6 papers
Probability-theoretic interpretation of degeneracy locus formulas
Richard Rimanyi
Schwartz-MacPherson classes of degeneracy loci of symmetric and skew-symmetric maps. Together with the known formulas for ordinary linear maps, this completes the stable SSM theory…
Combinatorial and algebraic proofs of Keller's -dilogarithm identity
Richard Rimanyi
The classical Durfee-square argument gives a combinatorial proof of the pentagon identity for the quantum dilogarithm. Just as the pentagon identity is associated with the qu…
Degenerations of multisingularities and Artin algebras
Jakub Koncki, Richárd Rimányi
We study the degeneration hierarchy of commutative, associative, finite-dimensional complex Artin algebras. Instead of studying degenerations in the Hilbert scheme, we introduce a…
Higher characteristic classes of multisingularity loci
Jakub Koncki, Richárd Rimányi
A map between manifolds induces stratifications of both the source and the target according to the occurring multisingularities. In this paper, we study universal expressions-calle…
Geometry of fibers of the multiplication map of deep linear neural networks
Simon Pepin Lehalleur, Richárd Rimányi
We study the geometry of the algebraic set of tuples of composable matrices which multiply to a fixed matrix, using tools from the theory of quiver representations. In particular,…
Fixed point counts and motivic invariants of bow varieties of affine type A
Ádám Gyenge, Richárd Rimányi
We compute the equivariant K-theory of torus fixed points of Cherkis bow varieties of affine type A. We deduce formulas for the generating series of the Euler numbers of these vari…