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Keywords: Metric Algebraic Geometry, reach, tubes, Schubert varieties, Grassmannians, distance optimization, random tensors, typical ranks, rank-approximations, applied algebraic geometry.
Tools: differential geometry, differential topology, integral geometry, random geometry, real algebraic geometry, o-minimal structures.
Publications and preprints
Publications and preprints
"What is the probability that a random symmetric tensor is close to rank-one?" with A. Cazzaniga and A. Lerario
SIAM Journal of Applied Algebra and Geometry, Vol. 8, Issue 2 (2024), pp.227-258 (arXiv, published version)
"Typical ranks of random order-three tensors" with P. Breiding and S. Eggleston
International Mathematics Research Notices, Volume 2025, Issue 4 (2025) (arXiv, published version)
"The Grassmann Distance Complexity" with A. Lerario
Preprint on arXiv, submitted (arXiv)
Talks
Talks
Typical ranks of random order-three tensors
Minisymposium Tensors in applications, SIAM Conference on Applied Algebraic Geometry (AG25), University of Wisconsin, Madison (USA), July 2025
Typical ranks of random order-three tensors
Junior GMP Seminar, SISSA, Trieste (Italy), January 2025
The Grassmann Distance Complexity
Conference Metric Algebraic Geometry, KTH Stockholm (Sweden), November 2024
The Grassmann Distance Degree
Geometric Structures Seminar, SISSA, Trieste (Italy), March 2024
What is the probability that a random symmetric tensor is close to rank-one?
Algebra group seminar, University of Osnabrück (Germany), October 2023
What is the probability that a random symmetric tensor is close to rank-one?
Minisymposium Tensors in applications, SIAM Conference on Applied Algebraic Geometry (AG23), TU Eindhoven (The Netherlands), July 2023
What is the probability that a random symmetric tensor is close to rank-one?
Applied CATS Seminar, KTH Stockholm (Sweden), March 2023
Equilibrium measures and logarithmic potential theory
Geometric Structures Seminar, SISSA, Trieste (Italy), April 2022
The volume of a tubular neighborhood of the real Veronese variety
Minisymposium Random Algebraic Geometry, SIAM Conference on Applied Algebraic Geometry (AG21), Texas A&M University (USA) (online), August 2021
Posters
Posters
The Grassmann Distance Complexity
MEGA 2024, MPI Leipzig & Universität Leipzig (Germany)
What is the probability that a random symmetric tensor is close to rank-one?
Foundations of Computational Mathematics 2023, Sorbonne Universitè, Paris (France)
The volume of a tubular neighborhood of the real Veronese variety
Conference Real Algebraic Geometry, CIRM Marseille (France)
The volume of a tubular neighborhood of the real Veronese variety
Conference Mathematics of Complex Data, KTH Stockholm (Sweden)
Conferences and schools
Conferences and schools
Organized
Organized
SISSA Junior Math Days 2024, 2 - 4/12/2024, SISSA, Trieste (Italy)
SISSA/IGaP Junior Geometry and Mathematical Physics Seminar, SISSA & IGaP, Trieste (Italy), October 2023 - June 2024
SISSA Junior Math Days 2023, 4 - 6/12/2023, SISSA, Trieste (Italy)
SISSA Junior Math Days 2022, 5 - 7/12/2022, SISSA, Trieste (Italy)
Stochastic Geometry Workshop, 23 - 25/11/2022, University of Osnabrück (Germany)
Attended
Attended
SIAM Conference on Applied Algebraic Geometry (AG25), University of Wisconsin, Madison (USA), July 2025
SLMath Summer School: New perspectives on discriminants and their applications, MPI-MiS Leipzig (Germany), June 2025
TiME 2025, Invariant Theory from classic to modern developments, Lie-Størmer Center, Tromsø (Norway), May 2025
Nonlinear Algebra meets Quantum Chemistry, MPI-MiS Leipzig (Germany), February 2025
Numerical (Nonlinear) Algebra in the Real World, MPI-CBG Dresden (Germany), February 2025
Metric Algebraic Geometry, KTH Stockholm (Sweden), November 2024
MEGA 2024, MPI-MiS Leipzig & Universität Leipzig (Germany), July 2024
Hypatia Graduate Summer School 2024, Centre de Recerca Matemàtica (CRM), Barcelona (Spain), June 2024
Research School in Real Algebraic Geometry, SISSA & IGaP, Trieste (Italy), Oct. 2023
SIAM Conference on Applied Algebraic Geometry (AG23), TU Eindhoven (The Netherlands), July 2023
Foundations of Computational Mathematics 2023 (FoCM23), Sorbonne Universitè, Paris (France), June 2023
Oberwolfach Seminar: Metric Algebraic Geometry, MFO, Oberwolfach (Germany), May 2023
Stochastic Geometry Workshop, University of Osnabrück (Germany), November 2022
Conference on Real Algebraic Geometry, CIRM Marseille (France), October 2022
AGATES Semester: Introductory school on tensors, University of Warsaw & IMPAN (Poland), September 2022
Three days between Analysis and Geometry, Università di Trento (Italy), August 2022
Topics in real and tropical algebraic geometry, Sophus Lie Center, Nordfjordeid (Norway), June 2022
ALTOGELIS Workshop, KTH Stockholm (Sweden), June 2022
Mathematics of Complex Data, KTH Stockholm (Sweden), June 2022
SIAM Conference on Applied Algebraic Geometry (AG21), Texas A&M University (USA) (online event), August 2021
Ongoing and future projects
Ongoing and future projects
Grassmann proximity
Grassmann proximity
We define an algebraic distance on the Grassmannian and study the algebraic complexity of nearest point problems for this metric.
Collaborators: H. Friedman (UC Berkeley) and B. Sturmfels (MPI-MiS, Leipzig)
Counting real critical points of distance functions on manifolds via absolute total curvature
Counting real critical points of distance functions on manifolds via absolute total curvature
We aim to use absolute total curvature to count the real critical points of distance functions on manifolds, focusing on real solutions with applications to optimization.
Collaborator: V. Shahverdi (KTH, Stockholm)
Optimal Schubert Calculus
Optimal Schubert Calculus
We define a function measuring how close it is a linear subspace to satisfying the conditions of a given Schubert problem on the Grassmannian. We study the critical points of such a function, with the aim of obtaining some new invariants of the given problem.
Collaborator: A. Lerario (SISSA, Trieste)
In the banner: Trieste seen from SISSA, July 2024
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