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