According to the work of Laitinen, Morimoto, Oliver and Pawałowski, a finite group has a smooth effective one fixed point action on some sphere if and only if is an Oliver group. For some finite Oliver groups of order up to , and for for , we present a strategy of excluding o…
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48 results for “Oliver groups”
New Oliver groups confirm a conjecture about sphere actions.
problem Confirming the Smith question for finite groups acting on spheres.
method Induction of group representations to find new Oliver groups.
result Found an infinite family of Oliver groups satisfying the Laitinen Conjecture.
Paper disproves a Smith conjecture about sphere actions.
problem Smith conjecture about sphere actions with two fixed points.
method Induction of group representations to show counterexamples.
result Negative answer to Smith conjecture for specific groups.
The game of plates and olives, introduced by Nicolaescu, begins with an empty table. At each step either an empty plate is put down, an olive is put down on a plate, an olive is removed, an empty plate is removed, or the olives on two plates that both have olives on them are combined on one of the two plates, with the …
Formula establishes determinant majorization for symmetric matrices.
problem Determining determinant majorization for symmetric matrices.
method Establishes determinant majorization formula for symmetric matrices using invariant Garding-Dirichlet polynomials.
result Formula for symmetric matrices.
We show that a complete flat pseudo-Riemannian homogeneous manifold with non-abelian linear holonomy is of dimension at least 14. Due to an example constructed in a previous article by Oliver Baues and the author, this is a sharp bound. Also, we give a structure theory for the fundamental groups of complete flat pseudo…
-Regret for Learning in Markov Decision Processes with Function Approximation and Low Bellman Rankcs.LG
In this paper, we consider the problem of online learning of Markov decision processes (MDPs) with very large state spaces. Under the assumptions of realizable function approximation and low Bellman ranks, we develop an online learning algorithm that learns the optimal value function while at the same time achieving ve…
Machine learning predicts Shafarevich-Tate group orders of elliptic curves.
problem Predicting the order of the Shafarevich-Tate group of elliptic curves.
method Train feed-forward neural network and regression models on elliptic curve invariants.
result Models achieve high accuracy () and predict orders not seen during training.
We study the sample complexity of model-based reinforcement learning (henceforth RL) in general contextual decision processes that require strategic exploration to find a near-optimal policy. We design new algorithms for RL with a generic model class and analyze their statistical properties. Our algorithms have sample …
Responds to a statistical method for policy learning.
problem Improving policy learning efficiency.
method Optimal retargeting approach.
result Discussion and response to previous work.
Binary differential equations at parabolic and umbilical points for -parameter families of surfacesmath.DG
We determine local topological types of binary differential equations of asymptotic curves at parabolic and flat umbilical points for generic -parameter families of surfaces in by comparing our projective classification of Monge forms and classification of general BDE obtained by Tari and Oliver. In pa…
The paper establishes a majorization result for symmetric matrices.
problem Majorization of symmetric matrices under certain conditions.
method Using Garding-Dirichlet operator and properties of -central operators.
result A definitive inequality for symmetric matrices.
We study the computational tractability of PAC reinforcement learning with rich observations. We present new provably sample-efficient algorithms for environments with deterministic hidden state dynamics and stochastic rich observations. These methods operate in an oracle model of computation -- accessing policy and va…
We present label gradient alignment, a novel algorithm for semi-supervised learning which imputes labels for the unlabeled data and trains on the imputed labels. We define a semantically meaningful distance metric on the input space by mapping a point (x, y) to the gradient of the model at (x, y). We then formulate an …
Proves existence of Killing fields in smooth spacetimes with compact Cauchy horizons.
problem Existence of Killing fields in smooth spacetimes with compact Cauchy horizons.
method Normalized surface gravity of compact non-degenerate Cauchy horizons in smooth vacuum spacetimes.
result Proves the Isenberg-Moncrief conjecture on the existence of Killing fields.
The underlying objective of food authentication studies is to determine whether unknown food samples have been correctly labelled. In this paper we study three near infrared (NIR) spectroscopic datasets from food samples of different types: meat samples (labelled by species), olive oil samples (labelled by their geogra…
Study reward-free RL in non-linear settings, improving efficiency and removing assumptions.
problem Improving sample efficiency in reward-free reinforcement learning for non-linear function approximation.
method Proposed RFOLIVE algorithm for minimal structural assumptions, analyzed hardness results for reward-free and reward-aware exploration.
result Statistical efficiency and hardness results under various structural assumptions, no need for reachability or explorability assumptions.
We prove that the second derived subdivision of any rectilinear triangulation of any convex polytope is shellable. Also, we prove that the first derived subdivision of every rectilinear triangulation of any convex 3-dimensional polytope is shellable. This complements Mary Ellen Rudin's classical example of a non-shella…
Often, more time is spent on finding a model that works well, rather than tuning the model and working directly with the dataset. Our research began as an attempt to improve upon a simple Recurrent Neural Network for answering "simple" first-order questions (QA-RNN), developed by Ferhan Ture and Oliver Jojic, from Comc…
New BE dimension measure reveals rich RL problems with sample-efficient algorithms.
problem Finding sample-efficient algorithms for complex RL problems.
method Introducing Bellman Eluder (BE) dimension and designing GOLF and OLIVE algorithms.
result GOLF and OLIVE algorithms learn near-optimal policies for low BE dimension problems with polynomial samples.
3D RadViz improves 3D data visualization of multidimensional datasets.
problem Tackles the challenge of visualizing multidimensional datasets in 3D.
method Develops RadViz3D, a 3D radial visualization tool with uniform anchor points.
result Improves the display of multidimensional datasets, especially for uncorrelated variables.
New link groups are derived from torus necklaces, connecting braid groups to reflection groups.
problem Understanding the relationship between braid groups and reflection groups.
method Constructing torus necklaces and linking them to braid groups of -reflection groups.
result Link groups of torus necklaces are precisely braid groups of -reflection groups, with meridians as braid reflections.
The study proves super-rigidity of Gromov's random monster group for various types of groups.
problem Super-rigidity of Gromov's random monster group in various group types.
method Proof of morphisms having finite image and introduction of hereditary super-rigidity.
result Gromov's random monster group has super-rigidity and hereditary super-rigidity with respect to certain groups.
We study the structure of the virtual braid group. It is shown that the virtual braid group is a semi--direct product of the virtual pure braid group and the symmetric group. Also, it is shown that the virtual pure braid group is a semi--direct product of free groups. From these results we obtain a normal form of words…
Virtual twin groups map to symmetric groups, revealing automorphism structure.
problem Understanding homomorphisms between virtual twin groups and symmetric groups.
method Using irreducible right-angled Coxeter groups and right-angled Artin groups.
result A complete description of homomorphisms between virtual twin groups and symmetric groups, including the structure of the automorphism group of .
Characterizes group connections on group bundles.
problem Understanding connections on group bundles.
method Characterizes connections as affine spaces and uses the Ambrose-Singer theorem.
result Group connections form an affine space over cocycles.
Totally Symmetric Setsmath.GR
Study on totally symmetric sets with group applications.
problem Understanding totally symmetric sets and their group applications.
method Survey of existing theory and applications to various groups.
result Exploration of totally symmetric sets in multiple group contexts.
Affine cactus groups are CAT(0) and hyperbolic.
problem Characterizing geometric properties of affine cactus groups.
method Analyzing CAT(0) and hyperbolic properties through group theory.
result Affine cactus groups of degree three are hyperbolic.
The study restricts groups in graph of groups structures.
problem Realizing groups as fundamental groups of graph of groups with restricted vertex groups.
method Analyzes restrictions on groups that can be realized and applies to manifold construction.
result Places constraints on groups that can be realized in graph of groups structures.
New Garside structures found for torus knot groups and related braid groups.
problem Finding Garside structures for torus knot groups and related braid groups.
method Introducing a new Garside monoid for -torus knot groups and other braid groups.
result New Garside structures for -torus knot groups and related braid groups are constructed.
Logarithmic separation profile in hyperbolic groups shows hierarchical structure.
problem Understanding hierarchical structure in hyperbolic groups with logarithmic separation.
method Proving groups with logarithmic separation split over cyclic groups and providing counterexamples.
result Not all groups with hierarchical structure have logarithmic separation profile.
New Garside structures derived from groups, leading to new group properties.
problem Creating Garside structures from groups and Artin groups.
method Method for turning direct product of a group G by Z into a Garside group.
result Proved new cases of K(π,1)-conjecture for some hyperbolic type Artin groups.
We describe a procedure for constructing a generalized Thompson group out of a family of groups that is equipped with what we call a cloning system. The previously known Thompson groups F, V, Vbr and Fbr arise from this procedure using, respectively, the systems of trivial groups, symmetric groups, braid groups and pur…
The group of 2-by-2 matrices with integer entries and determinant can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional torus. Thus this group is the beginning of three natural sequences of groups, name…
The study restricts normal subgroups of Kähler groups, proving specific cases and general restrictions.
problem Characterizing normal subgroups of Kähler groups.
method Analyzing embeddings and conjugation actions of surface groups and one-ended hyperbolic groups.
result Restrictions on normal subgroups of Kähler groups, including virtual direct products and surface group properties.
Toric reflection groupsmath.GR
New reflection groups derived from torus knots with finite meridians.
problem Understanding reflection groups derived from torus knot groups with finite meridians.
method Using the theory of J-groups and Coxeter groups, study quotients of torus knot groups.
result Classification of toric reflection groups and their properties.
Graphically discrete groups have strong rigidity properties.
problem Understanding the rigidity of group actions on graphs.
method Introducing graphical discreteness and proving rigidity properties.
result Free products of graphically discrete groups are action rigid.
Paper proves vanishing homology groups for certain hyperbolic groups.
problem Understanding homology groups of specific hyperbolic groups.
method Using twisted Wirtinger presentations to prove homology group vanishing.
result Second homology groups vanish for certain Gromov hyperbolic groups.
Study fundamental groups of geometric transformation groups using loop spaces.
problem Understanding fundamental groups of geometric transformation groups.
method Use differential forms on loop spaces to prove infinite fundamental groups.
result Proves infinite fundamental groups for specific geometric transformation groups.
Simple construction of Lie 2-groups from loop group extensions.
problem Constructing Lie 2-groups from loop group extensions.
method Using conjugation action of loop group on its central extension.
result Simple construction of string 2-group as a strict Fréchet Lie 2-group.
Study knot invariants using automorphism groups of free nilpotent groups.
problem Developing knot invariants using automorphism groups.
method Nilpotently -localization of knot groups and automorphism groups of free nilpotent groups.
result Maps from outer automorphism groups yield knot invariants.
We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface group. Also, we obtain a characterization of those Lie groups which admit a dens…
We exhibit a family of infinite, finitely-presented, nilpotent-by-abelian groups. Each member of this family is a solvable S-arithmetic group that is related to Baumslag-Solitar groups, and everyone of these groups has a quasi-isometry group that is virtually a product of a solvable real Lie group and a solvable p-adic…
The study shows that certain groups can be uniquely identified by their finite abelian summands.
problem Identifying groups based on their finite abelian summands.
method Analyzing hyperbolic groups as graphs of free groups with cyclic edge groups.
result Free products of free and surface groups are profinitely rigid.
Discrete Coxeter groupsmath.GT
Survey on Coxeter groups for Lie group examples.
problem Understanding Coxeter groups and their applications.
method Constructing discrete subgroups of Lie groups using Coxeter groups.
result Coxeter groups provide new examples in discrete subgroups of Lie groups.
In this paper, we briefly review some of the known results concerning the cohomological structures of the mapping class group of surfaces, the outer automorphism group of free groups, the diffeomorphism group of surfaces as well as various subgroups of them such as the Torelli group, the IA outer automorphism group of …
The paper studies actions on Bass-Serre trees and identifies new -simple groups.
problem Investigating actions of fundamental groups on Bass-Serre trees and their -algebraic properties.
method Analyzing boundary actions of fundamental groups of graphs of groups on their Bass-Serre trees.
result Identification of new families of -simple groups, including tubular groups and certain graphs of groups.
In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular, for two copies of the same group, the twisted product of group by itself throug…