Book:

Intersection Homology & Perverse Sheaves, with Applications to Singularities

Preprints:

Weighted Ehrhart theory via equivariant toric geometry. (with J. Schürmann)

Weighted Ehrhart theory via mixed Hodge modules on toric varieties. (with J. Schürmann)

Equivariant toric geometry and Euler-Maclaurin formulae. (with S. Cappell, J. Schürmann and J. Shaneson)

Higher Du Bois and higher rational singularities of hypersurfaces. (with R. Yang)

Publications:

Morse numbers of complex polynomials. (with M. Tibăr)

Brylinski-Radon transformation and generic projections. (with Y. Liu and B. Wang)

Hirzebruch-Milnor classes of hypersurfaces with nontrivial normal bundles and applications to higher du Bois and rational singularities. (with M. Saito and R. Yang)

Cohomology of Z-local systems on complex hyperplane arrangement complements. (with Y. Liu and B. Wang)

Equivariant toric geometry and Euler-Maclaurin formulae -- an overview. (with S. Cappell, J. Schürmann and J. Shaneson)

Hodge-theoretic variants of the Hopf and Singer Conjectures. (with D. Arapura and B. Wang)

On the topology of complex projective hypersurfaces

Linear optimization on varieties and Chern-Mather classes. (with J. Rodriguez, B. Wang and L. Wu)

Logarithmic cotangent bundles, Chern-Mather classes, and the Huh-Sturmfels Involution conjecture. (with J. Rodriguez, B. Wang and L. Wu)

Euclidean distance degree and limit points in a Morsification. (with M. Tibăr)

Mixed Hodge structures on Alexander modules. (with E. Elduque, C. Geske, M. Herradón Cueto and B. Wang)

Applications of singularity theory in applied algebraic geometry and algebraic statistics. (with J. Rodriguez and B. Wang)

Morse numbers of function germs with isolated singularities. (with M. Tibăr)

On singular variants of the Singer-Hopf Conjecture.

Alexander modules, Mellin transformation and variations of mixed Hodge structures. (with E. Elduque, M. Herradón Cueto and B. Wang)

Non-abelian Mellin Transformations and Applications. (with Y. Liu and B. Wang)

The vanishing cohomology of non-isolated hypersurface singularities. (with L. Păunescu and M. Tibăr)

Constructible sheaf complexes in complex geometry and Applications. (with J. Schürmann)

A Morse theoretic approach to non-isolated singularities and applications to optimization. (with J. Rodriguez and B. Wang)

Vanishing cohomology and Betti bounds for complex projective hypersurfaces. (with L. Păunescu and M. Tibăr)

Hodge theory on Alexander invariants -- a survey. (with E. Elduque, C. Geske, M. Herradón Cueto and B. Wang)

Aspherical manifolds, Mellin transformation and a question of Bobadilla-Kollár. (with Y. Liu and B. Wang)

Perverse sheaves on semi-abelian varieties. (with Y. Liu and B. Wang)

Euclidean distance degree of projective varieties. (with J. Rodriguez and B. Wang)

Topology of subvarieties of complex semi-abelian varieties. (with Y. Liu and B. Wang)

Higher order degrees of affine plane curve complements. (with E. Elduque)

Plethysm and cohomology representations of external and symmetric products. (with J. Schürmann)

Defect of Euclidean distance degree. (with J. Rodriguez and B. Wang)

Euclidean distance degree of the multiview variety. (with J. Rodriguez and B. Wang)

Spectral Hirzebruch-Milnor classes of singular hypersurfaces. (with M. Saito and J. Schürmann)

Thom-Sebastiani theorems for filtered D-modules and for multiplier ideals. (with M. Saito and J. Schürmann)

Perverse sheaves on semi-abelian varieties - a survey of properties and applications (with Y. Liu and B. Wang)

Notes on vanishing cycles and applications

Topological methods in algebraic geometry and algebraic statistics

Homological congruence formulae for characteristic classes of singular varieties. (with S. Yokura)

Generic vanishing for semi-abelian varieties and integral Alexander modules. (with Y. Liu and B. Wang)

Mellin transformation, propagation, and abelian duality spaces. (with Y. Liu and B. Wang)

On the signed Euler characteristic property for subvarieties of abelian varieties. (with E. Elduque and C. Geske)

Motivic zeta functions and infinite cyclic covers. (with M. Gonzalez Villa and A. Libgober)

Twisted Alexander invariants of complex hypersurface complements. (with K. Wong)

Equivariant characteristic classes of external and symmetric products of varieties. (with J. Schürmann)

Characteristic classes of mixed Hodge modules and applications. (with J. Schürmann)

Characteristic classes of symmetric products of complex quasi-projective varieties. (with S. Cappell, J. Schürmann, J. Shaneson and S. Yokura)

Spectral pairs, Alexander modules, and boundary manifolds. (with Y. Liu)

Twisted Novikov homology of complex hypersurface complements. (with S. Friedl)

Characteristic varieties of hypersurface complements. (with Y. Liu)

Motivic infinite cyclic covers. (with M. Gonzalez Villa and A. Libgober)

Hirzebruch-Milnor classes and Steenbrink spectra of certain projective hypersurfaces. (with M. Saito and J. Schürmann)

Intersection spaces, perverse sheaves and string theory.

Reidemeister torsion, peripheral complex, and Alexander polynomials of hypersurface complements. (with Y. Liu)

Characteristic classes of singular toric varieties. (with J. Schürmann)

Intersection spaces, perverse sheaves and type IIB string theory. (with M. Banagl and N. Budur)

L²-Betti numbers of hypersurface complements.

Characteristic classes of singular toric varieties, research announcement (with J. Schürmann)

Hirzebruch-Milnor classes of complete intersections. (with M. Saito and J. Schürmann)

Characteristic classes of Hilbert schemes of points via symmetric products. (with S. Cappell, T. Ohmoto, J. Schürmann and S. Yokura)

Characteristic numbers, genera, and resolutions.

Intersection Spaces and Hypersurface Singularities. (with M. Banagl)

Deformation of Singularities and the Homology of Intersection Spaces. (with M. Banagl)

Equivariant characteristic classes of complex algebraic varieties. (with S. Cappell, J. Schürmann and J. Shaneson)

Twisted genera of symmetric products. (with J. Schürmann)

Symmetric products of mixed Hodge modules. (with M. Saito and J. Schürmann)

Hirzebruch invariants of symmetric products. (with J. Schürmann)

Hodge polynomials of singular hypersurfaces. (with A. Libgober)

On Milnor classes of complex hypersurfaces.

Characteristic classes of complex hypersurfaces. (with S. Cappell, J. Schürmann and J. Shaneson)

Equivariant genera of complex algebraic varieties. (with S. Cappell and J. Shaneson)

L²-Betti numbers of plane algebraic curves. (with S. Friedl and C. Leidy)

Hodge genera of algebraic varieties, II. (with S. Cappell, A. Libgober and J. Shaneson)

Hodge-theoretic Atiyah-Meyer formulae and the stratified multiplicative property. (with J. Schürmann)

Intersection cohomology invariants of complex algebraic varieties. (with S. Cappell and J. Shaneson)

Hodge genera and characteristic classes of complex algebraic varieties. (with S. Cappell, A. Libgober and J. Shaneson)

Obstructions on fundamental groups of plane curve complements. (with C. Leidy)

Hodge genera of algebraic varieties, I. (with S. Cappell and J. Shaneson)

Euler characteristics of algebraic varieties. (with S. Cappell and J. Shaneson)

On the Alexander invariants of hypersurface complements.

Multivariable Alexander invariants of hypersurface complements. (with A. Dimca)

Higher-order Alexander invariants of plane algebraic curves, (with C. Leidy)

Intersection homology and Alexander modules of hypersurface complements.

A decomposition theorem for the Peripheral Complex associated with hypersurfaces.

Books Edited:

Proceedings of the International Conference on Singularity Theory and Applications (Hefei, China, 2011)

Topology of Stratified Spaces. (with G. Friedman, E. Hunsiker and A. Libgober)

Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry. (with S. Friedl and A. Suciu)

Proceedings of the Hyperplane Arrangements and Singularities Conference, Hyper-JARCS 2019 (with L. Păunescu, A. Suciu, T. Fukui, T. Kohno, M. Yoshinaga)

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)

Proceedings of the Proceedings of the Conference "Geometry, Topology and Algebra of Singular Spaces" (with C. Joita, R. Popescu, M. Tibăr)

Geometry and topology of aspherical manifolds (with L. Di Cerbo)

Class notes, Surveys:

Lecture notes in Algebraic Topology (I hope this will become a book one day.)
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.)

Ph.D. Thesis (University of Pennsylvania, May 2005):

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

Some talk slides:

Singularities through the lens of characteristic classes (Heidelberg minicourse).

A geometric perspective on generalized weighted Ehrhart theory.

On the geometry and topology of aspherical compact Kähler manifolds and related questions.

Singularities through the lens of characteristic classes (Seoul minicourse).

Applications of singularity theory to optimization (Lille minicourse).

Fundamental groups of complex quasiprojective manifolds and their Alexander type invariants (Jaca minicourse).

Lefschetz properties in the constructible context and applications.

Topology of complex projective hypersurfaces.

Homological duality: jumping loci, propagation, realization.

Perverse sheaves on semi-abelian varieties: properties and applications.

Measuring the complexity of hypersurface singularities in algebraic geometry and topology.

Topology of very affine manifolds.

Geometry and topology of external and symmetric products of varieties.

Motivic infinite cyclic covers.

Characteristic classes of mixed Hodge modules and applications.

Characteristic classes of Hilbert schemes of points via symmetric products.

Toric varieties, characteristic classes and lattice point counting.

Characteristic numbers of singular varieties.

L²-Betti numbers of hypersurface complements.

Video talks, Online lectures:

On the geometry and topology of aspherical compact Kähler manifolds and related questions, Conference on Singularity theory and hyperbolicity, Newton Institute, Cambridge, UK, March 18-22, 2024.
Higher du Bois and higher rational singularities of hypersurfaces, Cambridge Singularity Day, Newton Institute, Cambridge, UK, March 15, 2024.
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.