Fulvio Gesmundo

AGATES Semester - Fall 2022

AGATES is a thematic semester on Algebraic Geometry with Applications to TEnsors and Secants. The semester runs from September 12 to December 16, 2022 and focuses on a number of aspects of the geometry of tensors:

• Classical theory of tensors: identifiability, ranks and border ranks, secant varieties and their equations, apolarity and border apolarity.
• Applications in complexity theory: laser method, complexity of matrix multiplication, minimal border rank tensors, asymptotic invariants of tensors.
• Moduli spaces behind tensors: varieties of sums of powers, Hilbert schemes of points, varieties of commuting matrices.
• Applications in mathematical physics: quantum entanglement, geometric invariant theory and its applications, tensor networks.

Students and young researchers are particularly invited to attend. I help organizing the following events within the AGATES semester:

Summer School on the Geometry of Tensors

The Summer school is the first part of a 2-week kickoff event of the AGATES thematic semester. The purpose of the school is to provide PhD students and young researchers with an introduction to different perspectives on tensors in geometry, complexity theory and physics, as well as allow for interactions among experts and non-experts with different backgrounds. There will be four minicourses:

• Tensor Rank and Quantum Physics by Angelo Lucia
• Tensor Decomposition and theoretical computer science by Vladimir Lysikov
• Tensor Decomposition in Applied Geometry by Emanuele Ventura
• Tensor and secant varieties in Classical Algebraic Geometry by Alessandro Oneto

Kickhoff Workshop on Open Problems in the Geometry of Tensors

The Workshop is the second part of a 2-week kickoff event of the AGATES thematic semester. A wide range of research areas linked to tensor will be presented. The goal is to present problems, techniques and possible developments, that the participants can further pursue during the semester. Collaborations and discussions between participants will be encouraged. Further, the participants are invited to submit contributed talks, with a focus on open problems in their area of study.

Workshop on Algebraic Geometry and Complexity Theory

The main subject of this Workshop is complexity theory from algebraic and geometric point of view. It will focus on topics such as the complexity of matrix multiplication, geometric complexity theory, algebraic complexity classes, hardness of problems in algebraic combinatorics.