# About me

I am a PhD student at KU Leuven under the supervision of Prof. Fatemeh Mohammadi.

My research is funded by FWO fundamental research fellowship.

Email: francesca.zaffalon *at* kuleuven.be

Address: Celestijnenlaan 200B - box 2400, 3001 Leuven (Belgium)

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

My CV is available here.

## Education

PhD student, Department of Mathematics (Algebra) at 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

Combinatorics of Essential Sets for Positroids with Fatemeh Mohammadi, [arXiv], Algorithm - to appear in Journal of Algebra (2024)

Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes with Oliver Clarke, Fatemeh Mohammadi, [arXiv] - Journal of Algebra (2024)

Restricted Chain-Order Polytopes via Combinatorial Mutations with Oliver Clarke, Akihiro Higashitani, [arXiv] - submitted.

Progress on Infinite Cluster Categories Related to Triangulations of the (Punctured) Disk with Fatemeh Mohammadi, Job Daisie Rock, [arXiv] - submitted.

Computing positroid cells in the Grassmannian of lines, their boundaries and their intersections with Fatemeh Mohammadi, [arXiv] - submitted.

Master's thesis: Mutations of simplices and Deformations of fake weighted projective spaces in the setting of Fano search program. Supervised by Elisa Postinghel. Thesis and Slides

## Conference Talks

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. Slides

Computing positroid cells in the Grassmannian of lines, their boundaries and intersections - Tropical and Convex Geometry and Feynman integrals - 5 Sep. 2022. Slides

Computing positroid cells in the Grassmannian of lines, their boundaries and intersections - Algorithmic and Enumerative Combinatorics - 5 July 2022. Poster

## Seminar Talks

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. Notes

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

## Ongoing and Upcoming Activities

Tropical Geometry: Moduli spaces and matroids - Frankfurt 🇩🇪 (Speaker) - October 2024

## Past Activities

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