Related papers: On Weil-Stark elements, II: refined Stark conjectu…
We develop Jacobson's refinement of Engel's Theorem for Leibniz algebras. We then note some consequences of the result.
We reexamine the Riemann Rearrangement Theorem for different types of convergence. We consider series convergence with respect to a filter. We describe the Sum Range (SR) of a series along the 2n-filter and for statistically convergent…
A criterion for the validity of the Riemann hypothesis reduced the problem to the search for a certain estimate, for a hermitian form associated by means of the Weyl symbolic calculus of operators to a distribution in the plane of an…
Fundamental elements are certain special elements of affine Weyl groups introduced by Gortz, Haines, Kottwitz and Reuman. They play an important role in the study of affine Deligne-Lusztig varieties. In this paper, we obtain…
We adapt the conjectural local Langlands parameterization to split metaplectic groups over local fields. When $\tilde G$ is a central extension of a split connected reductive group over a local field (arising from the framework of Brylinski…
This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.
We introduce a new method for studying murmurations, based on random matrix theory. With this method, we exhibit murmurations or similar phenomena: assuming ratios conjectures, for elliptic curves ordered by height, quadratic twists of a…
In this paper we give refinements of some convex and log-convex moment inequalities of the first and second order using a special kind of positive semi-definite form. An open problem concerning eight parameter refinement of second order is…
In a recent paper, Roland Bacher conjectured three identities concerning Stern's sequence and its twist. In this paper we prove Bacher's conjectures. Possibly of independent interest, we also give a way to compute the Stern value (or…
Convection and turbulence in stellar atmospheres have a significant effect on the emergent flux from A-type stars. The recent theoretical advancements in convection modelling have proved a challenge to the observers to obtain measurements…
We review many of the recently developed applications of Heavy Quark Effective Theory techniques. After a brief update on Luke's theorem, we describe striking relations between heavy baryon form factors, and how to use them to estimate the…
Each time diffusion of elements is invoked in explaining abundance anomalies in a star, this supposes implicitly that a stratification process is in progress somewhere in that star. This means also, that the element abundances can still be…
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
We prove Lusztig's conjectures ${\bf P1}$--${\bf P15}$ for the affine Weyl group of type $\tilde{G}_2$ for all choices of parameters. Our approach to compute Lusztig's $\mathbf{a}$-function is based on the notion of a "balanced system of…
The purpose of this paper is to translate the expression of rank 2 cluster scattering diagrams via dilogarithm elements into via formal power series. As a corollary, we prove some conjectures introduced by Thomas Elgin, Nathan Reading, and…
The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl…
We introduce a type $A$ crystal structure on decreasing factorizations of fully-commutative elements in the 0-Hecke monoid which we call $\star$-crystal. This crystal is a $K$-theoretic generalization of the crystal on decreasing…
In 1988, Gross proposed a conjectural congruence between Stickelberger elements and algebraic regulators, which is often referred to as the refined class number formula. In this paper, we prove this congruence.
In our previous papers we introduced categorical invariants, which are, roughly speaking, sets of triangulated subcategories in a given triangulated category and their quotients. Here is extended the list of examples, where these sets are…
In accordance with P. Vogel, a set of algebra structures in Chern-Simons theory can be made universal, independent of a particular family of simple Lie algebras. In particular, this means that various quantities in the adjoint…