About:

I'm a Guest Professor at the Institut für Mathematik, Humboldt-Universität zu Berlin. I'll soon be at the University of Melbourne with a DECRA grant from the ARC.

I'm interested in algebraic geometry and the geometry of moduli spaces.

Email: scott.mullane_at_hu-berlin.de

Recent teaching:

WiSo22/23: Algebraic surfaces (Notes), Tues 13-17 RUD 25, 3.007 (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 21/22: Flat Geometry (Goethe Universität Frankfurt)

Research:

  • Definable structures on flat bundles,

with Ben Bakker (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) (arXiv).

  • The Hurwitz space Picard rank conjecture for d>g-1,

(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 (arXiv) (to appear)

  • k-differentials on curves and rigid cycles in moduli space,

Documenta Mathematica (arXiv) (to appear)

  • 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).