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Certain supersymmetric sigma models in 2+1 dimensions feature multi-soliton solutions, with and without scattering. We subject these systems to a non-anticommutative deformation by replacing the Grassmann algebra of the odd superspace…

In this letter, we establish a general fact about the convergence of images of families of closed analytic surfaces in the special linear group $\operatorname{SL}_2(\mathbb{C})$ under the quotient by its maximal compact subgroup…

We prove that the reduced group C*-algebras of infinite countable discrete groups having topologically-free extreme boundaries, or more generally groups that satisfy certain combinatorial property including all acylindrically hyperbolic…

This article is part of the program of studying large-scale geometric properties of totally disconnected locally compact groups, TDLC-groups, by analogy with the theory for discrete groups. We provide a characterization of hyperbolic…

We give, in dimensions three or greater, an example of a bounded, pseudoconvex, circular domain in complex space with smooth real analytic boundary and non-compact automorphism group which is not biholomorphically equivalent to any…

We prove the locally differentiable rigidity of generic partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from split symplectic Lie groups. We also gave a non-generic action rigidity example on…

We classify the finite groups whose non-linear irreducible characters that are not conjugate under the natural Galois action have distinct degrees, therefore extending the results in Berkovich et al. [Proc. Amer. Math. Soc. {\bf 115}…

Let H denote the 3-dimensional Heisenberg Lie group. The present paper classify all possible linear control systems on the homogeneous spaces of H through its closed subgroups and expose a detailed study on the control behavior…

We prove that every family of isospectral surfaces with discrete length spectrum arising from Sunada's method is finite. Furthermore, by introducing the topological notion of surfaces with self-duplicating ends, we show that every finite…

In this work, we describe how to obtain the structure of an infinite-dimensional Lie group on the group of compactly carried bundle automorphisms Autc(P) for a locally convex prinicpal bundle P over a finite-dimensional smooth sigma-compact…

This paper studies a non-trivial gradient K\"{a}hler-Ricci soliton, of complex dimension $n$, with an isometry group of dimension at least $n^2-1$. We show that the isometry group acts by cohomogeneity one and, consequently, admits a…

We establish some general principles and find some counter-examples concerning the Pontryagin reflexivity of precompact groups and P-groups. We prove in particular that: (1) A precompact Abelian group G of bounded order is reflexive iff the…

We begin the investigation of Gamma-limit groups, where Gamma is a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. Using the results of Drutu and Sapir, we adapt the results from math.GR/0404440 to…

In this series of two articles, we prove that every action of a finite group $G$ on a finite and contractible $2$-complex has a fixed point. The proof goes by constructing a nontrivial representation of the fundamental group of each of the…

In this second part we prove that, if $G$ is one of the groups $\mathrm{PSL}_2(q)$ with $q>5$ and $q\equiv 5\pmod {24}$ or $q\equiv 13 \pmod{24}$, then the fundamental group of every acyclic $2$-dimensional, fixed point free and finite…

We describe the global structure of totally disconnected locally compact groups having a linear open compact subgroup. Among the applications, we show that if a non-discrete, compactly generated, topologically simple, totally disconnected…

We classify up to equivalence all finite-dimensional irreducible representations of PSL2(Z) whose restriction to the commutator subgroup is diagonalizable.

In the moduli space of semistable $\text{SL}(r, \mathbb{C})$-Higgs bundles, we show that there exists a sublocus of the upward flow through a polystable $\mathbb{C}^{*}$-fixed point, which is Lagrangian on its intersection with the stable…

Let G_2 be the exceptional Lie group of automorphisms of the complex Cayley algebra and C be a generic, smooth, connected, projective curve over $\mathbb{C}$ of genus at least 2. For a complex Lie group G, let H^0(M(G),L^k) be the space of…

We prove that for a one-ended hyperbolic graph $X$, the size of the quotient $X/G$ by a group $G$ acting freely and cocompactly bounds from below the number of simplices in an Eilenberg-MacLane space for $G$. We apply this theorem to show…