Related papers: Beyond Expansion IV: Traces of Thin Semigroups
The union-closed sets conjecture states that in any nonempty union-closed family $\mathcal{F}$ of subsets of a finite set, there exists an element contained in at least a proportion $1/2$ of the sets of $\mathcal{F}$. Using the…
Spatially localised stationary patterns of arbitrary wide spatial extent emerge from subcritical Turing bifurcations in one-dimensional reaction-diffusion systems. They lie on characteristic bifurcation curves that oscillate around a…
We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…
We provide a novel upper-bound on Witsenhausen's rate, the rate required in the zero-error analogue of the Slepian-Wolf problem; our bound is given in terms of a new information-theoretic functional defined on a certain graph. We then use…
For any subgroup of $\mathrm{SL}(3,\mathbb{R})\ltimes\mathbb{R}^3$ obtained by adding a translation part to a subgroup of $\mathrm{SL}(3,\mathbb{R})$ which is the fundamental group of a finite-volume convex projective surface, we first show…
We consider a second order differential operator $\mathscr{A}$ on an (typically unbounded) open and Dirichlet regular set $\Omega\subset \mathbb{R}^d$ and subject to nonlocal Dirichlet boundary conditions of the form \[ u(z) = \int_\Omega…
We study the problem of resonant extraordinary transmission of electromagnetic and acoustic waves through subwavelength slits in an infinite plate, whose thickness is close to a half-multiple of the wavelength. We build on the…
We prove a conjecture of Kleinbock which gives a clear-cut classification of all extremal affine subspaces of $\mathbb{R}^n$. We also give an essentially complete classification of all Khintchine type affine subspaces, except for some…
In this paper we study (asymptotic) properties of the $*$-distribution of irreducible characters of finite quantum groups. We proceed in two steps, first examining the representation theory to determine irreducible representations and their…
This paper provides a unified approach to results on representations of affine Hecke algebras, cyclotomic Hecke algebras, affine BMW algebras, cyclotomic BMW algebras, Markov traces, Jacobi-Trudi type identities, dual pairs (Zelevinsky),…
We study a category of semiinfinite sheaves on the affine flag variety of a connected reductive algebraic group, with coefficients in a field of arbitrary characteristic, generalizing some results of Gaitsgory and showing that this category…
Semi-implicit variational inference (SIVI) is introduced to expand the commonly used analytic variational distribution family, by mixing the variational parameter with a flexible distribution. This mixing distribution can assume any density…
Starting from the Verma module of U_q sl(2) we consider the evaluation module for affine U_q sl(2) and discuss its crystal limit (q=0). There exists an associated integrable statistical mechanics model on a square lattice defined in terms…
We establish a "matrix simultaneous diagonalization theorem" for disconnected reductive groups which relaxes both the semisimplicity condition and the commutativity condition. As an application, we prove the following basic results…
On a smooth bounded Euclidean domain, Sobolev-subcritical fast diffusion with vanishing boundary trace is known to lead to finite-time extinction, with a vanishing profile selected by the initial datum. In rescaled variables, we quantify…
This work delves into the {\it quotient of an affine semigroup by a positive integer}, exploring its intricate properties and broader implications. We unveil an {\it associated tree} that serves as a valuable tool for further analysis.…
This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of…
We obtain quantitative versions of the Balog-Szemeredi-Gowers and Freiman theorems in the model case of a finite field geometry F_2^n, improving the previously known bounds in such theorems. For instance, if A is a subset of F_2^n such that…
The regularity of refinable functions has been investigated deeply in the past 25 years using Fourier analysis, wavelet analysis, restricted and joint spectral radii techniques. However the shift-invariance of the underlying regular setting…
We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the $q\to 1$ limit of the q-deformed affine $\hat{sl(2)}$ symmetry of the sine-Gordon theory, this limit occuring at the…