arXiv research

Classifies markings on translation surfaces from covering constructions.

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…

Predict cell loads in cellular networks using statistical learning of geometric marks.

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

The paper extends intensity models for limit order books using marked point processes.

Develops quasi-likelihood analysis for marked point processes and applies it to Hawkes processes.

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

This paper tackles efficient learning for factorial marked temporal point processes.

Introduces a new class of hybrid processes combining Markov chains and Hawkes processes.

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.

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.

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.

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

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.

Paper tackles reinforcement learning for asynchronous events.

A new double quasi-Poisson bracket on surface groups.

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

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

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…

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.'

Study periodic points on genus two surfaces, solving dynamics and geometry problems.

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…

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…

Study shows certain manifolds uniquely determined by X-ray data.

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.

A new method uses Transformers for efficient prediction of marked point processes.

Study on moduli spaces of branched projective structures on surfaces.

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…