Related papers: On the definition of stable transfer factors

This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals…

A character (ordinary or modular) is called orthogonally stable if all non-degenerate quadratic forms fixed by representations with those constituents have the same determinant mod squares. We show that this is the case provided there are…

Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of…

We show that if G is a finite constant group acting on a scheme X such that the order of G is invertible in the residue fields of X, then the G-equivariant motivic stable homotopy category of X is equivalent to the stabilization of the…

The goal of this paper is extend Kottwitz's theory of $B(G)$ for global fields. In particular, we show how to extend the definition of "$B(G)$ with adelic coefficients" from tori to all connected reductive groups. As an application, we give…

We stabilize the full Arthur-Selberg trace formula for the metaplectic covering of symplectic groups over a number field. This provides a decomposition of the invariant trace formula for metaplectic groups, which encodes information about…

We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…

This paper establishes suficient conditions for the orbital stability of one-parameter spatially periodic traveling-wave solutions for one-dimensional dispersive equations. Our method of proof combines known techniques with some new ideas.…

We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby…

According to the relative Langlands functoriality conjecture, an admissible morphism between the $L$-groups of spherical varieties should induce a functorial transfer of the corresponding local and global automorphic spectra. Via the…

Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…

This is the second article in a two-part series presenting a new proof comparing the non-invariant trace formula for a general linear group with that of one of its inner forms. In this article, we focus on the spectral side of the trace…

For a reductive group over a nonarchimedean local field, we define the stack of spherical Langlands parameters, using the inertia-invariants of the Langlands dual group. This generalizes the stack of unramified Langlands parameters in case…

We develop a theory of generalized characters of local systems in $\infty$-categories, which extends classical character theory for group representations and, in particular, the induced character formula. A key aspect of our approach is…

As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…

It is the second article of a series whose final goal is the stabilization of the twisted trace formula. Over a non archimedean field, we define (after Arthur) wheighted orbital integrals and their stable and endoscopic versions. We state…

The word stable is used to describe a situation when mathematical objects that almost satisfy an equation are close to objects satisfying it exactly. We study operator-algebraic forms of stability for unitary representations of groups and…

We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems…

In the theory of endoscopy appears transfer factors. They were defined by Langlands and Shelstad in the ordinary case and by Kottwitz and Shelstad in the twisted case. The definition is abstract. For classical groups, we compute explicitely…

Let $E$ be a separable quadratic extension of a locally compact field $F$ of positive characteristic. Asai \gamma-factors are defined for smooth irreducible representations \pi of ${\rm GL}_n(E)$. If \sigma is the Weil-Deligne…