- Intersection Homology & Perverse Sheaves, with Applications to Singularities
**Graduate Texts in Mathematics**, Vol. 281,**Springer**, 2019;**ISBN**: 978-3030276430.

**MAA Review, zbMATH Review**

**Erratum**

- Hodge-theoretic variants of the Hopf and Singer Conjectures. (with D. Arapura and B. Wang)
**arXiv:2310.14131.** - Morse numbers of complex polynomials. (with M. Tibăr)
**arXiv:2307.04032.** - Brylinski-Radon transformation and generic projections. (with Y. Liu and B. Wang)
**arXiv:2307.00352.** - Equivariant toric geometry and Euler-Maclaurin formulae. (with S. Cappell, J. Schürmann and J. Shaneson)
**arXiv:2303.16785.** - Hirzebruch-Milnor classes of hypersurfaces with nontrivial normal bundles and applications to higher du Bois and rational singularities. (with M. Saito and R. Yang)
**arXiv:2302.00970.** - Homological criterion for higher Du Bois and higher rational singularities. (with R. Yang)
**arXiv:2301.09084.** - Cohomology of Z-local systems on complex hyperplane arrangement complements. (with Y. Liu and B. Wang)
**arXiv:2209.13193.**

- Linear optimization on varieties and Chern-Mather classes. (with J. Rodriguez, B. Wang and L. Wu)
**Advances in Mathematicas**437 (2024), Paper No. 109443; DOI: 10.1016/j.aim.2023.109443 - Logarithmic cotangent bundles, Chern-Mather classes, and the Huh-Sturmfels Involution conjecture. (with J. Rodriguez, B. Wang and L. Wu)
**Comm. Pure Appl. Math.**77 (2024), no. 2, 1486-1508; DOI: 10.1002/cpa.22156. - Euclidean distance degree and limit points in a Morsification. (with M. Tibăr)
**Advances in Applied Mathematics**152 (2024), article 102597; DOI: 10.1016/j.aam.2023.102597. - Applications of singularity theory in applied algebraic geometry and algebraic statistics. (with J. Rodriguez and B. Wang)
**Handbook of Geometry and Topology of Singularities, vol. VII**(accepted);**arXiv:2305.19842.** - Mixed Hodge structures on Alexander modules. (with E. Elduque, C. Geske, M. Herradón Cueto and B. Wang)
**Memoirs of the American Mathematical Society**(accepted);**arXiv:2002.01589.** - Morse numbers of function germs with isolated singularities. (with M. Tibăr)
**Quarterly Journal of Mathematics**74 (2023), no. 4, 1535-1544; DOI: 10.1093/qmath/haad033. - On singular variants of the Singer-Hopf Conjecture.
**Mathematische Nachrichten**296 (2023), no. 11, 5232-5241; DOI: 10.1002/mana.202200322. - Alexander modules, Mellin transformation and variations of mixed Hodge structures. (with E. Elduque, M. Herradón Cueto and B. Wang)
**Advances in Mathematics**411 (2022), Paper No. 108798; DOI: 10.1016/j.aim.2022.108798. - Non-abelian Mellin Transformations and Applications. (with Y. Liu and B. Wang)
**Forum Math. Sigma 10**(2022), Paper No. e100; DOI: 10.1017/fms.2022.91. - The vanishing cohomology of non-isolated hypersurface singularities.
(with L. Păunescu and M. Tibăr)
**Journal of the London Mathematical Society**106 (2022), no. 1, 112-153; DOI: 10.1112/jlms.12570. - Constructible sheaf complexes in complex geometry and Applications. (with J. Schürmann)
**Handbook of Geometry and Topology of Singularities, vol. III**, pages 679-791, Springer, Cham, 2022; https://doi.org/10.1007/978-3-030-95760-5_10. - A Morse theoretic approach to non-isolated singularities and applications to optimization. (with J. Rodriguez and B. Wang)
**Journal of Pure and Applied Algebra**226 (2022), Issue 3, 106865; DOI: 10.1016/j.jpaa.2021.106865. - Vanishing cohomology and Betti bounds for complex projective hypersurfaces.
(with L. Păunescu and M. Tibăr)
**Annales de l'Institut Fourier**72 (2022) no. 4, pp. 1705-1731; DOI: 10.5802/aif.3486. - Hodge theory on Alexander invariants -- a survey. (with E. Elduque, C. Geske, M. Herradón Cueto and B. Wang)
**Topology and its Applications**313 (2022), article 107981; DOI: 10.1016/j.topol.2021.107981. - Aspherical manifolds, Mellin transformation and a question of Bobadilla-Kollár. (with Y. Liu and B. Wang)
**J. Reine Angew. Math. (Crelle's Journal)**781 (2021), 1-18; DOI: 10.1515/crelle-2021-0055. - Perverse sheaves on semi-abelian varieties. (with Y. Liu and B. Wang)
**Selecta Mathematica**27 (2021), article 30; DOI: 10.1007/s00029-021-00635-4. - Euclidean distance degree of projective varieties. (with J. Rodriguez and B. Wang)
**Int. Math. Res. Not.**Vol. 2021, Issue 20, Pages 15788-15802; DOI: 10.1093/imrn/rnz266 - Topology of subvarieties of complex semi-abelian varieties. (with Y. Liu and B. Wang)
**Int. Math. Res. Not.**Vol. 2021, Issue 14, Pages 11169-11208; DOI: 10.1093/imrn/rnaa242 - Higher order degrees of affine plane curve complements. (with E. Elduque)
**Indiana University Mathematics Journal**70 (2021), no. 1, 179-211; DOI: 10.1512/iumj.2021.70.8297. - Plethysm and cohomology representations of external and symmetric products.
(with J. Schürmann)
**Advances in Mathematics**375 (2020), 107373; DOI: 10.1016/j.aim.2020.107373. - Defect of Euclidean distance degree. (with J. Rodriguez and B. Wang)
**Advances in Applied Mathematics**121 (2020), 102101; DOI: 10.1016/j.aam.2020.102101 - Euclidean distance degree of the multiview variety. (with J. Rodriguez and B. Wang)
**SIAM J. Appl. Algebra Geometry**4 (2020), no. 1, 28-48; DOI: 10.1137/18M1233406 - Spectral Hirzebruch-Milnor classes of singular hypersurfaces. (with M. Saito and J. Schürmann)
**Mathematische Annalen**377 (2000), no. 1-2, 281-315; DOI: 10.1007/s00208-018-1750-4 - Thom-Sebastiani theorems for filtered D-modules and for multiplier ideals. (with M. Saito and J. Schürmann)
**Int. Math. Res. Not.**Vol. 2020, no. 1, 91-111; DOI: 10.1093/imrn/rny032. - Perverse sheaves on semi-abelian varieties - a survey of properties and applications
(with Y. Liu and B. Wang)
**European Journal of Mathematics**6 (2020), no. 3, 977-997; DOI: 10.1007/s40879-019-00340-9 - Notes on vanishing cycles and applications
**Journal of the Australian Mathematical Society**109 (2020), no. 3, 371-415; DOI: 10.1017/S1446788720000403. - Topological methods in algebraic geometry and algebraic statistics
**Rev. Roumaine Math. Pures Appl.**65 (2020), no. 3, 311-325; journal link. - Homological congruence formulae for characteristic classes of singular varieties. (with
S. Yokura)
**European Journal of Mathematics**5 (2019), no. 4, 1267-1292; DOI: 10.1007/s00208-018-1750-4 - Generic vanishing for semi-abelian varieties and integral Alexander modules. (with Y. Liu and B. Wang)
**Mathematische Zeitschrift**293 (2019), no. 1-2, 629-645; DOI: 10.1007/s00209-018-2194-y - Mellin transformation, propagation, and abelian duality spaces. (with Y. Liu and B. Wang)
**Advances in Mathematics**335 (2018), 231-260; DOI: 10.1016/j.aim.2018.07.012. - On the signed Euler characteristic property for subvarieties of abelian varieties. (with E. Elduque and C. Geske)
**Journal of Singularities**17 (2018), 368-387; DOI: 10.5427/jsing.2018.17p - Motivic zeta functions and infinite cyclic covers.
(with M. Gonzalez Villa and A. Libgober)
*in***Local and Global Methods in Algebraic Geometry**,**Contemp. Math.**712 (2018), pp. 117-141. - Twisted Alexander invariants of complex hypersurface complements.
(with K. Wong)
**Proc. Roy. Soc. Edinburgh Sect. A**148 (2018), no. 5, 1049-1073; DOI: 10.1017/S0308210518000094 - Equivariant characteristic classes of external and symmetric products of
varieties. (with J. Schürmann)
**Geometry & Topology**22 (2018), no. 1, 471-515; DOI: 10.2140/gt.2018.22.471. - Characteristic classes of mixed Hodge modules and applications. (with J. Schürmann)
*in***Schubert Varieties, Equivariant Cohomology and Characteristic Classes (Impanga 15)**, EMS Series of Congress Reports 2017, 159-202, European Mathematical Society Publishing House; DOI: 10.4171/182-1/8 - Characteristic classes of symmetric products of complex quasi-projective varieties. (with S. Cappell, J. Schürmann, J. Shaneson and S. Yokura)
**J. Reine Angew. Math. (Crelle's Journal)**728 (2017), 35-63; DOI: 10.1515/crelle-2014-0114. - Spectral pairs, Alexander modules, and boundary manifolds. (with Y. Liu)
**Selecta Mathematica**23 (2017), no. 3, 2261-2290; DOI: 10.1007/s00029-017-0333-7. - Twisted Novikov homology of complex hypersurface complements.
(with S. Friedl)
**Mathematische Nachrichten**290 (2017), no. 4, 604-612; DOI: 10.1002/mana.201600242. - Characteristic varieties of hypersurface complements. (with Y. Liu)
**Advances in Mathematics**306 (2017), 451-493; DOI: 10.1016/j.aim.2016.10.031 - Motivic infinite cyclic covers. (with M. Gonzalez Villa and A. Libgober)
**Advances in Mathematics**298 (2016), 413-447; DOI: 10.1016/j.aim.2016.04.019 - Hirzebruch-Milnor classes and Steenbrink spectra of certain projective hypersurfaces. (with M. Saito and J. Schürmann)
*in***Arbeitstagung Bonn 2013**, Progress in Mathematics 319, 265-287, Springer International Publishing 2016. - Intersection spaces, perverse sheaves and string theory.
**Journal of Singularities**15 (2016), 118-125; DOI: 10.5427/jsing.2016.15f - Reidemeister torsion, peripheral complex, and Alexander polynomials of hypersurface complements. (with Y. Liu)
**Algebr. Geom. Topol.**15 (2015), no. 5, 2757-2787; DOI: 10.2140/agt.2015.15.2757 - Characteristic classes of singular toric varieties. (with J. Schürmann)
**Comm. Pure Appl. Math.**68 (2015), no. 12, 2177-2236; DOI: 10.1002/cpa.21553. - Intersection spaces, perverse sheaves and type IIB string theory. (with M. Banagl and N. Budur)
**Adv. Theor. Math. Phys.**Vol. 18 (2014), no. 2, 363-399; DOI: http://dx.doi.org/10.4310/ATMP.2014.v18.n2.a3 - L
^{2}-Betti numbers of hypersurface complements.**Int. Math. Res. Not.**Vol. 2014, no. 17, 4665-4678; doi: 10.1093/imrn/rnt093 - Characteristic classes of singular toric varieties,
*research announcement*(with J. Schürmann)**Electron. Res. Announc. Math. Sci.**20 (2013), 109-120; DOI: 10.3934/era.2013.20.109 - Hirzebruch-Milnor classes of complete intersections. (with M. Saito and J. Schürmann)
**Advances in Mathematics**241 (2013), 220-245; DOI: 10.1016/j.aim.2013.04.001 - Characteristic classes of Hilbert schemes of points via symmetric products. (with S. Cappell, T. Ohmoto, J. Schürmann and S. Yokura)
**Geometry & Topology**17 (2013), no. 2, 1165-1198; DOI: 10.2140/gt.2013.17.1165 - Characteristic numbers, genera, and resolutions.
*in***Advances in Mathematics: Invited Contributions to the Seventh Congress of Romanian Mathematicians**, The Publishing House of the Romanian Academy, 2013, pp. 207-225. - Intersection Spaces and Hypersurface Singularities. (with M. Banagl)
**Journal of Singularities**5 (2012), 48-56; DOI: 10.5427/jsing.2012.5d - Deformation of Singularities and the Homology of Intersection Spaces. (with M. Banagl)
**Journal of Topology and Analysis**4 (2012), no. 4, 413-448; DOI: 10.1142/S1793525312500185 - Equivariant characteristic classes of complex algebraic varieties. (with S. Cappell, J. Schürmann and J. Shaneson)
**Comm. Pure Appl. Math.**65 (2012), no. 12, 1722-1769; DOI 10.1002/cpa.21427. - Twisted genera of symmetric products. (with J. Schürmann)
**Selecta Mathematica**18 (2012), no. 1, 283-317; DOI 10.1007/s00029-011-0072-0. - Symmetric products of mixed Hodge modules. (with M. Saito and J. Schürmann)
**J. Math. Pures Appl.**96 (2011), no. 5, 462-483; doi:10.1016/j.matpur.2011.04.003. - Hirzebruch invariants of symmetric products. (with J. Schürmann)
*in***Topology of Algebraic Varieties and Singularities**,**Contemp. Math.**538 (2011), pp. 163-177. - Hodge polynomials of singular hypersurfaces. (with A. Libgober)
**Michigan Math. J.**60 (2011), no. 3, 661-673. - On Milnor classes of complex hypersurfaces.
*in***Topology of Stratified Spaces**, MSRI Publications 58, Cambridge University Press, New York, 2011, pp. 161-175. - Characteristic classes of complex hypersurfaces. (with S. Cappell, J. Schürmann and J. Shaneson)
**Advances in Mathematics**225 (2010), no. 5, 2616-2647; doi:10.1016/j.aim.2010.05.007 - Equivariant genera of complex algebraic varieties. (with S. Cappell and J. Shaneson)
**Int. Math. Res. Not.**Vol. 2009, no. 11, 2013-2037; doi: 10.1093/imrn/rnp009 - L
^{2}-Betti numbers of plane algebraic curves. (with S. Friedl and C. Leidy)**Michigan Math. J.**58 (2009), no. 2, 411-421. - Hodge genera of algebraic varieties, II. (with S. Cappell, A. Libgober and J. Shaneson)
**Mathematische Annalen**345 (2009), no. 4, 925-972; DOI 10.1007/s00208-009-0389-6. - Hodge-theoretic Atiyah-Meyer formulae and the stratified multiplicative property. (with J. Schürmann)
*in***Singularities I: Algebraic and Analytic Aspects**,**Contemp. Math.**474 (2008), pp. 145-167. - Intersection cohomology invariants of complex algebraic varieties.
(with S. Cappell and J. Shaneson)
*in***Singularities I: Algebraic and Analytic Aspects**,**Contemp. Math.**474 (2008), pp. 15-25. - Hodge genera and characteristic classes of complex algebraic
varieties. (with S. Cappell, A. Libgober and J. Shaneson)
**Electron. Res. Announc. Math. Sci.**15 (2008), 1-7. - Obstructions on fundamental groups of plane curve complements. (with C. Leidy)
*in***Real and Complex Singularities**,**Contemp. Math.**459 (2008), pp. 117-130. - Hodge genera of algebraic varieties, I. (with S. Cappell and J. Shaneson)
**Comm. Pure Appl. Math.**61 (2008), no. 3, 422-449. - Euler characteristics of algebraic varieties. (with S. Cappell and J. Shaneson)
**Comm. Pure Appl. Math.**61 (2008), no. 3, 409-421. - On the Alexander invariants of hypersurface complements.
*in***Singularity Theory**, Proceedings of the 2005 Marseille Singularity School and Conference (Denis Cheniot et al, ed.), World Scientific, 2007, pp. 725-744. - Multivariable Alexander invariants of hypersurface complements. (with A. Dimca)
**Trans. Amer. Math. Soc.**359 (2007), no. 7, 3505-3528. - Higher-order Alexander invariants of plane algebraic curves, (with C. Leidy)
**Int. Math. Res. Not.**, Volume 2006 (2006), Article ID 12976, 23 pages. - Intersection homology and Alexander modules of hypersurface complements.
**Comment. Math. Helv.**81 (2006), no. 1, 123-155. - A decomposition theorem for the Peripheral Complex associated with
hypersurfaces.
**Int. Math. Res. Not.**43 (2005), 2627-2656.

- Proceedings of the International Conference on Singularity Theory and Applications (Hefei, China, 2011)
**Journal of Singularities**, vol. 5 (2012),**ISSN**: 1949-2006.

- Topology of Stratified Spaces.
(with G. Friedman, E. Hunsiker and A. Libgober)
**Mathematical Sciences Research Institute Publications**58, Cambridge University Press, New York, 2011;**ISBN**: 9780521191678.

- Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry.
(with S. Friedl and A. Suciu)
**Oberwolfach Reports**14 (2017), no. 4, 2987-3033.

- Proceedings of the Hyperplane Arrangements and Singularities Conference, Hyper-JARCS 2019
(with L. Păunescu, A. Suciu, T. Fukui, T. Kohno, M. Yoshinaga)
**Topology and its Applications**, vol. 313 (2022).

- The 16th International Workshop on Real and Complex Singularities (23-30 November 2020, virtual from ICMC-USP, São Carlos, Brazil)
(with M. Manoel, M. Aparecida Ruas, D. Trotman)
**Journal of Singularities**, vol. 25 (2022),**ISSN**: 1949-2006.

- Lecture notes in Algebraic Topology (I hope this will become a book one day.)
- Topology of complex projective hypersurfaces. (a neater version of my Summer School notes, aimed at novice readers.)
- Topology of complex projective hypersurfaces and of their complements (lecture notes for the CIMPA Research School "Singularities and Applications", July 12-23, 2021.)
- Vanishing Cycles and Applications. (lecture notes for a seminar at SMRI (Sydney) in February 2020.)
- Brief Overview of Intersection Homology and Applications. (lecture notes for a seminar at SMRI (Sydney) in February 2020.)
- Notes on Intersection Homology and Perverse Sheaves, with Applications to Singularities. (lecture notes for a topics course at UW-Madison in Fall 2016; this is now a book, published as Springer GTM Vol. 281.)
- Lecture notes on homotopy theory, spectral sequences, fiber bundles and characteristic classes. (lecture notes for an advanced algebraic topology course at UW-Madison in Spring 2018.)
- Notes on motivic integration and characteristic classes. (notes I wrote while attempting to learn this luring theory.)
- Alexander invariants of hypersurface complements. (notes for a series of lectures I gave at Tokyo University of Sciences and The University of Tokyo during the Summer of 2006.)

- Alexander invariants of hypersurface complements (Ph.D. Advisor: Julius Shaneson).

- Lefschetz properties in the constructible context, Workshop on Lefschetz Properties in Algebra, Geometry, Topology and Combinatorics, The Fields Institute, Toronto, May 15-19, 2023.
- Topology of complex projective hypersurfaces and of their complements, at the 2021-2022 CIMPA Research School "Singularities and Applications":
- recorded lectures for the online school, July 12-23, 2021.

- in person follow-up event in Sao Carlos, Brazil, July 11-22, 2022. (lectures are available on the YouTube channel of the Singularities Group at ICMC-Sao Carlos.)

- Characteristic classes of stratified spaces (lecture I, lecture II), at the "Topology, Stratified Spaces and Particle Physics Summer School", Fields Institute, Toronto, Canada, August 2016.
- Genera of complex varieties and singularities of proper maps, MSRI Workshop on "Recent Developments in Arrangements and Configuration Spaces", August 2006.
- Intersection Homology and Alexander Modules of Hypersurface Complements, MSRI Workshop on "Topology of Arrangements and Applications", October 2004.