Hello!

I am a postdoctoral researcher at the University of Vienna, working with Balázs Szendrői.

Between October 2024 and September 2026 I was a postdoc at the Max-Planck Institute for Mathematics in the Sciences in Leipzig, working with Bernd Sturmfels and Ran Tessler.

Email: francesca.zaffalon *at* univie.ac.at

I am interested in combinatorial algebraic geometry. Some things I like to think about are matroids, positroids and their applications to the study of the amplituhedron and positive geometries.

My CV is available here.

Education

PhD in Mathematics, KU Leuven, Belgium, Supervisor - Prof. Fatemeh Mohammadi.
Master Degree in Mathematics (Advanced Algebra and Geometry curriculum), University of Trento, Italy - 110/110 cum laude.
Bachelor Degree in Mathematics, University of Trento, Italy - 110/110 cum laude.

Research

The Self-Projecting Grassmannian

with Alheydis Geiger, [arXiv]

Connection Matrices in Macaulay2

with Paul Görlach , Joris Koefler, Anna-Laura Sattelberger, Mahrud Sayrafi, Hendrik Schroeder, Nicolas Weiss, [arXiv] - to appear in Journal of Software for Algebra and Geometry (2026)

How to stab a polytope

with Sebastian Seemann, [arXiv] - Le Matematiche, special issue on "Positive Geometries" (2025)

Combinatorics of Essential Sets for Positroids

with Fatemeh Mohammadi, [arXiv], Algorithm - Journal of Algebra (2024)

Restricted Chain-Order Polytopes via Combinatorial Mutations

with Oliver Clarke, Akihiro Higashitani, [arXiv] - European Journal of Combinatorics (2026)

Progress on Infinite Cluster Categories Related to Triangulations of the (Punctured) Disk

with Fatemeh Mohammadi, Job Daisie Rock, [arXiv] - Journal of Algebra and its Applications, special issue on "Cluster Algebras and Related Topics" (2025)

Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes

with Oliver Clarke, Fatemeh Mohammadi, [arXiv] - Journal of Algebra (2024)

Conference Talks

Generalizing self-duality in the Grassmannian - Algebraic and Geometric Aspects of the Theory of Hyperplane Arrangements - 3 June 2026
How to stab a polytope - Amplitudes and Algebraic Geometry - 25 Feb. 2026 - talk
Restricted Chain-Order Polytopes via Combinatorial Mutations - Recent Developments on Lattice Polytopes in Leipzig - 23 Jan. 2026
Combinatorics of the Amplituhedron - Chow Lectures by Nima Arkani-Hamed - 6 Oct. 2025 - talk
Essential Sets of Positroids - Tropical Geometry: Moduli spaces and matroids - 10 Oct. 2024
What is a positroid cell? - Combinatorial Algebraic Geometry from Physics - 15 May 2024
Computing Positroid Cells, Their Boundaries and Dimension - SIAM AG23 (Nonlinear Algebra in Particle Physics mini-symposium) - 12 July 2023
Toric degenerations of partial flag varieties and combinatorial mutations - Toric Degenerations - 6 Dec. 2022
Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes - Toric Degenerations and Mirror Symmetry in Kumamoto - 14 Oct. 2022
Toric degenerations of flag varieties and combinatorial mutations - Algebraic Geometry with Applications to TEnsors and Secants - 23 Sep. 2022.
Computing positroid cells in the Grassmannian of lines, their boundaries and intersections - Tropical and Convex Geometry and Feynman integrals - 5 Sep. 2022.

Seminar Talks

Generalizing self-duality in the Grassmannian - KTH Combinatorics Seminar - 29 Apr. 2026
The self-projecting Grassmannian - Nonlinear Algebra Seminar - 10 Feb. 2026
Self-duality in the Grassmannian - Seminar Algebra & Geometry, University of Vienna - 6 Nov. 2025
How to stab a polytope - Discrete Mathematics/Geometry seminar at TU Berlin - 12 Mar. 2025
How to stab a polytope - Positive Geometry Seminar - 12 Nov. 2024
Combinatorics of Positroids and the Amplituhedron - Matroids and Applications Weekly Reading Seminar - 18 Apr. 2024
Combinatorics of Essential Sets for Positroids - Seminar on Nonlinear Algebra - 22 Feb. 2024
Combinatorics of positroids - Workshop on Matroids and Applications - 21 Nov. 2023
What is... a positroid? - PhD Colloquia - 16 Oct. 2023
Toric degenerations of partial flag varieties via matching fields and combinatorial mutations - Online Algebraic Geometry Seminar - 23 Mar. 2023
Polyhedral Homotopy - Solving Polynomial Systems Reading Seminar - 16 Mar. 2023
Algebraic Geometry for Spaces of Tensors - Reading Seminar on Tensors - 21 Feb. 2023
Computing positroid cells of rank two - Weekly Algebra and Geometry Seminars - 15 Apr. 2022
Hilbert's 17th Problem and Artin's Solution - Real Algebraic Geometry Reading Seminars - 31 Mar. 2022.
Matroids, Matroid Polytopes and Bergman Fan - Combinatorial Hodge Theory Reading Seminars - 7 Mar. 2022

Teaching

Master Thesis supervision: Cas Proost, title "Toric Degenerations and Newton-Okounkov bodies", 2023/2024

co-supervised with Fatemeh Mohammadi @ KU Leuven

Teaching Assistant: Wiskunde I, Fall 2023

Bachelor of Biology and Bachelor of Geology @ KU Leuven, Prof. Marco Zambon

Teaching Assistant: Foundations of Combinatorial Algebraic Geometry, Spring 2023

Master of Mathematics @ KU Leuven, Prof. Fatemeh Mohammadi

Tutor: Geometry and Linear Algebra, Fall 2020

Bachelor's Degree in Computer, Communication and Electronic Engineering @ University of Trento, Prof. Alessandro Perotti and Prof. Elisa Postinghel

Tutor: Geometry and Linear Algebra, Fall 2019

Bachelor's Degree in Industrial Engineering @ University of Trento, Prof. Alessandro Perotti

Activities

Algebraic Combinatorics in Pisa - Pisa 🇮🇹 - June 2026
Algebraic and Geometric Aspects of the Theory of Hyperplane Arrangements - Kraków 🇵🇱 (Speaker) - June 2026
Amplitudes and Algebraic Geometry - Vienna 🇦🇹 (Speaker) - February 2026
Recent Developments on Lattice Polytopes in Leipzig - Leipzig 🇩🇪 (Speaker) - January 2026
Chow Lectures 2025 by Nima Arkani-Hamed - Leipzig 🇩🇪 (Preparatory lecture speaker) - October 2025
The Amplituhedron: Structure, Combinatorics and Positive Geometry - Les Diablerets 🇨🇭- July 2025
The 11th Conference of the Fachgruppe Computeralgebra - Leipzig 🇩🇪 - June 2025
Combinatorial Synergies East - Leipzig 🇩🇪 - March 2025
Macaulay2 in the Sciences - Leipzig 🇩🇪 - November 2024
Tropical Geometry: Moduli spaces and matroids - Frankfurt 🇩🇪 (Speaker) - October 2024
MEGA 2024 - Leipzig 🇩🇪 - July 2024
Research visit to the Nonlinear Algebra group at MPI for Mathematics in the Sciences - Leipzig 🇩🇪 (with FWO travel grant) - January to May 2024
Combinatorial Algebraic Geometry from Physics - Leipzig 🇩🇪 - May 2024
Combinatorial Coworkspace - Kleinwalsertal 🇦🇹 - March 2024
Positive Geometry in Particle Physics and Cosmology - Leipzig 🇩🇪 - February 2024
Amplitudes 2023 Summer School - CERN 🇨🇭- August 2023
SIAM AG23 - Eindhoven 🇳🇱 (with SIAM travel fellowship, Invited speaker) - July 2023
Tensors: Geometry and Applications - Reading seminar - Leuven 🇧🇪 - Spring 2023
Solving Polynomial Systems Reading Seminar - Leuven 🇧🇪 - Spring 2023
K-stability of Fano varieties and birational invariants - Trento 🇮🇹 - January 2023
Matroids and Tropical Combinatorics - London 🇬🇧 - January 2023
Toric Degenerations - Banff 🇨🇦 - December 2022
Research visit to Professor Akihiro Higashitani - Osaka 🇯🇵 - October 2022
Toric Degenerations and Mirror Symmetry in Kumamoto - Kumamoto 🇯🇵 (Invited speaker) - October 2022
Algebraic Geometry with Applications to TEnsors and Secants - Warsaw 🇵🇱 (Speaker) - September 2022
Tropical and Convex Geometry and Feynman integrals - Zurich 🇨🇭 (Invited speaker) - September 2022
Algorithmic and Enumerative Combinatorics Conference - Vienna 🇦🇹 - July 2022
Topics in Real and Tropical Algebraic Geometry - Nordfjordeid 🇳🇴 - June 2022
International School on Tropical Geometry - Valladolid 🇪🇸 - May 2022
Weekly Algebra and Geometry Seminars - Ghent 🇧🇪 - Spring 2022
Real Algebraic Geometry Reading Seminars - 💻 - Spring 2022
Combinatorial Hodge Theory Reading Seminars - Ghent 🇧🇪 - Spring 2022
Masterclass: Tensor decompositions and their applications - 💻 - November 2021
Combinatorics, Physics and Probability Seminar - 💻 - Fall 2021 and Spring 2022
Newton-Okounkov bodies and Fanosearch - Levico Terme 🇮🇹 - October 2021
What is... Seminar - Trento 🇮🇹 - 2020/2021

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