• Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-Lueck Inequality χ ≥ |σ|
  (with M. Albanese and L. Lombardi), arXiv.2311.10226v2.    Submitted, 2023.
• The signature of geometrically decomposable aspherical 4-manifolds (with M. Golla), arXiv.2306.15501v1.  Submitted, 2023.
• Generalized Graph Manifolds, Residually Finiteness, and the Singer Conjecture (with M. Hull),   arXiv:2108.09236v2.  Submitted, 2022.
• Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence (with M. Stern), arXiv:1909.05634v2.  Submitted, 2022.
• On the Betti Numbers of Finite Volume Hyperbolic Manifolds (with M. Stern), arXiv:2009.11431v2. To appear in J. Differential Geom.
• Aspherical 4-Manifolds, Complex Structures, and Einstein Metrics (with M. Albanese). J. Geom. Analysis (2024). https://doi.org/10.1007/s12220-024-01623-8
  
• Singer Conjecture for Varieties with Semismall Albanese Map and Residually Finite Fundamental Group (with L. Lombardi). Proc. Roy. Soc. Edinburgh Sect. A. DOI: https://doi.org/10.1017/prm.2024.52
• On the Hopf  Problem and a Conjecture of Liu-Maxim-Wang (with R. Pardini), Expo. Math 42 (2024), no. 2, 125543
• Extended Graph 4-Manifolds, and Einstein Metrics, Ann. Math. Qu\’e. 48 (2024), no. 1, 269-276.
• L2-Betti Numbers and Convergence of Normalized Hodge Numbers via the Weak Generic Nakano Vanishing Theorem (with L. Lombardi). Online first on July 2023 in Ann. Inst. Fourier.
• On the impossibility of four-dimensional complex-hyperbolic Einstein Dehn filling (with M. Golla), Proc. Amer. Math. Soc. 151 (2023), no. 1, 281-294. 
• Price inequality and Betti numbers growth on manifolds without conjugate points (with M. Stern), Comm. Anal. Geom. 30 (2022), no. 2, 297-334
• Moving Seshadri Constants, and Coverings of Varieties of Maximal Albanese Dimension (with L. Lombardi), Asian J. Math. (25) (2021), no. 2, 305-320. 
• On the Boundary Injectivity Radius of Buser-Colbois-Dodziuk-Margulis Tubes, Ann. Global Anal. Geom. 59 (2021), 285-295.
• Graph Theoretical Representation of Equity Indices and Their Centrality Measures (with S. Taylor),  Quant. Finance 21, no. 4 (2021), 523-537.
• Punctured spheres in complex hyperbolic surfaces and bielliptic ball quotient compactifications (with M. Stover), Trans. Amer. Math. Soc. 372 (2019), no. 7, 4627-4646.
• 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.
• Exceptional collections and the bicanonical map of Keum’s fake projective planes (with G. Di Brino), Commun. Contemp. Math. 20, no. 1 (2018), 1650066.
• Classification and arithmeticity of toroidal compactifications with 3\overline{c}_{2}=\overline{c}^2_1=3 (with M. Stover), Geom. Topol. (22), no. 4 (2018), 2465-2510.
• The Toledo invariant, and Seshadri constants of fake projective planes, J. Math. Soc. Japan 69, no. 4 (2017), 1601-1610.
• On the canonical divisor of smooth toroidal compactifications (with G. Di Cerbo), Math. Res. Lett. 24, no. 4 (2017), 1005-1022.
• 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.
• Multiple realizations of varieties as ball quotient compactifications (with M. Stover), Michigan Math. J. 65, no. 2 (2016), 441-447.
• Effective results for complex hyperbolic manifolds (with G. Di Cerbo), J. Lond. Math. Soc. (2) 91 (2015), no. 1, 89-104.
• Positivity in Kähler-Einstein theory (with G. Di Cerbo), Math. Proc. Cambridge Philos. Soc. 159 (2015), no. 2, 321-338.
• A sharp cusp count for complex hyperbolic surfaces and related results (with G. Di Cerbo),  Arch. Math. (Basel). 103, no. 1 (2014), 75-85.
• On Kähler-Einstein surfaces with edge singularities, J. Geom. Phys. 86 (2014), 414-421.
• Generic properties of homogeneous Ricci solitons, Adv. Geom. 14, no. 2 (2014), 225-237.
• Seiberg-Witten equations on surfaces of logarithmic general type, Internat. J. Math. 24, no. 9 (2013), 1350074, 23 pages.
• Finite-volume complex-hyperbolic surfaces, their toroidal compactifications, and geometric applications, Pacific J. Math. 255, no. 2 (2012), 305-315.
• Finite-volume complex surfaces without cuspidal Einstein metrics, Ann. Global Anal. Geom. 41, no. 3 (2012), 371-380.
• Seiberg-Witten equations on certain manifolds with cusps, New York J. Math. 17 (2011), 491-512.
• A gap property for the growth of closed 3-manifold groups, Geom. Dedicata 143 (2009), 193-199.
• Yamabe solitons, determinant of the Laplacian and the uniformization theorem for Riemann surfaces (with M. Disconzi), Lett. Math. Phys. 83 (2008), 13-18.
• Eigenvalues of the Laplacian under the Ricci flow, Rend. Mat. Appl. (7) 27, no. 2 (2007), 183-195.
• 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.
• 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. 

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