7 citations · 15 across the 11 of their papers we have counts for
12 papers
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…
The positive orthogonal Grassmannian
Yassine El Maazouz, Yelena Mandelshtam
The Plücker positive region of the orthogonal Grassmannian emerged as the positive geometry behind the ABJM scattering amplitudes. In this paper we initiate…
Combinatorics of Grasstopes
Yelena Mandelshtam, Dmitrii Pavlov, Elizabeth Pratt
A Grasstope is the image of the totally nonnegative Grassmannian under a linear map . This is a generaliza…
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…
Non-Rigid Rank-One Infinite Measures on the Circle
Hindy Drillick, Alonso Espinosa-Dominguez, Jennifer N. Jones-Baro +3
For a class of irrational numbers, depending on their Diophantine properties, we construct explicit rank-one transformations that are totally ergodic and not weakly mixing. We clas…
On Graphs Representable by Pattern-Avoiding Words
Yelena Mandelshtam
In this paper we study graphs defined by pattern-avoiding words. Word-representable graphs have been studied extensively following their introduction in 2000 and are the subject of…
Arrangements Of Minors In The Positive Grassmannian And a Triangulation of The Hypersimplex
Miriam Farber, Yelena Mandelshtam
The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities…
When Learners Surpass their Sources: Mathematical Modeling of Learning from an Inconsistent Source
Yelena Mandelshtam, Natalia Komarova
We present a new algorithm to model and investigate the learning process of a learner mastering a set of grammatical rules from an inconsistent source. The compelling interest of h…