Related papers: Le calcul de Schubert selon Schubert
A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.
We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric Littlewood-Richardson rule. One key ingredient of this…
The present report, has been inspired by the need of the author and its colleagues to understand the underlying theory of Wirtinger's Calculus and to further extend it to include the kernel case. The aim of the present manuscript is…
We obtain an explicit determinantal formula for the multiplicity of any point on a classical Schubert variety.
We connect generalized permutahedra with Schubert calculus. Thereby, we give sufficient vanishing criteria for Schubert intersection numbers of the flag variety. Our argument utilizes recent developments in the study of Schubitopes, which…
Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar…
A Newton-Okounkov polytope of a complete flag variety can be turned into a convex geometric model for Schubert calculus. Namely, we can represent Schubert cycles by linear combinations of faces of the polytope so that the intersection…
This is an elementary explanation of a cubic composition formula due to Ramanujan.
We present the basic theory of calculus on dual real numbers, and prove the counterpart of the ordinary fundamental theorem of calculus in the context of dual real numbers.
We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the cohomology ring of orthogonal flag varieties. We use these polynomials to describe the arithmetic…
This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled "Affine Schubert Calculus" that took place in July 2010…
We describe a large-scale computational experiment to study structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Schubert problems whose computed numbers of real solutions…
We apply the previous calculations of Chow-Witt rings of Grassmannians to develop an oriented analogue of the classical Schubert calculus. As a result, we get complete diagrammatic descriptions of the ring structure in Chow-Witt rings and…
In this paper we propose a calculus for expressing algorithms for programming languages transformations. We present the type system and operational semantics of the calculus, and we prove that it is type sound. We have implemented our…
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
This note is a complement to Pusz--Woronowicz's works on functional calculus for two positive forms from the viewpoint of operator theory. Based on an elementary, self-contained and purely Hilbert space operator explanation of their…
We study Hilbert's epsilon calculus and Hilbert's partial epsilon calculus in toposes.
This chapter combines an introduction and research survey about Schubert varieties. The theme is to combinatorially classify their singularities using a family of polynomial ideals generated by determinants.
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
In the note, the author discovers an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.