Events for 01/20/2021 from all calendars

Student/Postdoc Working Geometry Seminar

Time: 10:00AM - 11:00AM

Location: zoom

Speaker: A. Casarotti, Ferrara

Title: Defectiveness and Identifiability: a geometric point of view on tensor analysis

Abstract: Identifiability problems arise naturally in many fields of mathematics, from the abstract world of birational geometry to the applied setup of tensor analysis. In this talk we link the identifiability property for a variety X to its secant behavior and the geometry of the tangential contact loci. In the first part, after reviewing the main properties of the tangential contact locus associated to h general points of X, we give a numerical bound under which the non h-secant defectiveness ensures the h-identifiability, with h subgeneric. Note that this result is of birational nature and so does not strictly depend on the geometry of the particular tensor variety we choose. Finally we apply our result to many classes of varieties which play a central role in tensor analysis. In the second part we move on the generic rank case, where a clever use of the infinitesimal Bertini's theorem and an implementation of Noether-Fano's inequalities enable us to link the generic identifiability with the infinitesimal tangential contact locus. This finally shows the non generic identifiability for many partially symmetric tensors satisfying a mild numerical bound on their dimensions and degrees

Groups and Dynamics Seminar

Time: 12:00PM - 1:00PM

Location: online

Speaker: Ivan Mitrofanov, Ecole Normale Superieure, Paris

Title: Ordering Ratio function and Travelling Salesman Breakpoint for groups and metric spaces

Abstract: We study ordering ratio function -- an asymptotic invariant that describes how well a given metric space can be ordered. We say that an order is "good" if it can be effectively (with sub-linear competitive ratio) used as an universal order for solving traveling salesman problem. We describe connections of ordering ratio function with more traditional invariants, such as hyperbolicity, Assouad-Nagata dimension, number of ends and doubling. In particular, we characterize virtually free groups as those for which ordering ratio function satisfies $OR(3)<3$. We show that all $\delta$-hyberbolic uniformly discrete spaces can be ordered extremely effectively, with bounded ordering ratio function. We prove that all spaces of finite $AN$-dimension admit a logarithmic bound for this function, and under an additional hypothesis prove the converse, providing sufficient conditions when $OR(k)$ is linear. This talk is based on joint work with Anna Erschler.