651 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Divisible convex sets with properly embedded cones
In this article we construct many examples of properly convex irreducible
domains divided by Zariski dense relatively hyperbolic groups in every
dimension at least 3. This answers a question of Benoist. Relative
hyperbolicity and non-strict convexity are captured by a family of properly
embedded cones (convex hulls of points and ellipsoids) in the domain. Our
construction is most flexible in dimension 3 where we give a purely topological
criterion for the existence of a large deformation space of geometrically
controlled convex projective structures with totally geodesic boundary on a
compact 3-manifold.Comment: 90 pages. Comments are welcome
Noncommutative Ergodic Optimization
We extend the theory of ergodic optimization and maximizing measures to the
non-commutative field of C*-dynamical systems. We then provide a result linking
the ergodic optimizations of elements of a C*-dynamical system to the
convergence of certain ergodic averages in a suitable seminorm. We also provide
alternate proofs of several results in this article using the tools of
nonstandard analysis.Comment: This article is derived from a chapter of the author's doctoral
dissertation. It combines and extends two articles previously uploaded to the
arXiv:2109.10425 and arXiv:2109.13965. This version corrects a few minor
typos found in the first versio
Class numbers of multinorm-one tori
We present a formula for the class number of a multinorm one torus
associated to any \'etale algebra over a global field . This is deduced
from a formula for analogues of invariants introduced by T.~Ono, which are
interpreted as a generalization of Gauss genus theory. This paper includes the
variants of Ono's invariant for arbitrary -ideal class numbers and the
narrow version, generalizing results of Katayama, Morishita, Sasaki and Ono.Comment: 21 pages; comments welcom
-approach to the Saito vanishing theorem
We give an analytic approach to the Saito vanishing theorem by going back to
the original idea for the proof of the Kodaira-Nakano vanishing theorem. The
key ingredient is the curvature formula for Hodge bundles and the Higgs field
estimates for degenerations of Hodge structures
Temporo-spatial differentiations
Temporo-spatial differentiation problems were first introduced in \cite{Assani-Young} under the name of spatial-temporal differentiation problems. Given a probability space and measurable map , a temporo-spatial differentiation problem is concerned with the limiting behavior of the sequencewhere and is a sequence of measurable subsets of with positive measure. These problems were then generalized to the setting of non-autonomous dynamical systems in \cite{Non-AutonomousTSD}. We will present several of the basic aspects of temporo-spatial differentiation problems, including their connections with the field of ergodic optimization. We also present several positive convergence results for ``random temporo-spatial differentiation problems." We then discuss generalizations of temporo-spatial differentiation problems to the setting of actions of groups and semigroups other than , as well as the construction of pathological temporo-spatial differentiation problems.Doctor of Philosoph
Universal α-central extensions of Hom-Leibniz n-algebras
We construct homology with trivial coefficients of Hom-Leibniz n-algebras. We introduce and characterize universal (α)-central extensions of Hom-Leibniz n-algebras. In particular, we show their interplay with the zero-th and first homology with trivial coefficients. When n = 2 we recover the corresponding results on universal central extensions of Hom-Leibniz algebras. The notion of non-abelian tensor product of Hom-Leibniz n-algebras is introduced and we establish its relationship with universal central extensions. A generalization of the concept and properties of unicentral Leibniz algebras to the setting of Hom-Leibniz n-algebras is developed.Agencia Estatal de Investigación | Ref. MTM2016-79661-
The Complexity of Some Geometric Proof Systems
In this Thesis we investigate proof systems based on Integer Linear Programming. These methods inspect the solution space of an unsatisfiable propositional formula and prove that this space contains no integral points.
We begin by proving some size and depth lower bounds for a recent proof system, Stabbing Planes, and along the way introduce some novel methods for doing so.
We then turn to the complexity of propositional contradictions generated uniformly from first order sentences, in Stabbing Planes and Sum-Of-Squares.
We finish by investigating the complexity-theoretic impact of the choice of method of generating these propositional contradictions in Sherali-Adams
On homogeneous spaces for diagonal ind-groups
We study the homogeneous ind-spaces
where is a strict diagonal ind-group defined by a
supernatural number and is a parabolic ind-subgroup
of . We construct an explicit exhaustion of
by finite-dimensional partial flag
varieties. As an application, we characterize all locally projective
-homogeneous spaces, and some direct products of such
spaces, which are -homogeneous for a fixed
. The very possibility for a -homogeneous
space to be -homogeneous for a strict diagonal
ind-group arises from the fact that the automorphism
group of a -homogeneous space is much larger than
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