About:
I'm a DECRA Fellow at the University of Melbourne.
I'm interested in algebraic geometry and the geometry of moduli spaces.
Email: mullanes_at_unimelb.edu.au
Research:
Weil-Petersson volumes, stability conditions, and wall-crossing
with Lukas Anagnostou and Paul Norbury (arXiv)
Teichmüller curves in hyperelliptic components of meromorphic strata
with Martin Möller (and an appendix with Ben Bakker) (arXiv)
Definable structures on flat bundles,
with Ben Bakker, Bull. London Math. Soc. 55 (5) (2023), 2515-2524 (Journal, arXiv)
The Kodaira classification of the moduli of hyperelliptic curves,
with Ignacio Barros (arXiv)
On the Kodaira dimension of Hurwitz spaces,
with Gavril Farkas, Mathematische Zeitschrift (special volume dedicated to O. Debarre) 300 (4), 3417-3432 (2022) (Journal, arXiv).
The Hurwitz space Picard rank conjecture for d>g-1,
Advances in Mathematics 430 (2023) (Journal, arXiv).
Non-polyhedral effective cones from the moduli space of curves,
Transactions of the American Mathematical Society 374 (09), (2021) 6397-6415 (arXiv).
Strata of differentials of the second kind, positivity, and irreducibility of certain Hurwitz spaces,
Annales de l'Institut Fourier, Volume 72 (2022) no. 4, pp. 1379-1416 (arXiv).
k-differentials on curves and rigid cycles in moduli space,
Documenta Mathematica, 26 (2021) 1817–1850 (arXiv).
Two moduli spaces of Calabi-Yau type,
with Ignacio Barros, International Mathematics Research Notices 2021 (20), 15833-15849, (arXiv).
Cones of effective cycles in the moduli space of curves,
Oberwolfach Report 15 (2018), no. 3 (pdf)
On the effective cone of higher codimension cycles in the moduli space of marked genus g curves,
Mathematische Zeitschrift 295 (2020), no. 1, 265-288, (arXiv).
On the effective cone of the moduli space of marked genus g curves,
Advances in Mathematics 320 (2017), 500-519, (arXiv).
Effective divisors in the moduli space of marked genus g curves from abelian differentials,
Michigan Math. J. 67 (2018), 839–889, (Journal, pdf).
Divisorial strata of abelian differentials,
International Mathematics Research Notices 6 (2017), 1717-1748, (arXiv, Journal).
Recent teaching:
SoSe 22/23: Positivity in Algebraic Geometry (HU Berlin for the BMS)
WiSe 22/23: Algebraic surfaces (Notes) (HU Berlin for the BMS)
SoSe 21/22: Algebra/Zahlentheorie und ihre Didaktik (HU Berlin)
WiSe 21/22: Algebraic curves and Riemann surfaces (Notes), (HU Berlin for the BMS)
SoSe 20/21: Flat Surfaces (Goethe Universität Frankfurt)