Друзья!

Сегодня у нас пройдет семинар в зуме в 17 00. На нем выступит Каддаж Филипп.

Laplacians, Simplices and Electrical Networks

We explore the interplay between graph Laplacians, Euclidean simplices, and electrical metrics through the lens of Fiedler’s Gramm matrix–simplex correspondence. This yields a geometric perspective on elementary graph operations (edge removal, contraction, bridges, leaves) as deformations or projections of the associated simplex. This functoriality gives immediate eigenvalue stability results for graph Laplacians in terms of Steiner ellipsoid inclusions.
Next, we reinterpret the principal minors of the Dirichlet–to–Neumann response matrix as oriented volumes or inner products of wedge-normals in the simplex. This method allows us to also prove stability result for the minors of the persistent Laplacian which was previously unknown. Restating this in terms of Kenyon–Curtis–Ingerman–Morrow grove-count formulas this solves a non-trivial combinatorial problem. Finally, we apply these ideas to characterize
electrical resistance metrics and restate the M-Matrix inverse problem the language of electrical metrics and hyperacute simplices.


Ждем вас в 17 00
ссылка на зум

Meeting ID: 885 3663 5237
Passcode: 003817


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