All activities this week are at IMPAN.
Monday 26.09, 11:00 - 12:00, room 403 - Tim Seynnaeve, Universal equations for Lagrangian and isotropic Grassmannians.
Monday 26.09, 13:30 - 14:30, room 403 - Hirotachi Abo, Compatibility of eigenconfigurations.
Tuesday 27.09, 11:00 - 12:00, room 403 - Discussion group.
Thursday 29.09, 11:00 - 12:00, room 321 - Fulvio Gesmundo, An introduction to Strassen's spectral theory, part I.
Thursday 29.09, 14:30 - 15:30, room 321 - Fulvio Gesmundo, An introduction to Strassen's spectral theory, part II.
Friday 30.09, from 14:30, room 403 - Informal summary of discussions this week.
Abstracts:
Tim Seynnaeve, Universal equations for Lagrangian and isotropic Grassmannians:
Monday 26.09
It is known that any ordinary Grassmannian Gr(k,n) in its Plücker embedding is set-theoretically (but not scheme-theoretically) cut out by pulling back the unique defining equation of Gr(2,4) along natural projection and contraction maps. We prove an analogous result for Lagrangian and isotropic Grassmannians. This talk is based on joint work with Nafie Tairi.
Hirotachi Abo, Compatibility of eigenconfigurations
Monday 26.09
The left eigenvectors and right eigenvectors of a square matrix are distinct, but they are compatible. The purpose of this talk is two-fold; the first is to extend the concepts of left eigenvectors and right eigenvectors of a matrix to tensors, and the second is to explore the compatibility of such concepts for a ternary tensor.
Fulvio Gesmundo, An introduction to Strassen's spectral theory, parts I and II:
Thursday 29.09:
In 1988, V. Strassen introduced the asymptotic spectrum of tensors. This is a space of functions from the space of tensors of order k to the semiring of positive real numbers capturing the behaviour of tensors under successive Kronecker powers. Importantly, the asymptotic spectrum captures the asymptotic rank of a tensor, relevant in complexity theory, and the asymptotic subrank, relevant in quantum many-body physics. More generally, one can use the asymptotic spectrum to determine obstructions to degenerations of tensors. I will give an introduction to this theory, highlighting the role of representation and invariant theory. In particular, I will present the recent work by Christandl, Vrana, Zuiddam, determining ''universal spectral points''. If time permits, I will discuss possible generalizations of the theory to other settings, different notions of asymptotics and possible methods to determine spectral points.