Seminar Geometrie / Graduate Lectures

Vincenzo Galgano (MPI-CBG Dresden)
Secant varieties to some generalised Grassmannians

Abstract: Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematical areas. Any generalised Grassmannian G/P is a set of rank-1 "tensors" in the corresponding (minimal) irreducible representation, like Grassmannians for skew-symmetric tensors. The geometry of secant varieties to G/P is in general not completely understood. In this talk we discuss the 2nd secant variety to a generalised Grassmannian, and we give results on the identifiability and singularity in the case of Grassmannians. Some results are from a joint work with Reynaldo Staffolani.

09.04.2024 (Di)
Z21/242
15:00

Asgar Jamneshan (Koc University, Istanbul)
The inverse Gowers $U^3$-theorem and Conze-Lesigne factors

The Gowers uniformity $k$-norm on a finite abelian group measures the averages of complex functions on such groups over $k$-dimensional arithmetic cubes. The inverse question about these norms asks whether a large norm implies correlation with a function of algebraic origin.

The analogue of the Gowers uniformity norms for measure-preserving abelian actions is the Host-Kra-Gowers seminorms, which are intimately connected to the Host-Kra-Ziegler factors of such systems. The corresponding inverse question, in the dynamical setting, asks for a description of such factors in terms of systems of algebraic origin.

In this talk, we present a satisfactory answer to inverse question in the case of the Gowers $U^3$-norm in the combinatorial setting by completely classifying Host-Kra-Ziegler factors of order $2$, also known as Conze-Lesigne factors, for all countable measure-preserving abelian actions.