Dr. Matteo Costantini

Research Interests

I am interested in the geometry of affine invariant submanifolds of strata of abelian differentials. I am also interested in the study of representations of fundamental groups of Riemann surfaces and the corresponding flat vector bundles. In particular I like how algebraic geometry allows to study dynamical system invariants on the moduli space of flat vector bundles.  

Publications and Preprints

• The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials (with Martin Möller and Jonathan Zachhuber)  
        (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)  
        (arXiv:2006.12815 [math.AG] )

• The area is a good enough metric (with Martin Möller and Jonathan Zachhuber)  
        (arXiv:1910.14151 [math.AG] )

• Lyapunov exponents, holomorphic flat bundles and de Rham moduli space 
  (accepted in Israel Journal of Mathematics)  
        (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])