Scott Mullane

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

Events:

Organiser of this two-week MATRIX Workshop: Teichmüller Theory and Flat Structures (17 - 28 Mar 2025).

Organiser of: Points Counts of Moduli Stacks via Motives and Cohomology (Moduli retreat: 1-4 December 2025, Surf Coast, VIC)

Previously:

Humboldt-Universität zu Berlin - Guest Professor 2021-2023

Goethe-Universität Frankfurt - Humboldt Fellow 2018-2021

University of Georgia, Athens (UGA) - 2017-2018

Harvard University - 2016-2017

Boston College - Advisor: Dawei Chen, PhD 2016

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), Journal of the Institute of Mathematics of Jussieu 24 (4) (2025), 1521-1546 (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, Journal of Algebraic Geometry (to appear) (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:

Semester 2, 2024: Geometry (The University of Melbourne)

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)