Related papers: Degrees of rigidity for Souslin trees
We prove rigidity facts for groups acting on pseudo-Riemannian manifolds by preserving unparameterized geodesics.
In this paper, we prove two main theorems: conformal measure rigidity and ergodicity of horospherical foliations, especially in higher rank. Both theorems are new even for relatively Anosov groups. First, we establish a higher rank…
These are lectures given at the 2022 Arizona Winter School. It gives an introduction to the rigidity method for constructing automorphic forms for semisimple groups over function fields. The rigidity method leads to explicit constructions…
In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type $\tto$ factors arising from countable discrete groups. We give simple criteria for…
A forest is a generalization of a tree, and here we consider the Aronszajn and Suslin properties for forests. We focus on those forests satisfying coherence, a local smallness property. We show that coherent Aronszajn forests can be…
The cohomological rigidity problem for toric orbifolds asks when an integral cohomology isomorphism implies a homotopy equivalence. In this paper we reformulate the cohomological rigidity problem in the context of $4$-dimensional toric…
We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally…
Spanning tree modulus is a generalization of effective resistance that is closely related to graph strength and fractional arboricity. The optimal edge density associated with spanning tree modulus is known to produce two hierarchical…
We give a characterisation of quantum automorphism groups of trees. In particular, for every tree, we show how to iteratively construct its quantum automorphism group using free products and free wreath products. This can be considered a…
A Souslin algebra is a complete Boolean algebra whose main features are ruled by a tight combination of an antichain condition with an infinite distributive law. The present article divides into two parts. In the first part a representation…
We construct a smooth rational affine surface S with finite automorphism group but with the property that the group of automorphisms of the cylinder SxA^2 acts infinitely transitively on the complement of a closed subset of codimension at…
We study the structure of the soft SUSY-breaking terms obtained from large classes of 4-D Strings under the assumption of dilaton/moduli dominance in the process of SUSY-breaking. In particular, we first analyze in detail the…
In this paper we describe orbits of automorphism group on a horospherical variety in terms of degrees of homogeneous with respect to natural grading locally nilpotent derivations. In case of (may be non-normal) toric varieties a description…
A class of structures is monadically dependent if one cannot interpret all graphs in colored expansions from the class using a fixed first-order formula. A tree-ordered $\sigma$-structure is the expansion of a $\sigma$-structure with a…
We develop a rigidity theory for bar-joint frameworks in Euclidean $d$-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class.…
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…
Motivated by geometric origami and the straight skeleton construction, we outline a map between spaces of phylogenetic trees and spaces of planar polygons. The limitations of this map is studied through explicit examples, culminating in…
By Torelli topology the author understands aspects of the topology of surfaces (potentially) relevant to the study of Torelli groups. The present paper is devoted to a new approach to the results of W. Vautaw about Dehn multi-twists in…
In this note we prove the following results: $\bullet$ If a finitely presented group $G$ admits a strongly aperiodic SFT, then $G$ has decidable word problem. More generally, for f.g. groups that are not recursively presented, there exists…
We analyze a countable support product of a free Suslin tree which turns it into a highly rigid Kurepa tree with no Aronszajn subtree. In the process, we introduce a new rigidity property for trees, which says roughly speaking that any…