Related papers: On cuspidality of global Arthur packets for symple…
Automorphism groups of locally finite trees provide a large class of examples of simple totally disconnected locally compact groups. It is desirable to understand the connections between the global and local structure of such a group.…
We consider the global symplectic classification problem of plane curves. First we give the exact classification result under symplectomorphisms, for the case of generic plane curves, namely immersions with transverse self-intersections.…
We survey old and new results about the cohomology of the moduli space $A_g$ of principally polarized abelian varieties of genus $g$ and its compactifications. The main emphasis lies on the computation of the cohomology for small genus and…
We study the automorphism group of a unital, simple, $\mathcal{Z}$-stable $C^{*}$-algebra. In this paper, we generalize the results by the authors in \cite{pr_auto} to $\mathcal{Z}$-stable $C^{*}$-algebras $\mathfrak{A}$ such that…
We survey results arising from the study of domains in C^n with non-compact automorphism group. Beginning with a well-known characterization of the unit ball, we develop ideas toward a consideration of weakly pseudoconvex (and even…
Circle packings with specified patterns of tangencies form a discrete counterpart of analytic functions. In this paper we study univalent packings (with a combinatorial closed disk as tangent graph) which are embedded in (or fill) a…
We establish a structure theorem for the connected automorphism groups of smooth complete toroidal horospherical varieties, that is, toric fibrations over rational homogeneous spaces. The key ingredient is a characterization of the Demazure…
We look at the expectation values for quantized linear symplectic maps on the multidimensional torus and their distribution in the semiclassical limit. We construct super-scars that are stable under the arithmetic symmetries of the system…
Let $\pi$ be a unitary automorphic cuspidal representation of $GL_2(\mathbb{Q}_\mathbb{A})$ with Fourier coefficients $\lambda_\pi(n)$. Asymptotic expansions of certain sums of $\lambda_\pi(n)$ are proved using known functorial liftings…
In this paper we study the upper bound of wavefront sets of irreducible admissible representations of connected reductive groups defined over non-Archimedean local fields of characteristic zero. We formulate a new conjecture on the upper…
This paper explores relations between two separate worlds. They are the algebraic geometry of Alexander Grothendieck and the automorphic representation theory of Robert Langlands. The relation between them would be a very broad example of…
This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of…
In this paper, we construct and study derived character maps of finite-dimensional representations of $\infty$-groups. As models for $\infty$-groups we take homotopy simplicial groups, i.e. homotopy simplicial algebras over the algebraic…
Automorphisms of the quantum Schubert cell algebras ${\mathcal U}_q^\pm[w]$ of De Concini, Kac, Procesi and Lusztig and their restrictions to some key invariant subalgebras are studied. We develop some general rigidity results and apply…
A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…
We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic surface. We also classify simple Morse functions on symplectic surfaces with respect to actions…
The question studied here is the behavior of the Poisson bracket under C^0-perturbations. In this purpose, we introduce the notion of pseudo-representation and prove that for a normed Lie algebra, it converges to a representation. An…
Let $F$ be a CM field. In this paper, we prove the local-global compatibility for cohomological cuspidal automorphic representations of $\mathrm{GL}_n(\mathbb{A}_F)$ at $p \neq l$ by using certain potential automorphy theorems in some cases…
We prove that Kaletha's toral supercuspidal L-packets satisfy the twisted endoscopic character relation in some cases, including the case of general linear groups equipped with an involution. Consequently, we verify that Kaletha's…
Exact results from random matrix theory are used to systematically analyse the relationship between microscopic Dirac spectra and finite-volume partition functions. Results are presented for the unitary ensemble, and the chiral analogs of…