Related papers: Notes on the geometric Satake equivalence
We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality. We also prove a result of mixed mean inequality involving the symmetric means.
Fargues-Scholze developed a framework for the geometric Langlands program on the Fargues-Fontaine curve. In particular, they proved the geometric Satake equivalence on the moduli space of closed Cartier divisors on the curve. We prove the…
In this paper we study global distance estimates and uniform local volume estimates in a large class of sub-Riemannian manifolds. Our main device is the generalized curvature dimension inequality introduced by the first and the third author…
The paper studies the complex 1-dimensional polynomial vector fields with real coefficients under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a…
We prove the geometrical Satake isomorphism for a reductive group defined over F=k((t)), and split over a tamely ramified extension. As an application, we give a description of the nearby cycles on certain Shimura varieties via the…
The main purpose of this work is to generalize the $S^3_\bfw$ Sasaki join construction $M\star_\bfl S^3_\bfw$ described in \cite{BoTo14a} when the Sasakian structure on $M$ is regular, to the general case where the Sasakian structure is…
The main classical result of Schubert calculus is that multiplication rules for the basis of Schubert cycles inside the cohomology ring of the Grassmannian $G(n,m)$ are the same as multiplication rules for the basis of Schur polynomials in…
We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
In this letter we study a class of symmetries of the new translational extended shape invariant potentials. It is proved that a generalization of a compatibility condition introduced in a previous article is equivalent to the usual shape…
This paper is devoted to study the dispersive properties of the linear Klein-Gordon and wave equations on a class of locally symmetric spaces. As a consequence, we obtain the Strichartz estimate and prove global well-posedness results for…
This note presents a new equivalence to the Riemann Hypothesis by means of the Salem integral equation.
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
In their recent article, Min Ru and Paul Vojta, among other things, proved the so-called general theorem (arithmetic part) which can be viewed as an extension of Schmidt's subspace theorem. In this note, we extend their result by replacing…
In this note I discuss some features of the topological theory obtained from the Zakharov-Shabat (or general sl(2,C)) hierarchy, and comment on some possible physical and/or mathematical interpretations of it.
We give a new combinatorial description for stable Grothendieck polynomials in terms of subdivisions of Gelfand-Zetlin polytopes. Moreover, these subdivisions also provide a description of Lascoux polynomials. This generalizes a similar…
We establish a general criterion for the validity of inequalities of the following form: A certain convex combination of the values of a convex function at n points and of its value at a weighted mean of these n points is always greater or…
A different proof to a known criterion of derived equivalence implying birationality is given. Derived equivalent smooth projective curves over an algebraically closed field are proved to be isomorphic. A different proof of derived…
This note studies the existence of quotients by finite set theoretic equivalence relations. May 18: Substantial revisions with a new appendix by C. Raicu