Dr. Matteo Costantini

Teaching Sommersemester 2024

Special topics in Complex Geometry: Moduli of curves

Research Interests

I am interested in the geometry of affine invariant submanifolds of strata of abelian differentials and the moduli space of Riemann surfaces. I am also interested in the study of representations of fundamental groups of Riemann surfaces and the corresponding flat vector bundles.

Publications and Preprints

• Milnor-Wood inequality for klt varieties of general type and uniformization (with Daniel Greb)  
        (Bull. Lond. Math. Soc. 56 (2024), no. 7, 2552–2567, https://doi.org/10.1112/blms.13071) (arXiv:2303.17929[math.AG] )

• Chern classes of linear submanifolds with application to spaces of k-differentials and ball quotients  (with Martin Möller and Johannes Schwab)  
        (arXiv:2303.17929[math.AG] )

• Gap between Lyapunov exponents for Hitchin representations (with Florestan Martin-Baillon)  
        (Int. Math. Res. Not. IMRN(2024), no. 15, 11271–11291) ( arXiv:2211.03651[math.DS] )

• On the Kodaira dimension of moduli spaces of Abelian differentials (with Dawei Chen and Martin Möller)  
        (Camb. J. Math. 12 (2024), no. 3, 623–752.) (arXiv:2112.04238[math.AG] ) (GP/Pari files for the computer assisted proofs: minimalstratumsmallgenera, minimalstratumhighgenera)

• Integrals of ψ-classes on twisted double ramification cycles and spaces of differentials (with Adrien Sauvaget and Johannes Schmitt)  
        (Accepted in Trans. Amer. Math. Soc, arXiv:2112.04238[math.AG] )

• The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials (with Martin Möller and Jonathan Zachhuber)  
        (Forum of Mathematics, Pi , Volume 10 , 2022 , e16, DOI: https://doi.org/10.1017/fmp.2022.10) (arXiv:2006.12803 [math.AG] )

• diffstrata – a Sage package for calculations in the tautological ring of the moduli space of abelian differentials (with Martin Möller and Jonathan Zachhuber)  
       (Exp. Math. 32 (2023), no. 3, 545–565,DOI: 10.1080/10586458.2021.1980750)  (longer version: arXiv:2006.12815 [math.AG] )

• The area is a good enough metric (with Martin Möller and Jonathan Zachhuber)  
  (Ann. Inst. Fourier (Grenoble) 74 (2024), no. 3, 1017–1059)  (arXiv:1910.14151 [math.AG] )

• Lyapunov exponents, holomorphic flat bundles and de Rham moduli space 
  ( Israel J. Math. 240 (2020), no. 1, 345–415)  (arXiv:1810.12623 [math.GT] )

• The equation of the Kenyon-Smillie (2,3,4)-Teichmueller curve (with André Kappes) 
  (Journal of Modern Dynamics, Volume 11, 2017, 17-41) (arXiv:1601.02783v2 [math.GT])