Liana Heuberger

My current research is in birational geometry and toric geometry, specifically finding Fano varieties of dimension up to four which are either smooth or have mild singularities. A useful tool in achieving this is the combinatorics of polytopes, reflecting the geometry of (possibly singular) toric varieties they correspond to. My aim is to construct an explicit (partial) smoothing of these objects in order to obtain a Fano variety. I'm also interested in moduli spaces of quiver representations, quiver flag varieties and the McKay correspondence.

Here is a copy of my CV.

Here are photos from the Oberwolfach conference "K-stability, birational geometry and mirror symmetry" I co-organised in March 2024.

Here are photos from a conference I co-organised at the ICMS in Edinburgh in November 2018.

Member of the Department Equality and Diversity Committee of the Dept. of Mathematical Sciences at the University of Bath.

In 2023-2024 I have taught one half of the MsC course "Algebraic Curves" MA40188 at the University of Bath.

Where I'll be:

• [speaker] Mirror Symmetry for Cluster Varieties and Representation Theory (King's College London, 17-21 June 2024).

• [speaker] Fano and uniruled varieties (Będlewo, Poland, 8-12 July 2024).

• [speaker] Aggitate 2024: An LMS School on Moduli Theory in Algebraic Geometry (Uni. Essex, 22-26 July 2024).

• [participant] Algebraic Geometry in Cetraro (Cetraro, Italy, 9-13 September 2024).

• [speaker] Birational Geometry and Number Theory (Edinburgh, UK, 28 Oct-1 Nov 2024).

• [participant/speaker] Toric geometry workshop (Oberwolfach, 7-11 April 2025).

• [co-organiser] Algebra and Geometry from Africa (ICMS Edinburgh, 5-16 May 2025).

• [speaker] Structures and Symmetries in Algebraic Geometry (Krakow, 9-13 June 2025).

Recent past events

Scientific seminars: KCL, Marseille, Bordeaux.

PiWorks Seminar (Piscopia Initiative – Women and Other Researchers Keynote Series), February 2024.

Workshops and conference talks: 

• The McKay correspondence, tilting theory and related topics (Tokyo, December 2023).

• Modern perspectives on birational geometry (Taipei, August 2023).

• Toric degenerations (BIRS, Canada, December 2022).

• Rencontre Géométrie algébrique et complexe (CIRM Luminy December 2022).

• Edge Days (Edinburgh, November 2022).

Articles and preprints

Currently being refereed:

• "Quiver semi-invariants and SAGBI bases" (with Elana Kalashnikov).

• "On K-moduli of Fano threefolds with degree 28 and Picard rank 4" (with Andrea Petracci).

• "Mirror symmetry, Laurent inversion and the classification of Q-Fano threefolds" (with Tom Coates and Alexander M. Kasprzyk). 

• "Anticanonical divisors on Fano fourfolds".

Published and soon to appear:

• "Computation and data in the classification of Fano varieties" (with Gavin Brown, Tom Coates, Alessio Corti, Tom Ducat, and Al Kasprzyk), "Nankai Symposium on Mathematical Dialogues", Springer (to appear in June 2024).

• "A primer on toric varieties". Lecture notes for summer school courses that I have taught in Auckland, online and in Angers. In "New Zealand volume", European Journal of Mathematics 8, 733–737 (2022). 

• "Q-Fano threefolds and Laurent inversion", where I construct 100 deformation families of orbifold terminal Fano threefolds using a method introduced here and here. To appear in the Nagoya Mathematical Journal. 

• "Combinatorial Reid's Recipe for consistent dimer models" (with Alastair Craw and Jesùs Tapia Amador). In Épijournal de Géométrie Algébrique, Volume 5 (February 26, 2021) epiga:7224.

• "Mirror symmetry and the classification of orbifold del Pezzo surfaces" (with Akhtar, Coates, Corti, Kasprzyk, Oneto, Petracci, Prince and Tveiten). In Proceedings of the American Mathematical Society, 144 (2016), 513-527.

• "Del Pezzo surfaces with 1/3(1,1) points" (with Alessio Corti). In manuscripta math. 153, 71–118 (2017).