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SISSA Women in Mathematics 2021

Chiara Rigoni & Ada Boralevi
Schedule: 
Wednesday, May 12, 2021 - 09:30
Location: 
Zoom Meeting
Abstract: 

Chiara Rigoni:

"Metric measure spaces with a lower bound on the Ricci curvature"

Metric measure spaces play an important role in many fields of mathematics. In particular, they provide a natural generalization of manifolds admitting all kinds of singularities and still providing rich geometric structures. This talk presents a way to introduce a generalized notion of lower Ricci curvature bounds in this class of spaces, following an approach proposed by Lott-Villani and Sturm and based on optimal transport. We will also explore some of the analytic and geometric properties that this condition implies on the metric measure structure.

Ada Boralevi:

"Spaces of matrices with rank conditions"

The interest for spaces of matrices of constant and bounded rank, founded on the classical work by Kronecker and Weierstrass, bears to different contexts: linear algebra, theory of degeneracy of vector bundles, study of varieties with degenerate dual, to cite only a few. When analyzing these matrices, algebraicgeometry appears as a natural tool. The talk is meant as a gentle introduction to this theory, its main results and open questions.

 

There will be a small break between the two talks.

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