Research

My research is in algebraic geometry, with a particular focus on the interplay between birational and non-archimedean geometry. I work on problems concerning

degenerations of hyerkahler varieties and dual complexes
irreducible holomorphic symplectic varieties
non-archimedean approach to mirror symmetry and the SYZ conjecture
Berkovich spaces and non-archimedean retractions
real and non-archimedean Monge-Ampère equations
Fano manifolds and Fano convex polytopes

Publications and preprints

Regularity of the solution to a real Monge-Ampère equation on the boundary of a simplex

(with Rolf Andreasson, Jakob Hultgren, Mattias Jonsson, and Nicholas McCleerey)

preprint (2024)

Terminalizations of quotients of compact hyperkähler manifolds by induced symplectic automorphisms

(with Valeria Bertini, Annalisa Grossi, and Mirko Mauri),

preprint (2024)

Essential skeletons of pairs and Temkin's metric

(with Mirko Mauri and Matt Stevenson),

accepted for publication in Annali dell'Università di Ferrara (2024)

Tropical and non-Archimedean Monge-Ampère equations for a class of Calabi-Yau hypersurfaces

(with Jakob Hultgren, Mattias Jonsson, and Nicholas McCleerey),

Advances in Mathematics (2024)

The minimal projective bundle dimension and toric 2-Fano manifolds

(with Carolina Araujo, Roya Beheshti, Ana-Maria Castravet, Kelly Jabbusch, Svetlana Makarova, Nivedita Viswanathan, and an appendix by Will Reynolds),

preprint (2023)

Higher Fano manifolds

(with Carolina Araujo, Ana-Maria Castravet, Kelly Jabbusch, Svetlana Makarova, Libby Taylor, and Nivedita Viswanathan),

Proceedings of the Mathematical Congress of the Americas, Revista de la Unión Matemática Argentina (2021)

On the geometric P=W conjecture

(with Mirko Mauri and Matt Stevenson),

Selecta Mathematica (2022)

Toric geometry and integral affine structures in non-archimedean mirror symmetry

(with Léonard Pille-Schneider),

preprint (2021)

Log-Regular Models for Products of Degenerations

(with Morgan Brown),

Arc schemes and singularities, World Scientific (2020)

The essential skeleton of a product of degenerations

(with Morgan Brown),

Compositio Mathematica (2019)

Video

Geometry and Tacos, Dual complexes in birational and non-archimedean geometry

ATOM Lectures Series, Introduction to Berkovich geometry, lecture 1 and lecture 2

Berkovich approach to hyper-Kähler degenerations and character varieties, HSE, Moscow, 2019

Posters

Essential skeletons of pairs and the geometric P=W conjecture

Fourth Meeting for Young Women in Mathematics, Freiburg, Germany, 2019
BrAG 4th meeting, Liverpool, UK, 2019
Connections for Women: Derived Algebraic Geometry, Birational Geometry and Moduli Spaces, MSRI, 2019

The SYZ fibration hides an essential skeleton in the closet

Imperial FoNS Research Showcase, London, UK, 2018

Berkovich geometry approach to degenerations of hyper-Kähler varieties

Berkovich 30 years, Paris, July 2018

Berkovich spaces and essential skeleta

BrAG 3rd meeting, Cambridge, UK, 2017
GAeL (Géométrie Algébrique en Liberté), Bath, 2017