Publications & preprints

The parity module of a matroid

With Tom Braden, June Huh, Jacob P. Matherne, and Nicholas Proudfoot

The topology of Kähler manifolds and 1-forms without zeros

With Maurício Corrêa, János Kollár, and Stefan Schreieder

Invisible singularities in complex algebraic geometry

With Mauricio Correa, János Kollár, and Stefan Schreieder

Matroid correspondence

With Colin Crowley, Changxin Ding, Haoxi Hu, Arvind Kumar, Jonathan Montaño, Thai Thanh Nguyen, Anna Shapiro, Noah Solomon, and Juliet Whidden

Topology and Euler characteristics of tropical varieties

With Scott Hiatt, Connor Simpson, and Chenxi Wu

Euclidean distance degree defect of singular projective varieties

With Laurentiu Maxim and José Rodríguez

Vertex posets, monotone path polytopes, and Chow polynomials

With Mateusz Michałek and Leonid Monin

Tree metrics and log-concavity for matroids

With Federico Ardila-Mantilla, Sergio Cristancho, Graham Denham, Christopher Eur, and June Huh

To appear in Proceedings of the London Mathematical Society.

Spectral sequences, Massey products and homology of covering spaces

With Yongqiang Liu and Laurentiu Maxim

To appear in European Journal of Mathematics.

Bounded ratios for Lorentzian matrices

With Daoji Huang, June Huh, and Daniel Soskin

Linear operators preserving volume polynomials

With Lukas Grund, June Huh, Mateusz Michałek, and Hendrik Süß

Realizations of homology classes and projection areas

With Daoji Huang, June Huh, Mateusz Michałek, and Shouda Wang

Deformation openness of big fundamental groups and applications

With Ya Deng and Chikako Mese

L²-vanishing theorem and a conjecture of Kollár

With Ya Deng

Linear Chern–Hopf–Thurston conjecture

With Ya Deng

Singular Hodge theory for combinatorial geometries

With Tom Braden, June Huh, Jacob Matherne, and Nick Proudfoot

To appear in Journal of the American Mathematical Society.

Numerical computation of braid groups

With José Rodríguez

Maximal twisted Betti numbers of complex hyperplane arrangement complements

With Yongqiang Liu and Laurentiu Maxim

International Mathematics Research Notices, 2026, no. 6, Paper rnag050, 9 pp.

The Bergman fan of a polymatroid

With Colin Crowley, June Huh, Matt Larson, and Connor Simpson

Transactions of the American Mathematical Society 379 (2026), no. 5, 3239–3256.

Combinatorial flats and Schubert varieties of subspace arrangements

With Colin Crowley and Connor Simpson

Algebraic Combinatorics 8 (2025), no. 5, 1285–1312.

A new generic vanishing theorem on homogeneous varieties and the positivity conjecture for triple intersections of Schubert cells

With Jörg Schürmann and Connor Simpson

Compositio Mathematica 161 (2025), no. 1, 1–12.

Perverse sheaves on varieties with large fundamental groups

With Donu Arapura

Journal of Differential Geometry 129 (2025), no. 1, 1–15.

Hodge-theoretic variants of the Hopf and Singer conjectures

With Donu Arapura and Laurentiu Maxim

In Geometry and Topology of Aspherical Manifolds, 93–103, Contemporary Mathematics 816.

Brylinski–Radon transformation and generic projections

With Yongqiang Liu and Laurentiu Maxim

Proceedings of the American Mathematical Society 152 (2024), no. 12, 5279–5288.

Applications of singularity theory in applied algebraic geometry and algebraic statistics

With Laurentiu Maxim and José Rodríguez

Handbook of Geometry and Topology of Singularities, vol. VII, 767–818.

Cohomology of ℤ-local systems on complex hyperplane arrangement complements

With Yongqiang Liu and Laurentiu Maxim

International Mathematics Research Notices 2024, no. 15, 11092–11103.

Linear optimization on varieties and Chern–Mather classes

With Laurentiu Maxim, José Rodríguez, and Lei Wu

Advances in Mathematics 437 (2024), Paper 109443.

Logarithmic cotangent bundles, Chern–Mather classes, and the Huh–Sturmfels involution conjecture

With Laurentiu Maxim, José Rodríguez, and Lei Wu

Communications on Pure and Applied Mathematics 77 (2024), no. 2, 1486–1508.

Self-covering, finiteness, and fibering over a circle

With Lizhen Qin and Yang Su

Transactions of the American Mathematical Society 377 (2024), 1883–1914.

Mixed Hodge structures on Alexander modules

With Eva Elduque, Christian Geske, Moisés Herradón Cueto, and Laurentiu Maxim

Memoirs of the American Mathematical Society 296 (2024).

Non-abelian Mellin transformations and applications

With Yongqiang Liu and Laurentiu Maxim

Forum of Mathematics, Sigma 10 (2022), Paper e100, 17 pp.

Alexander modules, Mellin transformation and variations of mixed Hodge structures

With Eva Elduque, Moisés Herradón Cueto, and Laurentiu Maxim

Advances in Mathematics 411 (2022), Paper 108798, 27 pp.

Hodge theory on Alexander invariants — a survey

With Eva Elduque, Christian Geske, Moisés Herradón Cueto, and Laurentiu Maxim

Topology and its Applications 313 (2022), Paper 107981, 16 pp.

A semi-small decomposition of the Chow ring of a matroid

With Tom Braden, June Huh, Jacob Matherne, and Nick Proudfoot

Advances in Mathematics 409 (2022), Paper 108646, 49 pp.

A Morse theoretic approach to non-isolated singularities and applications to optimization

With Laurentiu Maxim and José Rodríguez

Journal of Pure and Applied Algebra 226 (2022), no. 3, Paper 106865, 23 pp.

Correlation bounds for fields and matroids

With June Huh and Benjamin Schröter

Journal of the European Mathematical Society 24 (2022), no. 4, 1335–1351.

Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár

With Yongqiang Liu and Laurentiu Maxim

Journal für die reine und angewandte Mathematik 781 (2021), 1–18.

Euclidean distance degree of projective varieties

With Laurentiu Maxim and José Rodríguez

International Mathematics Research Notices 2021, no. 20, 15788–15802.

Topology of subvarieties of complex semi-abelian varieties

With Yongqiang Liu and Laurentiu Maxim

International Mathematics Research Notices 2021, no. 14, 11169–11208.

Perverse sheaves on semi-abelian varieties

With Yongqiang Liu and Laurentiu Maxim

Selecta Mathematica 27 (2021), no. 2, Paper 30, 40 pp.

A numerical approach for computing Euler characteristics of affine varieties

With Xiaxin Li and José Rodríguez

In Mathematical Software — ICMS 2020, Lecture Notes in Computer Science 12097.

Defect of Euclidean distance degree

With Laurentiu Maxim and José Rodríguez

Advances in Applied Mathematics 121 (2020), 102101.

Lyubeznik numbers of irreducible projective varieties depend on the embedding

Proceedings of the American Mathematical Society 148 (2020), 2091–2096.

Perverse sheaves on semi-abelian varieties — a survey of properties and applications

With Yongqiang Liu and Laurentiu Maxim

European Journal of Mathematics 6 (2020), no. 3, 977–997.

Euclidean distance degree of the multiview variety

With Laurentiu Maxim and José Rodríguez

SIAM Journal on Applied Algebra and Geometry 4 (2020), no. 1, 28–48.

Computing Euler obstruction functions using maximum likelihood degrees

With José Rodríguez

International Mathematics Research Notices 2020, no. 20, 6699–6712.

Absolute sets and the decomposition theorem

With Nero Budur

Annales scientifiques de l’École Normale Supérieure (4) 53 (2020), no. 2, 469–536. Correction: (4) 55 (2022), no. 5, 1473–1474.

Cohomology jump loci of quasi-compact Kähler manifolds

With Nero Budur

Pure and Applied Mathematics Quarterly 16 (2020), no. 4, 981–999.

On the length of perverse sheaves and D-modules

With Nero Budur, Pietro Gatti, and Yongqiang Liu

Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie 62(110) (2019), no. 4, 355–369.

Generic vanishing for semi-abelian varieties and integral Alexander modules

With Yongqiang Liu and Laurentiu Maxim

Mathematische Zeitschrift 293 (2019), 629–645.

Mellin transformation, propagation, and abelian duality spaces

With Yongqiang Liu and Laurentiu Maxim

Advances in Mathematics 335 (2018), 231–260.

Algebraic surfaces with zero-dimensional cohomology support locus

Taiwanese Journal of Mathematics 22 (2018), no. 3, 607–614.

The monodromy theorem for compact Kähler manifolds and smooth quasi-projective varieties

With Nero Budur and Yongqiang Liu

Mathematische Annalen 371 (2018), no. 3–4, 1069–1086.

A family of compact complex-symplectic Calabi–Yau manifolds that are non-Kähler

With Lizhen Qin

Geometry & Topology 22 (2018), no. 4, 2115–2144.

Lefschetz classes on projective varieties

With June Huh

Proceedings of the American Mathematical Society 145 (2017), no. 11, 4629–4637.

Enumeration of points, lines, planes, etc.

With June Huh

Acta Mathematica 218 (2017), 297–317.

Cohomology support loci of local systems

With Nero Budur, Yongqiang Liu, and Luis Saumell

Michigan Mathematical Journal 66 (2017), no. 2, 295–307.

Local systems on analytic germ complements

With Nero Budur

Advances in Mathematics 306 (2017), 905–928.

Recent results on cohomology jump loci

With Nero Budur

In Hodge Theory and L²-analysis, ALM 39, 205–241.

The maximum likelihood degree of mixtures of independence models

With José Rodríguez

SIAM Journal on Applied Algebra and Geometry 1 (2017), no. 1, 484–506.

Maximum likelihood degree of Fermat hypersurfaces via Euler characteristics

Proceedings of the American Mathematical Society 144 (2016), no. 5, 3649–3655.

Rank one local systems and forms of degree one

With Nero Budur and Youngho Yoon

International Mathematics Research Notices 2016, no. 13, 3849–3855.

Torsion points on the cohomology jump loci of compact Kähler manifolds

Mathematical Research Letters 23 (2016), no. 2, 545–563.

Bounding the maximum likelihood degree

With Nero Budur

Mathematical Research Letters 22 (2015), no. 6, 1613–1620.

The signed Euler characteristic of very affine varieties

With Nero Budur

International Mathematics Research Notices 2015, 5710–5714.

Cohomology jump loci of differential graded Lie algebras

With Nero Budur

Compositio Mathematica 151 (2015), no. 8, 1499–1528.

Cohomology jump loci of quasi-projective varieties

With Nero Budur

Annales scientifiques de l’École Normale Supérieure 48 (2015), no. 1, 227–236.

Homomorphisms between fundamental groups of Kähler manifolds

Proceedings of the American Mathematical Society 139 (2011), no. 5, 1599–1603.