Push-pull operators on convex polytopes

On the commutativity of pull-back and push-forward functors on motivic constructible functions

In this article, we study the commutativity between the pull-back and the push-forward functors on constructible functions in Cluckers--Loeser motivic integration.

The push-forwards and pull-backs of $δ$-forms and applications to non-archimedean Arakelov geometry

We study two kinds of push-forwards of $δ$-forms and define the pull-backs of $δ$-forms. As a generalization of Gubler-Künnemann, we prove the projection formula and the tropical Poincaré-Lelong formula. As an application, we follow the idea of Gubler-Künnemann and generalize the notion of $δ$-forms on algebraic varieties, this allows us to define the first Chern forms for any piecewise smooth metrics.

Cherednik代数上完整模的回拉和推出函子

Pull-back and push-forward functors for holonomic modules over Cherednik algebras

本文在Cherednik代数层上，通过建立b-函数理论证明开嵌入和闭嵌入下完整性的保持，进而证明任意拟态射下推出和回拉保持完整性，并给出不可约完整模的分类及Ext-群的有限维性。

Push-pull operators on the formal affine Demazure algebra and its dual

In the present paper we introduce and study the push pull operators on the formal affine Demazure algebra and its dual. As an application we provide a non-degenerate pairing on the dual of the formal affine Demazure algebra which serves as an algebraic counterpart of the natural pairing on the T-equivariant oriented cohomology of G/B induced by multiplication and push-forward to a point. This paper can be viewed as the next step towards the `algebraization program' for equivariant oriented cohomology theories started in arXiv:0905.1341 and continued in arXiv:1208.4114 and arXiv:1209.1676; the …

凸多面体到直线的投影及更高一维普朗克系统

Projections of convex polytopes to a line and higher univariate Prony systems

研究凸多面体勒贝格测度到直线的推前，揭示其作为分段多项式密度的性质，并引入更高维普朗克系统，解决逆动量问题。