53 citations · 428 across the 47 of their papers we have counts for
39 papers · 1 filter
The main reasons for matrices multiplying to zero
Jakub Koncki, Richard Rimanyi
We provide an explicit description of the maximal-dimensional components of the variety parametrizing sequences of matrices of prescribed sizes whose product is zero.
Interpolation characterization of higher Thom polynomials
Richard Rimanyi
Thom polynomials provide universal formulas for the fundamental class of singularity loci in terms of characteristic classes. Ohmoto extended this notion to SSM-Thom polynomials, w…
Thom polynomials. A primer
Richard Rimanyi
The Thom polynomial of a singularity expresses the cohomology class of the -singularity locus of a map in terms of the map's simple invariants. In this informal survey -- ba…
Bow varieties: Stable envelopes and their 3d mirror symmetry
Tommaso Maria Botta, Richard Rimanyi
In this paper we study the elliptic characteristic classes known as ''stable envelopes'', which were introduced by M. Aganagic and A. Okounkov. We prove that for a rich class of ho…
Bow varieties---geometry, combinatorics, characteristic classes
R. Rimanyi, Y. Shou
Cherkis bow varieties are believed to be the set of spaces where 3d mirror symmetry for characteristic classes can be observed. We describe geometric structures on a large class of…
The -Selberg integral of type
Richard Rimanyi, Alexander Varchenko
We prove an -Selberg integral formula of type , in which the -Selberg integral is an element of the finite field with odd prime number…
The -Selberg Integral
Richard Rimanyi, Alexander Varchenko
We prove an -Selberg integral formula, in which the -Selberg integral is an element of the finite field with odd prime number of element…
Elliptic classes on Langlands dual flag varieties
Richard Rimanyi, Andrzej Weber
Characteristic classes of Schubert varieties can be used to study the geometry and the combinatorics of homogeneous spaces. We prove a relation between elliptic classes of Schubert…
-deformed Schubert calculus in equivariant cohomology, K-theory, and elliptic cohomology
Richard Rimanyi
In this survey paper we review recent advances in the calculus of Chern-Schwartz-MacPherson, motivic Chern, and elliptic classes of classical Schubert varieties. These three theori…
Elliptic classes of Schubert varieties
Shrawan Kumar, Richárd Rimányi, Andrzej Weber
We introduce new notions in elliptic Schubert calculus: the (twisted) Borisov-Libgober classes of Schubert varieties in general homogeneous spaces G/P. While these classes do not d…
Characteristic classes of symmetric and skew-symmetric degeneracy loci
Sutipoj Promtapan, Richard Rimanyi
We give two formulas for the Chern-Schwartz-MacPherson class of symmetric and skew-symmetric degeneracy loci. We apply them in enumerative geometry, explore their algebraic combina…
Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety
Richárd Rimányi, Andrey Smirnov, Alexander Varchenko +1
Let be a holomorphic symplectic variety with a torus action and a finite fixed point set of cardinality . We assume that elliptic stable envelope exists for …
Elliptic classes of Schubert varieties via Bott-Samelson resolution
Richard Rimanyi, Andrzej Weber
Based on recent advances on the relation between geometry and representation theory, we propose a new approach to elliptic Schubert calculus. We study the equivariant elliptic char…
3d Mirror Symmetry and Elliptic Stable Envelopes
Richárd Rimányi, Andrey Smirnov, Alexander Varchenko +1
We consider a pair of quiver varieties (X;X') related by 3d mirror symmetry, where X =T*Gr(k,n) is the cotangent bundle of the Grassmannian of k-planes of n-dimensional space. We g…
Characteristic classes of orbit stratifications, the axiomatic approach
Laszlo M. Feher, Richard Rimanyi, Andrzej Weber
Consider a complex algebraic group acting on a smooth variety with finitely many orbits, and let be an orbit. The following three invariants of can be char…
Motivic characteristic classes in cohomological Hall algebras
Richard Rimanyi
The equivariant Chern-Schwartz-MacPherson (CSM) class and the equivariant Motivic Chern (MC) class are important characteristic classes of singular varieties in cohomology and K th…
Motivic Chern classes and K-theoretic stable envelopes
Laszlo M. Feher, Richard Rimanyi, Andrzej Weber
We study a K-theoretic characteristic class of singular varieties, namely the equivariant motivic Chern class. We prove that the motivic Chern class is characterized by an axiom sy…
Chern-Schwartz-MacPherson classes of degeneracy loci
L. M. Feher, R. Rimanyi
The Chern-Schwartz-MacPherson class (CSM) and the Segre-Schwartz-MacPherson class (SSM) are deformations of the fundamental class of an algebraic variety. They encode finer enumera…
Quadric rank loci on moduli of curves and K3 surfaces
Gavril Farkas, Richard Rimanyi
Given two vector bundles E and F on a variety X and a morphism from Sym^2(E) to F, we compute the cohomology class of the locus in X where the kernel of this morphism contains a qu…
Elliptic and K-theoretic stable envelopes and Newton polytopes
R. Rimányi, V. Tarasov, A. Varchenko
In this paper we consider the cotangent bundles of partial flag varieties. We construct the -theoretic stable envelopes for them and also define a version of the elliptic stable…
Equivariant Chern-Schwartz-MacPherson classes in partial flag varieties: interpolation and formulae
R. Rimanyi, A. Varchenko
Consider the natural torus action on a partial flag manifold . Let be an open Schubert variety, and let be its torus equivariant Cher…
Dynamical Gelfand-Zetlin algebra and equivariant cohomology of Grassmannians
R. Rimanyi, A. Varchenko
We consider the rational dynamical quantum group and introduce an -module structure on $\oplus_{k=0}^n H^*_{GL_n\times\C^\times}(T^*Gr(k,n))'$, where $H^*_{G…
Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety
R. Rimanyi, V. Tarasov, A. Varchenko
We consider the cotangent bundle of a partial flag variety, , , and the torus $T=(\C^\times)^{n+1}$ equivariant K-theory algebra $…
On the Cohomological Hall Algebra of Dynkin quivers
R. Rimanyi
Consider the Cohomological Hall Algebra as defined by Kontsevich and Soibelman, associated with a Dynkin quiver. We reinterpret the geometry behind the multiplication map in the CO…