Publications and Preprints

  • Linear optimization on varieties and Chern-Mather classes , with Laurentiu Maxim, Jose Rodriguez and Lei Wu. Preprint.

  • 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. Preprint.

  • Self-Covering, Finiteness, And Fibering Over A Circle , with Lizhen Qin and Yang Su. Preprint.

  • Perverse sheaves on varieties with large fundamental groups , with Donu Arapura. Preprint.

  • Non-abelian Mellin Transformations and Applications, with Yongqiang Liu and Laurentiu Maxim. Preprint.

  • Alexander modules, Mellin transformation and variations of mixed Hodge structures, with Eva Elduque, Moises Herradon Cueto and Laurentiu Maxim. Preprint.

  • 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.

  • 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. To appear in Adv. Math.

  • 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.

  • 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.