Zobrazeno 1 - 10
of 407
pro vyhledávání: '"Sottile, Frank"'
In this paper, we give a rule for the multiplication of a Schubert class by a tautological class in the (small) quantum cohomology ring of the flag manifold. As an intermediate step, we establish a formula for the multiplication of a Schubert class b
Externí odkaz:
http://arxiv.org/abs/2406.05311
Autor:
Sottile, Frank
We sketch an assortment of problems that were posed -- and not yet solved -- during problem sessions at the conference ``Approximation Theory and Numerical Analysis meet Algebra, Geometry, and Topology'', which was held at the Palazzone Cortona 5--9
Externí odkaz:
http://arxiv.org/abs/2308.03211
Autor:
Bates, Daniel J., Breiding, Paul, Chen, Tianran, Hauenstein, Jonathan D., Leykin, Anton, Sottile, Frank
Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equations based on the classical theorem of B\'ezout. This was decisively link
Externí odkaz:
http://arxiv.org/abs/2302.08585
Publikováno v:
J. Softw. Alg. Geom. 14 (2024) 87-95
The Macaulay2 package RealRoots provides symbolic methods to study real solutions to systems of polynomial equations. It updates and expands an earlier package developed by Grayson and Sottile in 1999. We provide mathematical background and descripti
Externí odkaz:
http://arxiv.org/abs/2208.05576
Autor:
Faust, Matthew, Sottile, Frank
We study the spectra of operators on periodic graphs using methods from combinatorial algebraic geometry. Our main result is a bound on the number of complex critical points of the Bloch variety, together with an effective criterion for when this bou
Externí odkaz:
http://arxiv.org/abs/2206.13649
Autor:
Sottile, Frank, Yahl, Thomas
As Jordan observed in 1870, just as univariate polynomials have Galois groups, so do problems in enumerative geometry. Despite this pedigree, the study of Galois groups in enumerative geometry was dormant for a century, with a systematic study only o
Externí odkaz:
http://arxiv.org/abs/2108.07905
The Macaulay2 package NumericalSchubertCalculus provides methods for the numerical computation of Schubert problems on Grassmannians. It implements both the Pieri homotopy algorithm and the Littlewood-Richardson homotopy algorithm. Each algorithm has
Externí odkaz:
http://arxiv.org/abs/2105.04494
We initiate a study of the Euclidean Distance Degree in the context of sparse polynomials. Specifically, we consider a hypersurface f=0 defined by a polynomial f that is general given its support, such that the support contains the origin. We show th
Externí odkaz:
http://arxiv.org/abs/2012.06350
We present numerical homotopy continuation algorithms for solving systems of equations on a variety in the presence of a finite Khovanskii basis. These take advantage of Anderson's flat degeneration to a toric variety. When Anderson's degeneration em
Externí odkaz:
http://arxiv.org/abs/2008.13055