Skip to main content
Department of Mathematics College of Liberal Arts and Sciences

Publications

  1. Symplectically aspherical Kaehler manifolds, scalar curvature, and the fundamental group (with A. Dranishnikov and E. Jauhari), arXiv:2607.05170v1. Submitted, 2026.
  2. Price Inequality and the Growth of Harmonic Functions on Non-Positively Curved Manifolds (with H. Hunter and A. Thrasher), arXiv:2601.08804v2. Submitted, 2026.
  3. A rigidity theorem for Einstein 4-manifolds with semi-definite sectional curvature, and its consequences, arXiv:2503.09570v2. Submitted, 2025.
  4. Curvature, Macroscopic Dimensions, and Symmetric Products of Surfaces (with A. Dranishnikov and E. Jauhari), arXiv2503.01779v5.   Submitted, 2025.
  5. The signature of geometrically decomposable aspherical 4-manifolds (with M. Golla), arXiv.2306.15501v1.  Submitted, 2023.
  6. Singer Conjecture for Varieties with Semismall Albanese Map and Residually Finite Fundamental Group (with L. Lombardi). Proc. Roy. Soc. Edinburgh Sect. A. 156 (2026), Issue 1, 122-128.
  7. Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-Lueck Inequality χ ≥ |σ|
    (with M. Albanese and L. Lombardi). Math. Proc. Cambridge Philos. Soc. 179 (2025), no. 3, 541-555.
  8. On the Betti Numbers of Finite Volume Real- and Complex-Hyperbolic Manifolds (with M. Stern). J. Differential Geom.130 (2025), no. 2, 343-402.
  9. Generalized Graph Manifolds, Residually Finiteness, and the Singer Conjecture (with M. Hull). Contemp. Math. 816 (2025), 123-150.
  10. Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence (with M. Stern). J. Geom. Analysis 35 (2025), no. 1, Paper No 16, 26pp.
  11. Aspherical 4-Manifolds, Complex Structures, and Einstein Metrics (with M. Albanese). J. Geom. Analysis 34 (2024), no. 7, Paper No. 193, 8pp.
  12. On the Hopf  Problem and a Conjecture of Liu-Maxim-Wang (with R. Pardini), Expo. Math 42 (2024), no. 2, 125543.(10 pp)
  13. Extended Graph 4-Manifolds, and Einstein Metrics, Ann. Math. Qu’e. 48 (2024), no. 1, 269-276.
  14. L2-Betti Numbers and Convergence of Normalized Hodge Numbers via the Weak Generic Nakano Vanishing Theorem (with L. Lombardi), Ann. Inst. Fourier (Grenoble) 74 (2024), no. 1, 423-449.
  15. On the impossibility of four-dimensional complex-hyperbolic Einstein Dehn filling (with M. Golla), Proc. Amer. Math. Soc. 151 (2023), no. 1, 281-294. 
  16. Price inequality and Betti numbers growth on manifolds without conjugate points (with M. Stern), Comm. Anal. Geom. 30 (2022), no. 2, 297-334.
  17. Moving Seshadri Constants, and Coverings of Varieties of Maximal Albanese Dimension (with L. Lombardi), Asian J. Math. (25) (2021), no. 2, 305-320. 
  18. On the Boundary Injectivity Radius of Buser-Colbois-Dodziuk-Margulis Tubes,Ann. Global Anal. Geom. 59 (2021), 285-295.
  19. Graph Theoretical Representation of Equity Indices and Their Centrality Measures (with S. Taylor),  Quant. Finance 21, no. 4 (2021), 523-537.
  20. Punctured spheres in complex hyperbolic surfaces and bielliptic ball quotient compactifications (with M. Stover), Trans. Amer. Math. Soc. 372 (2019), no. 7, 4627-4646.
  21. On Seshadri constants of varieties with large fundamental group (with G. Di Cerbo), Ann. Sc. Norm. Super. Pisa Cl. Sci. (19), no. 1 (2019), 335-344.
  22. Exceptional collections and the bicanonical map of Keum’s fake projective planes (with G. Di Brino), Commun. Contemp. Math. 20, no. 1 (2018), 1650066.
  23. Classification and arithmeticity of toroidal compactifications with 3overline{c}_{2}=overline{c}^2_1=3 (with M. Stover), Geom. Topol. (22), no. 4 (2018), 2465-2510.
  24. The Toledo invariant, and Seshadri constants of fake projective planes, J. Math. Soc. Japan 69, no. 4 (2017), 1601-1610.
  25. On the canonical divisor of smooth toroidal compactifications (with G. Di Cerbo), Math. Res. Lett. 24, no. 4 (2017), 1005-1022.
  26. Bielliptic ball quotient compactifications and lattices in PU(2, 1) with finitely generated commutator subgroup (with M. Stover),  Ann. Inst. Fourier (Grenoble) (67), no. 1 (2017), 315-328.
  27. Multiple realizations of varieties as ball quotient compactifications (with M. Stover), Michigan Math. J. 65, no. 2 (2016), 441-447.
  28. Effective results for complex hyperbolic manifolds (with G. Di Cerbo), J. Lond. Math. Soc. (2) 91 (2015), no. 1, 89-104.
  29. Positivity in Kähler-Einstein theory (with G. Di Cerbo), Math. Proc. Cambridge Philos. Soc. 159 (2015), no. 2, 321-338.
  30. A sharp cusp count for complex hyperbolic surfaces and related results (with G. Di Cerbo),  Arch. Math. (Basel). 103, no. 1 (2014), 75-85.
  31. On Kähler-Einstein surfaces with edge singularities, J. Geom. Phys. 86 (2014), 414-421.
  32. Generic properties of homogeneous Ricci solitons, Adv. Geom. 14, no. 2 (2014), 225-237.
  33. Seiberg-Witten equations on surfaces of logarithmic general type, Internat. J. Math. 24, no. 9 (2013), 1350074, 23 pages.
  34. Finite-volume complex-hyperbolic surfaces, their toroidal compactifications, and geometric applications, Pacific J. Math. 255, no. 2 (2012), 305-315.
  35. Finite-volume complex surfaces without cuspidal Einstein metrics, Ann. Global Anal. Geom. 41, no. 3 (2012), 371-380.
  36. Seiberg-Witten equations on certain manifolds with cusps, New York J. Math. 17 (2011), 491-512.
  37. A gap property for the growth of closed 3-manifold groups, Geom. Dedicata 143 (2009), 193-199.
  38. Yamabe solitons, determinant of the Laplacian and the uniformization theorem for Riemann surfaces (with M. Disconzi), Lett. Math. Phys. 83 (2008), 13-18.
  39. Eigenvalues of the Laplacian under the Ricci flow, Rend. Mat. Appl. (7) 27, no. 2 (2007), 183-195.
  40. On isochronous Shabat-Yamilov-Toda lattices: equilibrium configurations, behavior in their neighborhood, Diophantine relations and conjectures (with F. Calogero and R. Droghei), Phys. Lett. A 355 (2006), 262-270.
  41. On isochronous Bruschi-Ragnisco-Ruijsenaars-Toda lattices: equilibrium configurations, behavior in their neighborhood, Diophantine relations and conjectures (with F. Calogero and R. Droghei),  J. Phys. A: Math. Gen. 39 (2006), 313-325.

PhD Thesis, Stony Brook University, May 2011: Aspects of the Seiberg-Witten Equations on Manifolds with Cusps. Adviser: Prof. Claude LeBrun

Research supported in part by the National Science Foundation, by a Simons Postdoctoral Fellowship, by a Renaissance Technologies Fellowship, and by a Marie Curie Fellowship.