arXiv research

New Legendrian knots found with equivalent Stein traces.

New proof of wave trace formula for 3D-contact manifolds.

Clarifies a trace for Heisenberg operators on contact manifolds.

We prove that the trace of the logarithmic term of the Toeplitz kernel on a contact manifold is a contact invariant, generalizing K. Hirachi's invariant for the Szego kernel on a CR manifold. When the base manifold is the three-sphere, this vanishes identically.

Improved contact tracing models outperform NIST challenge results.

Study gradient flow of phase transitions with fixed contact angle.

We study the structure underlying Ng's conjecture, which relates the degree $0$ abelian knot contact homology of a knot $K$ to the coordinate ring of the $SL_2(\mathbf{C})$-character variety $X(Σ_2 K)$ of the $2$-fold branched cover of the $3$-sphere branched along $K$. Our approach is based on the study of (meridional…

New method detects close contacts to prevent SARS-CoV-2 spread.

We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct steady nonsingular solutions to the Euler equations on a Riemannian $S^3$ whose flowlines trace out closed curves of all possible knot and link types simultaneously. Using careful contact-topological …

Modeling infection hotspots to quantify effects of contact tracing and testing.

A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolods. All con…

The paper proves new curvature estimates in quaternionic contact geometry.

In this paper we study the small time asymptotics for the heat kernel on a sub-Riemannian manifold, using a perturbative approach. We then explicitly compute, in the case of a 3D contact structure, the first two coefficients of the small time asymptotics expansion of the heat kernel on the diagonal, expressing them in …

In this paper we produce several new invariants for CR and contact manifolds by looking at the noncommutative residue traces of various geometric projections. In the CR setting these operators arise from the Kohn-Rossi complex and include the Szegö projections on forms. In the contact setting they stem from the general…

We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray-Singer torsion on any 3-dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. In fact th…

This paper tackles efficient testing strategies for COVID-19 by using a partially observable MDP approach.

We prove several relations between spectrum and dynamics including wave trace expansion, sharp/improved Weyl laws, propagation of singularities and quantum ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional quasi-contact case. A key role in all results is played by the presence of abnormal geodesi…

We propose a purely algebraic approach to construct invariants of transversal links in the standard contact structure on the 3-sphere generalizing Jones' approach to invariant of usual links. The only geometry used is the analogue of Alexander and Markov theorems. More precisely, we construct a trace on a certain cubic…

This paper has four main parts. In the first part, we construct a noncommutative residue for the hypoelliptic calculus on Heisenberg manifolds, that is, for the class of Heisenberg PsiDOs introduced by Beals-Greiner and Taylor. This noncommutative residue appears as the residual trace on integer order Heisenberg PsiDOs…

CRISP predicts individual-level COVID-19 risk based on contact data.

We give an explicit construction of the Honda--Kazez--Matić gluing maps in terms of contact handles. We use this to prove a duality result for turning a sutured manifold cobordism around, and to compute the trace in the sutured Floer TQFT. We also show that the decorated link cobordism maps on the hat version of link F…

In the 3-dimensional Riemannian geometry, contact structures equipped with an adapted Riemannian metric are divergence-free, nondegenerate eigenforms of the Laplace-Beltrami operator. We trace out a 2-d analogue of this fact: there is a close relationship between the topology of the contact structure on a convex surfac…

We show that the $(4,5)$- and $(5,6)$-torus knots admit ghost characters. Consequently, these knots provide counterexamples to Ng's conjecture, which proposes an isomorphism between the complexification of degree $0$ abelian knot contact homology and the coordinate ring of the character variety of the $2$-fold branched…

We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows over closed prequantized symplectic manifolds in the context of geometric quantization of Kostant and Souriau. We express the associated evolution operators via paral…

R-circles in general three dimensional CR manifolds (of contact type) are the analogues to traces of Lagrangian totally geodesic planes on the sphere viewed as the boundary of two dimensional complex hyperbolic space. They form a family of certain legendrian curves on the manifold. We prove that a diffeomorphism betwee…

A conformal metric on a 4-ball induces on the boundary 3-sphere a conformal metric and a trace-free second fundamental form. Conversely, such a data on the 3-sphere is the boundary of a unique selfdual conformal metric, defined in a neighborhood of the sphere. In this paper we characterize the conformal metrics and tra…

An efficient algorithm for aligning diffusion trees to networks with information asymmetry.

Defines Wodzicki residue using groupoids and fibered distributions.

Agent-based model compares different COVID-19 testing policies and their effectiveness.

This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.

Study of torus surgeries on knot traces, finding exotic surfaces and traces.

Classifies knot traces with specific trisection genus limits.

Guillemin trace formula adapted for group actions.

Paper derives trace formula for magnetic Laplacian at zero energy.

In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch-Payne-Schiffer , Brock}, Raulot-Savo and Dittmar.

New methods derive a generalized Frenkel trace formula for Lie groups.

Examines a new type of analytic torsion on Riemannian manifolds.

Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.

Introduces a new model for mapping matrices to matrices, subsuming linear regression.

CausalSim corrects bias in trace-driven simulations for more accurate results.

New findings on knots and their traces, distinguishing L-space knots by their 0-trace.

This paper investigates the strength of the trace field as a commensurability invariant of hyperbolic 3-manifolds. We construct an infinite family of two-component hyperbolic link complements which are pairwise incommensurable and have the same trace field, and infinitely many 1-cusped finite volume hyperbolic 3-manifo…

We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.

Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.

Sharp inequality found on three-balls for fourth order Sobolev traces.

Infinite knots have non-integer trace values.

Introduces expected eligibility traces for more efficient credit assignment in reinforcement learning.

Quantum trace map defined for 3-manifolds with torus boundaries.