arXiv research

Local method identifies causal relations in Markov equivalent DAGs.

The paper extends local h-principles to complex structures on Stein manifolds.

Extends Gromov non-squeezing to locally conformally symplectic structures.

We obtain universal models for several types of locally conformal symplectic manifolds via pullback or reduction. The relation with recent embedding results for locally conformal Kähler manifolds is discussed.

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups whic…

Study groups with polynomial growth, finding structure and applications.

New scoring rule predicts causal relations from data with selection bias.

Investigate local Lie group structure of bisections over compact manifolds

Classifies complex Dirac structures with invariants and local structure.

Local tri-Hamiltonian structure for Ablowitz-Ladik hierarchy established.

Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The argument is based on a study of the Dirac operator defined with respect to the Killing connection. The existence of asympto…

In this paper we introduce the notion of deformation cohomology for singular foliations and related objects (namely integrable differential forms and Nambu structures), and study it in the local case, i.e., in the neighborhood of a point.

Study of recurrent Lorentzian Weyl spaces with detailed local and global structures.

All local solutions of the two dimensional Einstein-Weyl equations are found, and related to the compact examples which I obtained in "Moebius structures and two dimensional Einstein-Weyl geometry" J. reine angew. Math. 504 (1998).

Construct quaternionic-Kähler metrics from special Kähler manifolds with specific BPS structure variations.

Molino's description of Riemannian foliations on compact manifolds is generalized to the setting of compact equicontinuous foliated spaces, in the case where the leaves are dense. In particular, a structural local group is associated to such a foliated space. As an application, we obtain a partial generalization of res…

We present some examples of locally conformal symplectic structures of the first kind on compact nilmanifolds which do not admit Vaisman metrics. One of these examples does not admit locally conformal Kähler metrics and all the structures come from left-invariant locally conformal symplectic structures on the correspon…

Study local geometry of bi-contact structures on 3-manifolds.

We study bi-Hamiltonian systems of hydrodynamic type with non-singular (semisimple) non-local bi-Hamiltonian structures and prove that such systems of hydrodynamic type are diagonalizable. Moreover, we prove that for an arbitrary non-singular (semisimple) non-locally bi-Hamiltonian system of hydrodynamic type, there ex…

Study holonomy in pseudo-Hermitian geometry structures.

Unified framework for Arnold-type invariants via dual complexes and finite-difference structures.

HSSE framework embeds single-cell RNA-seq data at multiple scales.

We define pointwise partial differential relations for holomorphic discs. Given a relative homotopy class, a relation, and a generic almost complex structure we provide the moduli space of discs which have an injective point with the structure of a smooth manifold. Applications to the local behaviour are given and an a…

Study structural invariants of Goursat distributions related to curve singularities.

The paper generalizes Hodge theory to semisimple local systems and proves a geometric Decomposition theorem.

Alternative proof and description of orientations for instanton moduli spaces.

Model for dynamic relational data with regime changes.

We consider the problem of structure learning for Gaifman models and learn relational features that can be used to derive feature representations from a knowledge base. These relational features are first-order rules that are then partially grounded and counted over local neighborhoods of a Gaifman model to obtain the …

The abstract introduces golden Finsler structures and explores their local and global properties.

In this work, we formalize the problem of causal inference over graph-based relational time-series data where each node in the graph has one or more time-series associated to it. We propose causal inference models for this problem that leverage both the graph topology and time-series to accurately estimate local causal…

We interpret the variational inference of the Stochastic Gradient Descent (SGD) as minimizing a new potential function named the \textit{quasi-potential}. We analytically construct the quasi-potential function in the case when the loss function is convex and admits only one global minimum point. We show in this case th…

We prove some general results about the relation between the 1-cocycles of an arbitrary Lie algebroid $A$ over $M$ and the leaves of the Lie algebroid foliation on $M$ associated with $A$. Using these results, we show that a ${\cal E}^1(M)$-Dirac structure $L$ induces on every leaf $F$ of its characteristic foliation a…

In this paper the author determines necessary and sufficient conditions for existence of the Ehresmann connection on a manifold foliated by locally free action of the commutative Lie group. Also here we describe structure of $C_0(M)|_L$ for a leaf $L \subset M$ in case such a connection exists. Finally we give some res…

Conflict sets are loci of intersecting wavefronts emanating from $l$ different surfaces. We show that generically conflict sets are Legendrian: locally they admit the structure of wavefronts. Simple stable singularities for this problem in $\R^n$ occur when $0 \leq n-l \leq 4$. Other related sets, such as kite curves a…

We introduce a new algebraic structure called \textit{local biquandles} and show how colorings of oriented classical link diagrams and of broken surface diagrams are related to tribracket colorings. We define a (co)homology theory for local biquandles and show that it is isomorphic to Niebrzydowski's tribracket (co)hom…

We synthesize and extend the previous ideas about appearance of both noncommutative and Finsler geometry in string theory with nonvanishing B--field and/or anholonomic (super) frame structures \cite{vstring,vstr2,vnonc,vncf}. There are investigated the limits to the Einstein gravity and string generalizations containin…

In this note we clarify the relation between extended world-sheet supersymmetry and generalized complex structure. The analysis is based on the phase space description of a wide class of sigma models. We point out the natural isomorphism between the group of orthogonal automorphisms of the Courant bracket and the group…

Study bihamiltonian structures and Frobenius manifolds for specific Toda hierarchies.

Sharp bounds on diameter and eigenvalues for amply regular graphs.

In this paper we address the problem of modeling relational data, which appear in many applications such as social network analysis, recommender systems and bioinformatics. Previous studies either consider latent feature based models but disregarding local structure in the network, or focus exclusively on capturing loc…

Let $G/H$ be a contractible homogeneous Sasaki manifold. A compact locally homogeneous aspherical Sasaki manifold $Γ\big\backslash G/H$ is by definition a quotient of $G/H$ by a discrete uniform subgroup $Γ\leq G$. We show that a compact locally homogeneous aspherical Sasaki manifold is always quasi-regular, that is, $…

The goal of this work is to generalize the Gauss-Bonnet and Poincaré-Hopf Theorems to the case of orbifolds with boundary. We present two such generalizations, the first in the spirit of Satake. In this case, the local data (i.e. integral of the curvature in the case of the Gauss-Bonnet Theorem and the index of the vec…

The conformal Codazzi structure is an intrinsic geometric structure on strictly convex hypersufaces in a locally flat projective manifold. We construct the GJMS operators and the Q-curvature for conformal Codazzi structures by using the ambient metric. We relate the total Q-curvature to the logarithmic coefficient in t…

We show that symplectic forms taming complex structures on compact manifolds are related to special types of almost generalized Kähler structures. By considering the commutator $Q$ of the two associated almost complex structures $J_{\pm}$, we prove that if either the manifold is 4-dimensional or the distribution ${Im} …

It is known that the computation of the Poisson cohomology is closely related to the classification of singularities of Poisson structures. In this paper, we will first look for the normal forms of germs at (0,0) of Poisson structures on the real (or complex) plane and recall a result given by Arnold. Then, we will com…

Novel TRI-GNN framework improves graph classification robustness.

Proposes a method to improve hierarchical clustering using set-level structural priors.

These are notes for four lectures on higher structures in M-theory as presented at workshops at the Erwin Schroedinger Institute and Tohoku University. The first lecture gives an overview of systems of multiple M5-branes and introduces the relevant mathematical structures underlying a local description of higher gauge …