Dr. Matteo Costantini

Email	costanti(at)math.uni-bonn.de
Office	2.003
Address	Endenicher Allee 60, 53115 Bonn, Germany

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Lehre im Sommersemester 2020:

Hauptseminar Geometrie (S2D1), Graduate Seminar on Differential Geometry (S4D1)
(organized with Prof. Hamenstädt)

Graduate Seminar on Global analysis (S4B3)
(organized with Prof. Lesch and Dr. van den Dungen )

Sprechstunde: Nach Vereinbarung

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Lehre im Wintersemester 2019/20:

Advanced Topics in Geometry

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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]) 

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My thesis, Lyapunov exponents on character varieties and Teichmüller curves, was defended on September 12, 2018, and was supervised by Prof. Dr. Martin Möller.

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In my master thesis I studied algebraic cycles on K3 surfaces. I focused on understanding some recent articles related to conjectures about 0-cycles on this surfaces. I took my master degree in Milan (Italy) with Prof. Van Geemen as my advisor.