Generalizations of LG/CY correspondence. Talk at Newton Institute, Cambridge, March 18 2024

Braid monodomry and Alexander polynomils of real plane curves. (to appear in Beitrage zur Algebra und Geometrie)

Meromorphic functions without real critical values and related braids. (with B.Shapiro) to appear in Europ. J.Math.

Remarks on semi-simplicity of Alexander modules. J.Sing. 25 (2022) p 325-330.

Ranks of homotopy and cohomology groups for rationally elliptic spaces and algebraic varieties. Homology Homotopy and application. 24 (2022), no.2 93-113. (with S.Yokura).

Self-products of rationally elliptic spaces and inequalities between the ranks of homotopy and homology groups.Topology Appl. 313 (2022) Paper No.107986. (with S.Yokura).

Complements to ample divisors and Singularities. Handbook of Geometry a\ nd Topology of Singularities.Springer, 501-567, 2021.

Free quotients of fundamental groups of quasi-projective varieties. (with J.I.Cogolludo). Proc. Edinb. Math. Soc. (2), 64 (2021) no.4 924-946.

Stringy E-functions of Pfaffian-Grassmannian double mirrors (with L.Borisov). Algebraic Geometry 6(4),(2019),486-515

Strata of discriminantal arrangements (with S.Settepanella). J. Singularities 18 (2018), 440-454. .

Motivic zeta functions and infinite cyclic covers (with M.Gonzalez-Villa and L.Maxim). Local and global methods in algebraic geometry, 117-141, Contemp. Math., 712, Amer. Math. Soc., Providence, RI, 2018.

Elliptic genus of singular algebraic varieties and quotients. J. Phys. A 51 (2018), no. 7, 073001.

Albanese varieties of cyclic covers of the projective plane and orbifold pencils (with E.Artal-Bartolo and J.I.Cogolludo-Augustin). Nagoya Math. J. 227 (2017), 189-213.

Motivic infinite cyclic covers (with M.Gonzalez-Villa and L.Maxim). Adv. Math. 298 (2016) 413-447.

Elliptic genus of phases of N=2 theories. Comm. Math. Phys. 340 (2015), no. 3, 939-958.

Albanese varieties of abelian covers. J. Singul. 12 (2015), 105-123.

Multivariable Hodge theoretical invariants of germs of plane curves (with Pierrette Cassou-Nogues). II. Valuation theory in interaction, 82-135, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2014.

Mordell-Weil groups of elliptic threefolds and the Alexander module of plane curves (with J.I.Cogolludo-Augustin), J. Reine Angew. Math. 697 (2014), 15-5.

Depth of cohomology support loci for quasi-projective varieties via orbifold pencils (with E.Artal Bartolo and J.I.Cogolludo-Augustin). Rev. Mat. Iberoam. 30 (2014), no. 2, 373-404.

Topology of algebraic curves [book review]. Bull. Amer. Math. Soc. (N.S.) 51 (2014), no. 3, 479-489.

On Mordell-Weil groups of isotrivial abelian varieties over function fields. Math. Ann. 357 (2013), no. 2, 605-629.

Characters of fundamental groups of curve complements and orbifold pencils (with E.Artal Bartolo and J.I.Cogolludo-Augustin). Configuration spaces, 81-109, CRM Series, 14, Ed. Norm., Pisa, 2012.

On combinatorial invariance of the cohomology of the Milnor fiber of arrangements and the Catalan equation over function fields. Arrangements of hyperplane. Sapporo 2009, 175-187, Adv. Stud. Pure Math., 62, Math. Soc. Japan, Tokyo, 2012.

Factors of Jacobians and isotrivial elliptic surfaces. J. Singul. 5 (2012), 115-123.

Hodge polynomials of singular hypersurfaces (with L.Maxim). Michigan Journal of Math. vol 60 (3).2011.

Sequences of LCT-polytopes (with M.Mustata). Math. Res. Lett. 18 (2011), no. 4, 733-746.

Multivariable Hodge theoretical invariants of germs of plane curves (with Pierrette Cassou-Nogues. J. Knot Theory Ramifications 20 (2011), no. 6, 787-805.

Elliptic genera, real algebraic varieties and quasi-Jacobi forms. Topology of stratified spaces, 95-120, Math. Sci. Res. Inst. Publ., 58, Cambridge Univ. Press, Cambridge, 2011.

Development of the theory of Alexander invariants in algebraic geometry. Topology of algebraic varieties and singularities, 3-17, Contemp. Math., 538, Amer. Math. Soc., Providence, RI, 2011.

Hodge genera of algebraic varieties, II (with Sylvain E. Cappell, Laurentiu Maxim and Julius L. Shaneson). Math. Annalen. 345 (2009), no.4, 925-972.

Cohomology of bundles on homological Hopf manifold. sci.China Ser. A 52 (2009),no 12, 2688-2698

Non vanishing loci of Hodge numbers of local systems, Manuscripta Math. 128, 1-31 (2009).

Higher elliptic genera (with L.Borisov). Math. Res. Lett. 15 (2008), no. 3, 511-520.

Hodge genera and characteristic classes of complex algebraic varieties (with S.Cappell,L.Maxim and J.Shaneson). Electron. Res. Announc. Math. Sci. 15 (2008), 1-7.

Lectures on topology of complements and fundamental groups. Singularity theory, 71-137, World Sci. Publ., Hackensack, NJ, 2007.

Problems in topology of the complements to plane singular curves. Singularities in geometry and topology, 373-387, World Sci. Publ., Hackensack, NJ, 2007.

Local topology of reducible divisors (with A.Dimca). Real and complex singularities, 99-111, Trends Math., Birkhäuser, Basel, 2007.

Homotopy groups of complements to ample divisors. Singularity theory and its applications, 179-204, Adv. Stud. Pure Math., 43, Math. Soc. Japan, Tokyo, 2006.

Regular functions transversal at infinity (with A.Dimca). Tohoku Math. J. (2) 58 (2006), no. 4, 549-564.

Discrete torsion, orbifold elliptic genera and the chiral de Rham complex (with M.Szczesny). Pure Appl. Math. Q. 2 (2006), no. 4, Special Issue: In honor of Robert D. MacPherson. Part 2, 1217-1236.

McKay correspondence for elliptic genera (with L.Borisov) Ann. of Math. (2) 161 (2005), no. 3, 1521-1569.

Isolated non-normal crossings. Real and complex singularities, 145-160, Contemp. Math., 354, Amer. Math. Soc., Providence, RI, 2004.

Counting rational maps onto surfaces and fundamental groups (with T.Bandman). Internat. J. Math. 15 (2004), no. 7, 673-690.

Zariski-van Kampen theorem for higher-homotopy groups (with D.Cheniot). J. Inst. Math. Jussieu 2 (2003), no. 4, 495-527.

Generalizations of the odd degree theorem and applications (with S.Friedland). Israel J. Math. 136 (2003), 353-371.

Elliptic genera of singular varieties (with L.Borisov) Duke Math. J. 116 (2003), no. 2, 319-351.

Elliptic genera of singular varieties, orbifold elliptic genus and chiral de Rham complex. (with L.Borisov). Mirror symmetry, IV (Montreal, QC, 2000), 325-342, AMS/IP Stud. Adv. Math., 33, Amer. Math. Soc., Providence, RI, 2002.

Eigenvalues for the monodromy of the Milnor fibers of arrangements. Trends in singularities, 141-150, Trends Math., Birkhäuser, Basel, 2002.

Homotopy groups of complements and nonisolated singularities (with M.Tibar). Int. Math. Res. Not. 2002, no. 17, 871-888.

Hodge decomposition of Alexander invariants. Manuscripta Math. 107 (2002), no. 2, 251-269.

First order deformations for rank one local systems with a non-vanishing cohomology. Arrangements in Boston: a Conference on Hyperplane Arrangements (1999). Topology Appl. 118 (2002), no. 1-2, 159-168.

Characteristic varieties of algebraic curves. Applications of algebraic geometry to coding theory, physics and computation (Eilat, 2001), 215-254, NATO Sci. Ser. II Math. Phys. Chem., 36, Kluwer Acad. Publ., Dordrecht, 2001.

Cohomology of local systems (with S.Yuzvinsky). Arrangements. Tokyo 1998, 169-184, Adv. Stud. Pure Math., 27, Kinokuniya, Tokyo, 2000.

Cohomology of the Orlik-Solomon algebras and local systems (with S.Yuzvinsky). Compositio Math. 121 (2000), no. 3, 337-361.

Elliptic genera of toric varieties and applications to mirror symmetry (with L.Borisov). Invent. Math. 140 (2000), no. 2, 454-485.

Abelian branched covers of projective plane. Singularity theory (Liverpool, 1996), xxi, 281-289, London Math. Soc. Lecture Note Ser., 263, Cambridge Univ. Press, Cambridge, 1999.

Chern classes and the periods of mirrors. Math. Res. Lett. 6 (1999), no. 2, 141-149.

The topology of complements to hypersurfaces and nonvanishing of a twisted de Rham cohomology. Singularities and complex geometry (Beijing, 1994), 116-130, AMS/IP Stud. Adv. Math., 5, Amer. Math. Soc., Providence, RI, 1997.

Position of singularities of hypersurfaces and the topology of their complements. Algebraic geometry, 5. J. Math. Sci. 82 (1996), no. 1, 3194-3210.

Automorphisms of desingularizations of quotients and equivariant McKay correspondence. C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), no. 8, 907-912.

Differential forms on complete intersections and a related quotient module. Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993), 295-305, Israel Math. Conf. Proc., 9, Bar-Ilan Univ., Ramat Gan, 1996.

On the zeta function of monodromy of a polynomial map. Compositio Math. 95 (1995), no. 3, 287-307.

Groups which cannot be realized as fundamental groups of the complements to hypersurfaces in CN. Algebraic geometry and its applications (West Lafayette, IN, 1990), 203-207, Springer, New York, 1994.

Homotopy groups of the complements to singular hypersurfaces. II. Ann. of Math. (2) 139 (1994), no. 1, 117-144.

Topological invariants of affine hypersurfaces: connectivity, ends, and signature. Duke Math. J. 70 (1993), no. 1, 207-227.

Lines on Calabi-Yau complete intersections, mirror symmetry, and Picard-Fuchs equations (with J.Teitelbaum). Internat. Math. Res. Notices 1993, no. 1, 29-39.

Erratum: "An obstruction to smoothing of Gorenstein surface singularities (with S.Yau)'' [Comment. Math. Helv. 65 (1990), no. 3, 413-433;]. Comment. Math. Helv. 67 (1992), no. 4, 670.

On the homology of finite abelian coverings. Topology Appl. 43 (1992), no. 2, 157-166.

An obstruction for smoothing of Gorenstein surface singularities (with S.Yau). Comment. Math. Helv. 65 (1990), no. 3, 413-433.

Uniqueness of the complex structure on Kähler manifolds of certain homotopy type (with J.Wood). J. Differential Geom. 32 (1990), no. 1, 139-154.

On topological complexity of solving polynomial equations of special type. Transactions of the Seventh Army Conference on Applied Mathematics and Computing (West Point, NY, 1989), 475-478, ARO Rep., 90-1, U.S. Army Res. Office, Research Triangle Park, NC, 1990

Invariants of plane algebraic curves via representations of the braid groups. Invent. Math. 95 (1989), no. 1, 25-30.

Theta characteristics on singular curves, spin structures and Rohlin theorem. Ann. Sci. Ecole Norm. Sup. (4) 21 (1988), no. 4, 623-635.

On divisibility properties of braids associated with algebraic curves. Braids (Santa Cruz, CA, 1986), 387-398, Contemp. Math., 78, Amer. Math. Soc., Providence, RI, 1988.

Fundamental groups of the complements to plane singular curves. Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 29-45, Proc. Sympos. Pure Math., 46, Part 2, Amer. Math. Soc., Providence, RI, 1987.

On pi_2 of the complements to hypersurfaces which are generic projections. Complex analytic singularities, 229-240, Adv. Stud. Pure Math., 8, North-Holland, Amsterdam, 1987.

Remarks on moduli spaces of complete intersections (with J.Wood). The Lefschetz centennial conference, Part I (Mexico City, 1984), 183-194, Contemp. Math., 58, Amer. Math. Soc., Providence, RI, 1986.

On the homotopy type of the complement to plane algebraic curves. J. Reine Angew. Math. 367 (1986), 103-114.

Homotopy groups of the complements to singular hypersurfaces. Bull. Amer. Math. Soc. (N.S.) 13 (1985), no. 1, 49-52.

A characterization of plane curve singularities with one characteristic pair. Amer. J. Math. 106 (1984), no. 2, 505-507.

Alexander modules of plane algebraic curves. Low-dimensional topology (San Francisco, Calif., 1981), 231-247, Contemp. Math., 20, Amer. Math. Soc., Providence, R.I., 1983.

Alexander invariants of plane algebraic curves. Singularities, Part 2 (Arcata, Calif., 1981), 135-143, Proc. Sympos. Pure Math., 40, Amer. Math. Soc., Providence, RI, 1983.

Differentiable structures on complete intersections. II (with J.Wood), Singularities, Part 2 (Arcata, Calif., 1981), 123-133, Proc. Sympos. Pure Math., 40, Amer. Math. Soc., Providence, RI, 1983.

Alexander polynomial of plane algebraic curves and cyclic multiple pl anes. Duke Math. J. 49 (1982), no. 4, 833-851.

Differentiable structures on complete intersections (with J.Wood). I. Topology 21 (1982), no. 4, 469-482.

On the fundamental group of the complement to a discriminant variety (with I.Dolgachev). Algebraic geometry (Chicago, Ill., 1980), pp. 1-25, Lecture Notes in Math., 862, Springer, Berlin-New York, 1981.

On the topological structure of even-dimensional complete intersections(with J.Wood). Trans. Amer. Math. Soc. 267 (1981), no. 2, 637-660.

Levine's formula in knot theory and quadratic reciprocity law. Enseign. Math. (2) 26 (1980), no. 3-4, 323-331 (1981).

Congruences modulo powers of 2 for the signature of complete intersections (with J.Wood and D.Zagier). Quart. J. Math. Oxford Ser. (2) 31 (1980), no. 122, 209-218.

Some properties of the signature of complete intersections. Proc. Amer. Math. Soc. 79 (1980), no. 3, 373-375.

Diffeomorphic complete intersections with different multidegrees (with J.Wood). Bull. Amer. Math. Soc. (N.S.) 2 (1980), no. 3, 459-461.

On the topology of some even-dimensional algebraic hypersurfaces. Topology 18 (1979), no. 3, 217-222.

On the fundamental group of the space of cubic surfaces. Math. Z. 162 (1978), no. 1, 63-67.

A geometrical procedure for killing the middle dimensional homology groups of algebraic hypersurfaces. Proc. Amer. Math. Soc. 63 (1977), no. 2, 198-202.

Numerical characteristics of systems of lines on complete intersections. (Russi\ an) Mat. Zametki 13 (1973), 87-96.

Numerical characterisitcs, English version