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Publications and Preprints

Hodge-theoretic variants of the Hopf and Singer Conjectures
, with Donu Arapura and Laurentiu Maxim. Preprint

Brylinski-Radon transformation and generic projections, with Yongqiang Liu and Laurentiu Maxim. Preprint

Applications of singularity theory in applied algebraic geometry and algebraic statistics
, with Laurentiu Maxim and Jose Rodriguez. Preprint.

A new generic vanishing theorem on homogeneous varieties and the positivity conjecture for triple intersections of Schubert cells, with Jörg Schürmann and Connor Simpson. Preprint

Cohomology of Z-local systems on complex hyperplane arrangement complements, with Yongqiang Liu and Laurentiu Maxim. Preprint

Linear optimization on varieties and Chern-Mather classes
, with Laurentiu Maxim, Jose Rodriguez and Lei Wu. Adv. Math. 437 (2024), Paper No. 109443.

The Bergman fan of a polymatroid
, with Colin Crowley, June Huh, Matt Larson and Connor Simpson. Preprint.

Logarithmic cotangent bundles, Chern-Mather classes, and the Huh-Sturmfels Involution conjecture
, with Laurentiu Maxim, Jose Rodriguez and Lei Wu. Comm. Pure Appl. Math. 77 (2024), no. 2, 1486–1508.

Self-Covering, Finiteness, And Fibering Over A Circle , with Lizhen Qin and Yang Su. To appear in Trans. Amer. Math. Soc.

Perverse sheaves on varieties with large fundamental groups , with Donu Arapura. To appear in J. Differential Geom.

Non-abelian Mellin Transformations and Applications, with Yongqiang Liu and Laurentiu Maxim. Forum Math. Sigma 10 (2022), Paper No. e100, 17 pp.

Alexander modules, Mellin transformation and variations of mixed Hodge structures, with Eva Elduque, Moises Herradon Cueto and Laurentiu Maxim. Adv. Math. 411 (2022), Paper No. 108798, 27 pp.

Hodge theory on Alexander invariants -- a survey, with Eva Elduque, Christian Geske, Moises Herradon Cueto and Laurentiu Maxim. Topology Appl. 313 (2022), Paper No. 107981, 16 pp.

Singular Hodge theory for combinatorial geometries, with Tom Braden, June Huh, Jacob Matherne and Nick Proudfoot. Preprint.

Aspherical manifolds, Mellin transformation and a question of Bobadilla-Kollar, with Yongqiang Liu and Laurentiu Maxim. *J. Reine Angew. Math.* 781 (2021), 1-18.

A semi-small decomposition of the Chow ring of a matroid, with Tom Braden, June Huh, Jacob Matherne and Nick Proudfoot. Adv. Math. 409 (2022), Paper No. 108646, 49 pp.

Mixed Hodge Structures on Alexander Modules, with Eva Elduque, Christian Geske, Moises Herradon Cueto and Laurentiu Maxim. To appear in Mem. Amer. Math. Soc.

A Morse theoretic approach to non-isolated singularities and applications to optimization, with Laurentiu Maxim and Jose Rodriguez. *J. Pure Appl. Algebra * 226 (2022), no. 3, Paper No. 106865, 23 pp.

A numerical approach for computing Euler characteristics of affine varieties, with Xiaxin Li and Jose Rodriguez. Mathematical Software -- ICMS 2020. Lecture Notes in Computer Science, vol 12097.

Defect of Euclidean distance degree, with Laurentiu Maxim and Jose Rodriguez. *Adv. in Appl. Math. * 121 (2020), 102101

Lyubeznik numbers of irreducible projective varieties depend on the embedding. *Proc. Amer. Math. Soc. *148 (2020), 2091-2096

Perverse sheaves on semi-abelian varieties -- a survey of properties and applications, with Yongqiang Liu and Laurentiu Maxim. *Eur. J. Math.* 6 (2020), no. 3, 977-997.

Euclidean distance degree of projective varieties, with Laurentiu Maxim and Jose Rodriguez. *Int. Math. Res. Not.* 2021, no. 20, 15788-15802.

Euclidean distance degree of the multiview variety, with Laurentiu Maxim and Jose Rodriguez. *SIAM J. Appl. Algebra Geom. * 4 (2020), no. 1, 28-48.

Correlation bounds for fields and matroids, with June Huh and Benjamin Schroter. *J. Eur. Math. Soc. * 24 (2022), no. 4, 1335-1351.

Perverse sheaves on semi-abelian varieties, with Yongqiang Liu and Laurentiu Maxim. *Selecta Math. (N.S.) * 27 (2021), no. 2, Paper No. 30, 40 pp.

Numerical computation of braid groups, with with Jose Rodriguez. Preprint.

Computing Euler obstruction functions using maximum likelihood degrees., with with Jose Rodriguez. *Int. Math. Res. Not. * 2020, no. 20, 6699-6712.

Mellin transformation, propagation, and abelian duality spaces, with Yongqiang Liu and Laurentiu Maxim. * Adv. Math. * 335 (2018), 231-260.

On the length of perverse sheaves and D-modules, with Nero Budur, Pietro Gatti and Yongqiang Liu. *Bull. Math. Soc. Sci. Math. Roumanie (N.S.) * 62(110) (2019), no. 4, 355-369.

Generic vanishing for semi-abelian varieties and integral Alexander modules, with Yongqiang Liu and Laurentiu Maxim. *Math. Z. * volume 293, 629-645(2019)

Topology of subvarieties of complex semi-abelian varieties, with Yongqiang Liu and Laurentiu Maxim. *Int. Math. Res. Not. * 2021, no. 14, 11169-11208

Absolute sets and the Decomposition Theorem, with Nero Budur. *Ann. Sci. Ecole Norm. Sup. * (4) 53 (2020), no. 2, 469-536.

Correction to ``Absolute sets and the decomposition theorem'' Ann. Sci. Éc. Norm. Supér. (4) 55 (2022), no. 5, 1473-1474.

Algebraic surfaces with zero dimensional cohomology support locus, *Taiwanese J. Math.* 22 (2018), no. 3, 607-614.

Cohomology jump loci of quasi-compact Kahler manifolds, with Nero Budur. *Pure Appl. Math. Q.* 16 (2020), no. 4, 981-999.

Lefschetz classes on projective varieties, with June Huh. *Proc. Amer. Math. Soc. * 145 (2017), no. 11, 4629-4637.

The monodromy theorem for compact Kahler manifolds and smooth quasi-projective varieties, with Nero Budur and Yongqiang Liu. *Math. Ann.* 371 (2018), no. 3-4, 1069-1086.

Enumeration of points, lines, planes, etc, with June Huh. *Acta Mathematica* 218 (2017), 297-317.

A Family of Compact Complex-Symplectic Calabi-Yau Manifolds that are Nonkahler, with Lizhen Qin. *Geom. Topol.* Volume 22, Number 4 (2018), 2115-2144.

Cohomology support loci of local systems, with Nero Budur, Yongqiang Liu and Luis Saumell. * Michigan Math. J. * 66 (2017), no. 2, 295-307.

Maximum likelihood degree of Fermat hypersurfaces via Euler characteristics. * Proc. Amer. Math. Soc. * 144 (2016), no. 5, 3649-3655.

Local systems on analytic germ complements, with Nero Budur. * Adv. Math. * 306 (2017), 905-928

Recent results on cohomology jump loci, with Nero Budur. * Hodge Theory and L2-analysis, * ALM 39, Higher Education Press and International Press (2017), 205-241.

The maximum likelihood degree of mixtures of independence models, with Jose Rodriguez. * SIAM J. Appl. Algebra Geom. * 1 (2017), no. 1, 484-506.

Rank one local systems and forms of degree one, with Nero Budur and Youngho Yoon. * Int. Math. Res. Not. * (2016), no.13, 3849-3855.

Bounding the maximum likelihood degree, with Nero Budur. * Math. Res. Lett. * 22 (2015), no.6, 1613-1620.

The signed Euler characteristic of very affine varieties , with Nero Budur. * Int. Math. Res. Notices. * (2015) Vol. 2015, 5710-5714.

Torsion points on the cohomology jump loci of compact Kahler manifolds , * Math. Res. Lett. * 23 (2016), no.2, 545-563.

Cohomology jump loci of differential graded Lie algebras , with Nero Budur. * Compositio Math. * 151, no. 8 (2015), 1499-1528.

Cohomology jump loci of quasi-projective varieties, with Nero Budur. * Ann. Sci. Ecole Norm. Sup. * 48 , no. 1 (2015), 227-236.

Homomorphisms between fundamental groups of Kahler manifolds, *Proc. Amer. Math. Soc. *139 (2011), no. 5, 1599-1603.