arXiv research

We classify GL(2,R) invariant point markings over components of strata of Abelian differentials. Such point markings exist only when the component is hyperelliptic and arise from marking Weierstrass points or two points exchanged by the hyperelliptic involution. We show that these point markings can be used to determin…

We show that all GL(2,R) equivariant point markings over orbit closures of translation surfaces arise from branched covering constructions and periodic points, completely classify such point markings over strata of quadratic differentials, and give applications to the finite blocking problem.

Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of point patterns, produces characteristics (marks) of the points. One aims at learnin…

New model captures time and mark inter-dependence in TPPs.

Disk and sphere graphs embed quasi-isometrically in R^2.

Proves Grothendieck-Teichmüller group acts on specific mapping class groups.

We study body-and-hinge and panel-and-hinge chains in R^d, with two marked points: one on the first body, the other on the last. For a general chain, the squared distance between the marked points gives a Morse-Bott function on a torus configuration space. Maximal configurations, when the distance between the two marke…

The study finds rational points on specific types of hypersurfaces.

Neural marked point processes show saturation with complexity, leading to new simple architectures.

We introduce a class of hybrid marked point processes, which encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class amalgamates such existing processes, it also contains novel processes with complex dynamics. These processes are defined implicitly via their intensity and a…

A new method clusters rows of a matrix of point processes.

The paper models user-advertiser interactions using point processes.

Paper introduces a neural network-based non-stationary influence kernel for complex event data.

This paper extends the analysis of Muni Toke and Yoshida (2020) to the case of marked point processes. We consider multiple marked point processes with intensities defined by three multiplicative components, namely a common baseline intensity, a state-dependent component specific to each process, and a state-dependent …

New method models MTPP without predefined intensity functions.

We show that the mapping class group of a handlebody of genus at least 2 (with any number of marked points or spots) is exponentially distorted in the mapping class group of its boundary surface. The same holds true for solid tori with at least two marked points or spots.

Three elements generate balanced superelliptic mapping class groups.

This paper introduces the factorial marked temporal point process model and presents efficient learning methods. In conventional (multi-dimensional) marked temporal point process models, event is often encoded by a single discrete variable i.e. a marker. In this paper, we describe the factorial marked point processes w…

Framework handles both exchangeable and non-exchangeable event sequences without tuning.

We develop a quasi-likelihood analysis procedure for a general class of multivariate marked point processes. As a by-product of the general method, we establish under stability and ergodicity conditions the local asymptotic normality of the quasi-log likelihood, along with the convergence of moments of quasi-likelihood…

Quantum duality map extended to general marked surfaces and its compatibility with skein algebras proven.

The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is given. The semi-stable and unstable cases are new, and it is shown that the flow …

Study Farrell cohomology for non-orientable surfaces, classifying subgroup conjugacy.

Estimates the rational homological dimension of Riemann surfaces with boundary and marked points.

A new framework generates high-dimensional event sequences efficiently.

Disk and sphere graphs embed quasi-isometrically into Euclidean spaces.

We show that all GL(2, R)-equivariant point markings over orbit closures of primitive genus two translation surfaces arise from marking pairs of points exchanged by the hyperelliptic involution, Weierstrass points, or the golden points in the golden eigenform locus. As corollaries, we classify the holomorphically varyi…

A new double quasi-Poisson bracket on surface groups.

In a wide variety of applications, humans interact with a complex environment by means of asynchronous stochastic discrete events in continuous time. Can we design online interventions that will help humans achieve certain goals in such asynchronous setting? In this paper, we address the above problem from the perspect…

Under the assumption that the X-ray transform over symmetric solenoidal 2-tensors is injective, we prove that smooth compact connected manifolds with strictly convex boundary, no conjugate points and a hyperbolic trapped set are locally marked boundary rigid.

We describe the moduli space of stable rank 2 parabolic bundles over an elliptic curve with 3 marked points.

We show that, on an oriented compact surface, two sufficiently $C^2$-close Riemannian metrics with strictly convex boundary, no conjugate points, hyperbolic trapped set for their geodesic flows, and same marked boundary distance, are isometric via a diffeomorphism that fixes the boundary. We also prove that the same co…

The study examines flip-graphs of non-orientable surfaces and their diameters.

We are interested in the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a triangulated marked surface $\mathbf{S}$ (without punctures). We prove that the spherical twist group ST of $\mathcal{D}$ is isomorphic to a subgroup (generated by braid twists) of the mapping class group …

Combining several previously known arguments, we prove marked length spectrum rigidity for surfaces with nonpositively curved Riemannian metrics away from a finite set of cone-type singularities with cone angles $>2π$. With an additional condition, we can weaken the requirement on one metric to `no conjugate points.'

It is known that every nontrivial knot has at least two quadrisecants. Given a knot, we mark each intersection point of each of its quadrisecants. Replacing each subarc between two nearby marked points with a straight line segment joining them, we obtain a polygonal closed curve which we will call the quadrisecant appr…

A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.

PUMA augments models to remove unique data points without performance loss.

This paper defines several algebras associated to an oriented surface $S$ with a finite set of marked points on the boundary. The first is the skein algebra $Sk_q(S)$, which is spanned by links in the surface which are allowed to have endpoints at the marked points, modulo several locally defined relations. The product…

Let $Σ$ be a surface with either boundary or marked points, equipped with an arbitrary framing. In this note we determine the action of the associated "framed mapping class group" on the homology of $Σ$ relative to its boundary (respectively marked points), describing the image as the kernel of a certain crossed homomo…

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish va…

Two Anosov metrics with same boundary distance are isometric.

We establish a product formula for Gromov-Witten invariants for closed, connected, relatively semi-positive Hamiltonian fibrations over any symplectic base. Furthermore, we show that the fibration projection induces a locally trivial (orbi-)fibration map from the moduli space of pseudo-holomorphic maps with marked poin…

Computes the decomposition of rank-three bundles over the projective line with three marked points.

Study of Teichmüller space geometry using infinitesimal and global methods.

Compute central extension of mapping class group from stated skein algebra

We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of the…

Study on moduli spaces of branched projective structures on surfaces.