Algebraic Geometry with Applications to TEnsors and Secants: 12 Sep – 16 Dec 2022

Annoucement

We are pleased to announce a semester focused on tensors in geometry. The program is a part of series of research oriented Simons Semesters at the Banach Center in Warsaw (Poland), 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. To contact the organizers, please write to fgaluppi who is at impan.pl.

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

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.

Registration

Schedule and 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 Tue)
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 below, weekly activities will be held at the Banach Center in Warsaw and at the University of Warsaw. These will include research seminars, lectures, and lecture series given by the leaders of our program. Participation of postdocs and PhD students will be especially encouraged. 

Participants