The semester has ended. Thanks to everybody for participation!

How to Acknowledge the Semester

In publications an acknowledgement "This work is partially supported by  the Thematic Research Programme "Tensors: geometry, complexity and quantum entanglement", University of Warsaw, Excellence Initiative – Research University and the Simons Foundation Award No. 663281 granted to the Institute of Mathematics of the Polish Academy of Sciences for the years 2021-2023.” would be appreciated. In addition, please mention the name of the semester (Algebraic Geometry with Applications to Tensors and Secants) or its acronym (AGATES) in your publication.

Participants are also kindly asked to add a "Report number" to all publications posted on, which are related to participation in the Simons Semester AGATES, Sep 12-Dec 16, 2022. The code to add is:


One can add this code:
1) upon a submission of the paper,
2) upon submitting a revision,
3) without changing the paper.

For 1), and 2), one just adds the report number as a part of Metadata. For 3), in personal arxiv account, click "journal-ref" and add the code in the field "Report number".


We are pleased to announce a semester focused on tensors in geometry. The program is a part of series of

with supplementary funding from IMPAN, and NCN. All events are scheduled to be in-person and in Warsaw at IMPAN and MIM UW.

The organizers of the semester are Jarosław Buczyński, Weronika Buczyńska, Francesco Galuppi, Joachim Jelisiejew.

Previous Simons Semesters in Warsaw connected to algebraic geometry were minipages (2016)  and VAT (2018).

Participation of postdocs and PhD students is especially encouraged. 

Focus points

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

Main events

Week I, 12 Sep-16 Sep Introductory school
Week II, 19 Sep-23 Sep Kickoff workshop
Week III, 26 Sep-30 Sep
Week IV, 4 Oct-7 Oct Tensors from the physics viewpoint (starts on Tue), click here for Monday Oct 3rd
Week V, 10 Oct-14 Oct
Week VI, 17 Oct-21 Oct
Week VII, 24 Oct-28 Oct Geometry of secants workshop
Week VIII, 2 Nov-4 Nov
Week IX, 7 Nov-10 Nov
Week X, 14 Nov-18 Nov Algebraic geometry and complexity theory workshop
Week XI, 21 Nov-25 Nov Tensors in statistics, optimization and machine learning
Week XII, 28 Nov-2 Dec
Week XIII, 5 Dec-9 Dec Deformation theory workshop
Week XIV, 12 Dec-16 Dec

In addition to the events listed above, weekly activities will be held at the Banach Center in Warsaw. These will include research seminars, lectures, lecture series given and discussion groups. The current schedule is being updated weekly under the Schedule menu. In order to receive e-mail updates about seminars and activities (including the non-workshop activities of Weeks III, V, VI, VIII, IX, XII, XIV), please sign up to the mailing list agates which is at by one of the following options:

  1. If you want to sign up with a google e-mail address, then click the list link above and request a permission to join the group.
  2. If you want to sign up with a non-google e-mail address, then email one of the organisers and request adding your email manually.