5 citations · 7 across the 7 of their papers we have counts for
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Nonnegative conorms, regular matroids, and the tropical Schottky problem
Yelena Mandelshtam
We prove that a positive-definite quadratic form has nonnegative conorms if and only if it is matroidal, resolving a conjecture of Dutour Sikirić and Kummer. We show that the posit…
Tropical KP Theory on Banana Curves
Simonetta Abenda, Türkü Özlüm Çelik, Claudia Fevola +1
The Kadomtsev-Petviashvili (KP) equation is the cornerstone of integrable systems, whose solutions reflect deep connections in algebraic geometry. Banana curves are reducible ratio…
Crossing the transcendental divide: from translation surfaces to algebraic curves
Türkü Özlüm Çelik, Samantha Fairchild, Yelena Mandelshtam
We study constructing an algebraic curve from a Riemann surface given via a translation surface, which is a collection of finitely many polygons in the plane with sides identified…
Hirota Varieties and Rational Nodal Curves
Claudia Fevola, Yelena Mandelshtam
The Hirota variety parameterizes solutions to the KP equation arising from a degenerate Riemann theta function. In this work, we study in detail the Hirota variety arising from a r…
KP Solitons from Tropical Limits
Daniele Agostini, Claudia Fevola, Yelena Mandelshtam +1
We study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations. Riemann's theta function becomes a finite exponential su…
Pencils of Quadrics: Old and New
Claudia Fevola, Yelena Mandelshtam, Bernd Sturmfels
Two-dimensional linear spaces of symmetric matrices are classified by Segre symbols. After reviewing known facts from linear algebra and projective geometry, we address new questio…