Publications related to Hilbert series and Hilbert polynomial

On the fundamental domain of affine Springer fibers

Let G be a connected reductive algebraic group over an algebraically closed field k,gamma is an element of g( k(( epsilon ))) a semisimple regular element, we introduce a fundamental domain F gamma for the affine Springer fibers X gamma. We show that the p ...

Springer Heidelberg2017

Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth

Michaël Unser, John Paul Ward, Quy Ha Nguyen

The Poisson summation formula (PSF) describes the equivalence between the sampling of an analog signal and the periodization of its frequency spectrum. In engineering textbooks, the PSF is usually stated formally without explicit conditions on the signal f ...

2017

Homology of the three flag Hilbert Scheme

Daniele Boccalini

We prove the existence of an affine paving for the three-step flag Hilbert scheme that parametrizes flag of three 0-dimensional subschemes of length, respectively, n, n+1 and n+2 that are supported at the origin of the affine plane. This is done by showing ...

EPFL2016

Formal Verification of Integer Multipliers by Combining Gröbner Basis with Logic Reduction

Mathias Soeken

Formal verification utilizing symbolic computer algebra has demonstrated the ability to formally verify large Galois field arithmetic circuits and basic architectures of integer arithmetic circuits. The technique models the circuit as Gröbner basis polynom ...

IEEE2016

Innovative photo-Fenton catalysis by PE-FeOx films leading to methylene blue (MB) degradation: Kinetics, surface properties and mechanism

César Pulgarin, Juan Kiwi, Rosendo Sanjines, Laura Victoria Suárez Murillo, Huiyu Dong

This study reports an innovative preparation polyethylene-FeOx (PE-FeOx films) leading to the degradation of the methylene blue (MB) dye under low intensity sunlight/visible light (>400 nm). The intermediate highly oxidative radicals generated by PE-FeOx l ...

Elsevier2016

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function u in multivariate polynomial spaces

P_\Lambda := span\{y \mapsto y^\nu | \nu \in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma := [-1,1]^d

, based on the sa ...

MATHICSE2015

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

Hilbert Schemes as Moduli of Higgs Bundles and Local Systems

We construct five families of 2D moduli spaces of parabolic Higgs bundles (respectively, local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve (respectively, twisted cotangent ...

Oxford University Press2014

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

2014

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate func- tions based on random sampling according to a given probability measure. Recent work has shown th ...

MATHICSE2014

Hilbert series and Hilbert polynomial

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On the fundamental domain of affine Springer fibers

Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth

Homology of the three flag Hilbert Scheme

Formal Verification of Integer Multipliers by Combining Gröbner Basis with Logic Reduction

Innovative photo-Fenton catalysis by PE-FeOx films leading to methylene blue (MB) degradation: Kinetics, surface properties and mechanism

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Hilbert Schemes as Moduli of Higgs Bundles and Local Systems

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth

Homology of the three flag Hilbert Scheme

Innovative photo-Fenton catalysis by PE-FeOx films leading to methylene blue (MB) degradation: Kinetics, surface properties and mechanism

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Hilbert Schemes as Moduli of Higgs Bundles and Local Systems

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

On the fundamental domain of affine Springer fibers

Formal Verification of Integer Multipliers by Combining Gröbner Basis with Logic Reduction

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension