Classifies 1-connected Lorentzian manifolds with essential conformal groups.
problem Classifying Lorentzian manifolds with specific conformal groups.
method Proves existence of a metric making the manifold homogeneous and plane wave.
result Completes the classification of 1-connected Lorentzian manifolds with transitive conformal groups.
We study pseudo-Riemanniasn manifolds (M,g) with transitive group of conformal transformation which is essential, i.e. does not preserves any metric conformal to g. All such manifolds of Lorentz signature with non exact isotropy representation of the stability subalgebra are described. A construction of essential c…
Compact complex manifolds with specific group actions are conformally flat.
problem Compact complex manifolds with invariant conformal holomorphic structures.
method Study of manifolds with transitive and essentially acting complex semi-simple Lie groups.
result If a complex semi-simple Lie group acts transitively and essentially, the manifold is conformally flat.
Semisimple Lie groups act transitively on pseudo-Riemannian manifolds, making them flat.
problem Understanding actions of semisimple Lie groups on pseudo-Riemannian manifolds.
method Analyzing the pseudo-Riemannian Lichnerowicz conjecture in homogeneous settings.
result Compact pseudo-Riemannian manifolds on which a semisimple group acts conformally, essentially and transitively, are conformally flat.
Study of pseudo-Riemannian manifolds with M{ö}bius group actions.
problem Characterizing pseudo-Riemannian manifolds with specific group actions.
method Analyzing the action of the conformal group on compact manifolds.
result If the non-compact semi-simple part of the conformal group is M{ö}bius, the manifold is conformally flat.
Study non-transitive pseudo-Anosov flows using group actions.
problem Characterize pseudo-Anosov flows in 3-manifolds.
method Extend pseudo-Anosov action to non-transitive flows, use group actions on orbit spaces and boundary at infinity.
result Pseudo-Anosov flows in 3-manifolds are determined by their group actions on boundary at infinity.
Study character varieties of a Coxeter group in hyperbolic and Anti-de Sitter spaces.
problem Characterize the geometric transitions of a Coxeter group's holonomy representations.
method Analysis of rigidity properties and character varieties in hyperbolic and Anti-de Sitter spaces.
result Description of singularity at the collapse of a right-angled cuboctahedron.
We explicitly describe the Teichmuller space TH_n of hyperelliptic surfaces in terms of natural and effective coordinates as the space of certain (2n-6)-tuples of distinct points on the ideal boundary of the Poincare disc. We essentially use the concept of a simple earthquake which is a particular case of a Fenchel-Nie…
We define transit clusters to simplify causal diagrams and preserve their essential properties.
problem Clustering variables in causal diagrams can alter essential properties of causal effects.
method We define transit clusters and provide an algorithm to find them, ensuring they preserve causal effect identifiability.
result Transit clusters simplify causal effect identification and maintain their essential properties.
Paper details how to smoothly transition from EONIA to ESTR without significant financial impact.
problem Transition from EONIA to ESTR impacts financial instruments, especially OTC derivatives.
method Detailed analysis of how clean discounting approach based on ESTR affects pricing of OIS, IRS, and XVAs.
result The transition to EONIA-free pricing framework is safe and consistent, ensuring complete elimination of EONIA.
The paper proves conditions for the isomorphism between standard and dual Artin groups.
problem Conditions for the isomorphism between standard and dual Artin groups.
method Analyzes Coxeter systems and their actions on reduced words to prove isomorphisms.
result Proves conditions for the isomorphism between standard and dual Artin groups.
The paper studies a relative version of non-positive immersion for 2-complex pairs and shows conditions under which a transitivity law holds.
problem The study of collapsing non-positive immersion for 2-complex pairs and its implications.
method Introduced a relative version of collapsing non-positive immersion for 2-complex pairs (L,K) and proved a transitivity law under certain conditions. result Under certain conditions, a transitivity law holds: If (L,K) has relative collapsing non-positive immersion and K has collapsing non-positive immersion, then L has collapsing non-positive immersion. The paper extends group constructions to coset geometries, creating new ways to combine geometries.
problem Combining and gluing incidence geometries in a general framework.
method Extending classical group-theoretic constructions to coset geometries.
result Provides a general framework for combining or gluing incidence geometries.
Dual-T method improves transition matrix estimation in noisy label learning.
problem Large estimation error in noisy class posterior leads to poor transition matrix estimation.
method Introducing an intermediate class to avoid direct estimation of noisy class posterior, factorizing the transition matrix into two easier-to-estimate matrices.
result The dual-T estimator leads to better classification performances.
The study proves unique harmonic functions and combinatorial properties of vertex-transitive graphs.
problem Proving combinatorial properties of vertex-transitive graphs.
method Using harmonic functions and quasi-isometry to R, proving uniqueness and combinatorial results. result Connective constant of non-degenerate vertex-transitive graphs is at least the golden mean.
Proves constraints on groups extending Möbius transformations on spheres.
problem Constraints on groups extending Möbius transformations on spheres.
method Proved constraints through group transitivity and topological entropy analysis.
result Groups must be 4-transitive or arc 4-transitive, and contain elements of positive topological entropy.
The paper proves n-transitivity for equivariant diffeomorphisms of manifolds.
problem Proving n-transitivity for equivariant diffeomorphisms. method Analyzing the group of equivariant diffeomorphisms on proper smooth G-manifolds. result The group of equivariant diffeomorphisms acts n-transitively on M. Some groups of real analytic diffeomorphism act n-transitively for each finite n.
Starting with Lie's classification of finite-dimensional transitive Lie algebras of vector fields on C2 we construct Lie algebras of vector fields on the bundle C2×C by lifting the Lie algebras from the base. There are essentially three types of transitive lifts and we compute all o…
This paper studies actions of solvable Lie groups on nilpotent Lie groups.
problem Characterizing which solvable Lie groups can act simply transitively on nilpotent Lie groups.
method Using Lie algebra properties and semisimple splitting, the paper provides methods to check for such actions.
result A full description of possibilities for actions up to dimension 4.
In this paper, we study the behavior of Ricci-flat Kähler metrics on Calabi-Yau manifolds under algebraic geometric surgeries: extremal transitions or flops. We prove a version of Candelas and de la Ossa's conjecture: Ricci-flat Calabi-Yau manifolds related by extremal transitions and flops can be connected by a path c…
Develops a new framework for conditional independence.
problem Generalizing previous notions of conditional independence.
method Introduces transition probability spaces and transitional random variables.
result Satisfies all desired relevance relations except symmetry.
Consider a connected manifold of dimension at least two and the group of compactly supported diffeomorphisms that are compactly supported isotopic to the identity. This group acts n-transitive: Any tuple of n points can be moved to any other tuple of n points by a compactly supported diffeomorphism that is compac…
Using a characterization of parabolics in reductive Lie groups due to Furstenberg, elementary properties of buildings, and some algebraic topology, we give a new proof of Tits' classification of 2-transitive Lie groups.
The notion of n-transitivity can be carried over from groups of diffeomorphisms on a manifold M to groups of bisections of a Lie groupoid over M. The main theorem states that the n-transitivity is fulfilled for all n∈N by an arbitrary group of Cr-bisections of a Lie groupoid Γ of class Cr, w…
Study groups acting on trees with specific local actions, proving cohomology vanishing or infinite.
problem Understanding bounded cohomology of groups with prescribed local actions.
method Proving vanishing or infinite bounded cohomology based on the 2-transitivity of F′. result Vanishing or infinite bounded cohomology depending on F′'s 2-transitivity. New method improves robustness of deep learning with noisy labels.
problem Robust deep learning on corrupted labels with noisy samples.
method Meta-transition adaptation through clean meta data guidance.
result More accurate estimation of noise transition matrix and classifier parameters.
The existence of nonconstant harmonic Dirichlet functions on a Cayley graph of a discrete group is equivalent to the nonvanishing of the first L2-cohomology of the given group. It was first proven by Cheeger and Gromov that such functions do not exists on the Cayley-graph of an amenable group. The result was extended u…
Study assesses climate risks on supply chains and financial systems using detailed firm emissions data.
problem Lack of firm-level CO2 emissions data hinders assessment of transition risks from carbon pricing.
method Used detailed Hungarian firm emissions data and a simple economic ABM model to simulate carbon pricing impacts.
result 45% of companies are directly exposed to carbon pricing, leading to significant economic and financial losses.
This paper shows semi-equivelar toroidal maps are vertex-transitive covers.
problem Understanding the relationship between semi-equivelar and vertex-transitive toroidal maps.
method Proving semi-equivelar toroidal maps are quotients of vertex-transitive toroidal maps.
result Each semi-equivelar toroidal map has a finite vertex-transitive cover.
A novel approach models rating transitions using Lie groups and Deep Learning.
problem Modeling rating transitions with geometric properties and stochastic processes.
method Introducing Itô-SDEs on Lie groups, using TimeGAN for calibration, and examining rating matrix properties.
result The geometric approach using Lie groups and Deep Learning generates a good fit for rating transitions.
To any connected and simply connected nilpotent Lie group N, one can associate its group of affine transformations Aff(N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N, via such affine transformations. We succeed in translating the existence questio…
Weakly-irreducible not irreducible subalgebras of $\so(1,n+1)$ were classified by L. Berard Bergery and A. Ikemakhen. In the present paper a geometrical proof of this result is given. Transitively acting isometry groups of Lobachevskian spaces and transitively acting similarity transformation groups of Euclidean spaces…
The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation group, together with a diagram of how these groups are connected. In addition, we de…
We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial d-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on n≤13 vertices. With the exception of act…
New proof shows almost all surface group actions are dense.
problem Transitivity of normal subgroups on character varieties.
method Proved almost minimal action of non-trivial normal subgroups.
result Almost all points in character variety have dense orbits.
Study shows certain surface homeomorphisms groups can't be precompact.
problem Understanding precompactness of groups of surface homeomorphisms.
method Analyzing subgroup properties and transitivity of homeomorphisms.
result No subgroup of surface homeomorphisms can be Roelcke precompact.
This paper constructs quandles with abelian inner automorphism groups from graphs, proving their homogeneity.
problem Finding quandles with specific automorphism properties.
method Starting from simple graphs, the paper constructs quandles with abelian inner automorphism groups and proves their homogeneity.
result Homogeneous quandles with abelian inner automorphism groups are constructed from vertex-transitive graphs.
This paper shows how post-Lie algebra structures can be induced by simply transitive NIL-affine actions.
problem Understanding which solvable Lie groups can act simply transitively on nilpotent Lie groups.
method Introducing post-Lie algebra structures and showing their correspondence with simply transitive actions.
result Simply transitive NIL-affine actions induce complete post-Lie algebra structures in the 2-step nilpotent case.
634 vertex-transitive and over 10^103 non-vertex-transitive 27-vertex triangulations of octonionic projective plane.
problem Constructing and classifying triangulations of the octonionic projective plane.
method Combinatorial construction and analysis of symmetry groups.
result Found 634 vertex-transitive and over 10^103 non-vertex-transitive 27-vertex triangulations.
We establish a canonical correspondence between connected quandles and certain configurations in transitive groups, called quandle envelopes. This correspondence allows us to efficiently enumerate connected quandles of small orders, and present new proofs concerning connected quandles of order p and 2p. We also present…
Let G be a closed transitive subgroup of Homeo(S^1) which contains a non-constant continuous path f: [0,1] --> G. We show that up to conjugation G is one of the following groups: SO(2,R), PSL(2,R), PSL_k(2,R), Homeo_k(S^1), Homeo(S^1). This verifies the classification suggested by Ghys [Enseign. Math. 47 (2001) 329-407…
4 flat 3-manifolds realized in hyperbolic 4-space.
problem Realizing flat 3-manifolds in hyperbolic 4-space.
method Using finite-volume hyperbolic 4-manifolds with cusp sections.
result 6 closed orientable flat 3-manifolds realized as cusp sections.
Big mapping class groups of infinite type surfaces have infinite asymptotic dimension.
problem Understanding asymptotic dimension of big mapping class groups of infinite type surfaces.
method Analyzing big mapping class groups with coarsely bounded generating sets and essential shifts.
result Big mapping class groups of infinite type surfaces have infinite asymptotic dimension.
Study chaotic behavior in homeomorphism groups of countable products of spaces.
problem Investigate chaotic behavior in homeomorphism groups of countable products of various metrizable topological spaces.
method Construct numerous examples of chaotic groups of homeomorphisms of countable products of spaces.
result New chaotic groups of homeomorphisms of countable products of various metrizable topological spaces are discovered.
The paper uses machine learning and Lie groups to improve rating transitions and XVA calculations.
problem Improving rating transitions and XVA calculations using machine learning and Lie groups.
method Modeling rating transitions as SDEs on Lie groups, calibrating to historical and market data, applying Girsanov theorem, and using Deep Learning.
result Improves rating transitions and XVA calculations, making the model more robust.
This work proposes a new feature for transportation mode classification using GPS trajectories.
problem Classifying transportation modes from GPS trajectories to optimize urban mobility.
method The Ordinal Pattern Transition Graph and its self-transition probability are used for classification.
result The proposed feature outperforms existing methods in transportation mode classification.
A framework combining HSMM and survival analysis for lifecycle-oriented mobility analysis.
problem Understanding individual metro usage dynamics over multi-year horizons.
method A state-based lifecycle modeling framework integrating HSMM and discrete-time survival analysis.
result Identification of interpretable mobility states, transition dynamics, and state-dependent exit and re-entry processes.