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Schubert Calculus on the Arithmetic Grassmannian
Arithmetic Grassmannian Schubert Calculus
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2015/12/17
Let G be the arithmetic Grassmannian over SpecZ with the natural invariant KÄahler metric on G(C). We study the combinatorics of
the arithmetic Schubert calculus in the Arakelov Chow ring CH(G)
THE CONNECTION BETWEEN REPRESENTATION THEORY AND SCHUBERT CALCULUS
CONNECTION BETWEEN REPRESENTATION SCHUBERT CALCULUS
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2015/12/17
Our aim here is to describe a direct and natural connection between the representation theory of GLn and the Schubert calculus, which goes via the Chern-Weil
theory of characteristic classes. Indeed,...
Discrete Symbol Calculus
sublinear complexity inversion of elliptic operators square root of elliptic operators
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2015/7/14
This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space x and frequency ξ. The symbol smoot...
Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus
homogeneous spaces generalized Schubert calculus
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2015/7/14
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We
give various ext...
Tools for Malliavin calculus in UMD Banach spaces
Malliavin calculus Skorohod integral anticipating processes Meyer inequalities UMD Banach space type 2 space chain rule
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2012/4/16
In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in p...
Context-free manifold calculus and the Fulton-MacPherson Operad
Embedding calculus Fulton-MacPherson operad Algebraic Topology
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2012/4/18
The paper gives an explicit description of the Weiss embedding tower in terms of spaces of maps of truncated modules over the framed Fulton-MacPherson operad.
Golden Quantum Oscillator and Binet-Fibonacci Calculus
Golden Quantum Oscillator Binet-Fibonacci Calculus Quantum Algebra
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2011/9/19
Abstract: The Binet-Fibonacci formula for Fibonacci numbers is treated as a q-number (and q-operator) with Golden ratio bases $q=\phi$ and $Q=-1/\phi$. Quantum harmonic oscillator for this Golden calc...
Paraproducts via $H^\infty$-functional calculus
paraproducts Davies-Gaffney estimates Hardy spaces Carlesonmeasures H1-functional calculus
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2011/9/19
Abstract: Let $X$ be a space of homogeneous type and let $L$ be a sectorial operator with bounded holomorphic functional calculus on $L^2(X)$. We assume that the semigroup $\{e^{-tL}\}_{t>0}$ satisfie...
The alpha-calculus-cum-alpha-analysis of r-th order derivative of zeta(s,alpha)
Hurwitz zeta function Bernoulli polynomials /numbers Number Theory
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2011/9/14
Abstract: For the higher order derivative(with respect to the first variable) of Hurwitz zeta function,we discuss as a function of the second variable,the location and the nature of its singularities ...
Relative commutator calculus in Chevalley groups
Relative commutator calculus Chevalley groups Rings and Algebras
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2011/9/9
Abstract: We revisit localisation and patching method in the setting of Chevalley groups. Introducing certain subgroups of relative elementary Chevalley groups, we develop relative versions of the con...
On the logarithimic calculus and Sidorenko's conjecture
logarithimic calculus Sidorenko's conjecture Combinatorics
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2011/8/26
Abstract: We study a type of calculus for proving inequalities between subgraph densities which is based on Jensen's inequality for the logarithmic function. As a demonstration of the method we verify...
Malliavin Calculus and Self Normalized Sums
Malliavin calculus multiple stochastic integrals Steinn’s method self-normalized sums limit theorems
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2011/8/23
Abstract: We study the self-normalized sums of independent random variables from the perspective of the Malliavin calculus. We give the chaotic expansion for them and we prove a Berry-Ess\'een bound w...
The power quantum calculus and variational problems
Quantum variational problems n q-power difference operator generalized Norlund sum
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2011/8/23
Abstract: We introduce the power difference calculus based on the operator $D_{n,q} f(t) = \frac{f(qt^n)-f(t)}{qt^n -t}$, where $n$ is an odd positive integer and $0
Calculus of Tangent Sets and Derivatives of Set Valued Maps under Metric Subregularity Conditions
Bouligand tangent sets Ursescu tangent sets metric regularity set-valued derivatives
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2011/8/23
Abstract: In this paper we intend to give some calculus rules for tangent sets in the sense of Bouligand and Ursescu, as well as for corresponding derivatives of set-valued maps. Both first and second...
The non-autonomous chiral model and the Ernst equation of General Relativity in the bidifferential calculus framework
non-autonomous chiral model bidifferential calculus framework Ernst equation General Relativity
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2011/7/7
We generate exact solutions of the non-autonomous chiral model, which in particular arises in General Relativity, using a general result of the bidifferential calculus approach to integrable PDDEs. In...