with K. Kurdyka), Proceedings of 12th
MSJ-IRI symposium "Singularity theory and its applications".
Advances Studies in Pure Mathematics 43, Mathematical
Society of Japan, 2006, pp. 137--178 ,
Integrability
of some functions on semi-analytic sets, in Singularitées
franco-japonaises, Brasselet, Suwa eds., Seminaires et
Congrès 10, SMF 2005, 243-254, -
Bi-Lipschitz
trivialization of the distance function to a stratum of a
stratification, Ann. Pol. Math., 87 (2005), 213-218,
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Newton-Puiseux
Roots of Jacobian Determinants , (with T.-C. Kuo), J.
Algebraic Geometry, 13 (2004), 570-601
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Topology
of Injective Endomorphisms of Real Algebraic Varieties,
Math. Annalen, 328 (2004) 353-372
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Invariants
of Bi-Lipschitz Equivalence of Real Analytic Functions,
(with J.P. Henry), in Geometric Singularity Theory, Banach
Center Publications 65, PWN, Warszawa 2004, 67-75,
Motivic-type
Invariants of Blow-analytic Equivalence, (with S. Koike),
Ann. Institut Fourier 53 , 7(2003), 2061-2104,
Existence of Moduli for bi-Lipschitz Equivalence of
Analytic Functions, (with J.-P. Henry), Compositio Math.
136 (2003), 217-235
On the
Preparation Theorem for Subanalytic Functions, University
of Angers preprint no. 108, September 2000, in New
Developments in Singularity Theory, D. Siersma et al.
(eds), Kluver Academic Publisher, 2001, pp. 193-215.
Characteristic
Classes of Hypersurfaces , (with P. Pragacz), J. Algebraic
Geometry , 10 (2001), 63-79 .
Proof of
Gradient Conjecture of R. Thom,
(with K. Kurdyka and T. Mostowski), Annals of Mathematics,
152 (2000),763-792,
Newton
Polygon Relative to an Arc, (with T.-C. Kuo), in Real and
Complex Singularities (Sao Carlos, 1998), Chapman &
Hall Res. Notes Math., 412 (2000), 76-93