arXiv research

The paper studies the twisted Calabi flow on Kähler manifolds.

Zeta functions for non-unitary twists are shown to have analytic continuation.

Survey on twisted dynamical zeta functions and Fried's conjecture.

Reconstruct Lie structures from functional-analytic data on groupoids.

Given a closed symplectic 4-manifold $(X,ω)$, we define a twisted version of the Gromov-Taubes invariants for $(X,ω)$, where the twisting coefficients are induced by the choice of a surface bundle over $X$. Given a fibered 3-manifold $Y$, we similarly construct twisted Lefschetz zeta functions associated with surface b…

Study of twisted Ruelle zeta function on hyperbolic manifolds and its relation to analytic torsion.

Analogous zeta function for twisted Alexander invariants defined.

Develops graphical calculus for monoidal categories with twisted pivotal structures.

Proves volume conjecture for twist knots using complex analysis.

We use SMC with twist functions to improve probabilistic inference in LLMs.

For $2+1$ spacetime dimensions, we derive sufficient conditions for the twisting function in a twisted product spacetime, such that there is a global foliation by spacelike CMC surfaces.

The paper generalizes inequalities on almost Kähler manifolds.

Tête-à-tête graphs were introduced by N. A'Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed tête-à-tête graphs provide a generalization which define mixed tête-à-tête twists, which are pseudo-periodic automorphisms on surfaces. We characterize the mixed tête-à-tête twists as those p…

Locally maximizing orbits studied in twist maps and billiards.

We introduce a notion of the twist of an isometry of the hyperbolic plane. This twist function is defined on the universal covering group of orientation-preserving isometries of the hyperbolic plane, at each point in the plane. We relate this function to a function defined by Milnor and generalised by Wood. We deduce v…

We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle $(E,H_0)$ over a Riemann surface $X$. It is already known the gradient flow with initial data $(A_0,φ_0)$ converges to a critical point $(A_\infty, φ_\infty)$ of this functional. Using a modified Chern-Wei…

Prove integrality of genus-$g$ indices with adjoint Reidemeister torsions for twist knots and meridians.

Analytic torsion equals dynamical zeta function for certain bundles.

Innovative warping labeling for twisted knots and braids.

Study characterizes 2-Killing vector fields on complex spacetimes.

Solves generalized twisted rabbit problems for higher degree polynomials.

Study of twisted $L^2$-torsion on 3-manifold character varieties.

We construct a new infinite family of ideal triangulations and H-triangulations for the complements of twist knots, using a method originating from Thurston. These triangulations provide a new upper bound for the Matveev complexity of twist knot complements. We then prove that these ideal triangulations are geometric. …

In this paper we study a proposal of Nekrasov, Rosly and Shatashvili that describes the effective twisted superpotential obtained from a class S theory geometrically as a generating function in terms of certain complexified length-twist coordinates, and extend it to higher rank. First, we introduce a higher rank analog…

In this paper we give an explicit formula for the twisted Alexander polynomial of any torus link and show that it is a locally constant function on the $SL(2, \mathbb C)$-character variety. We also discuss similar things for the higher dimensional twisted Alexander polynomial and the Reidemeister torsion.

Self-distillation improves constrained language generation by aligning models with target distributions.

This paper studies twisted signature invariants and twisted linking forms, with a view towards obstructions to knot concordance. Given a knot $K$ and a representation $ρ$ of the knot group, we define a twisted signature function $σ_{K,ρ} \colon S^1 \to \mathbb{Z}$. This invariant satisfies many of the same algebraic pr…

Improves inference-time alignment for diffusion models without updating weights.

We study incompressible surfaces constructed by Culler-Shalen theory in the context of twisted Alexander polynomials. For a $1$st cohomology class of a $3$-manifold the coefficients of twisted Alexander polynomials induce regular functions on the $SL_2(\mathbb{C})$-character variety. We prove that if an ideal point giv…

We characterize the fractional Dehn twist coefficient of a braid in terms of a slope of the homogenization of the Upsilon function, where Upsilon is the function-valued concordance homomorphism defined by Ozsváth, Stipsicz, and Szabó. We use this characterization to prove that $n$-braids with fractional Dehn twist coef…

This paper gives an explicit formula for the SL_2(C)-non-abelian Reidemeister torsion as defined in [Dub06] in the case of twist knots. For hyperbolic twist knots, we also prove that the non-abelian Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape o…

On a spin manifold with conformal cusps, we prove under an invertibility condition at infinity that the eta function of the twisted Dirac operator has at most simple poles and is regular at the origin. For hyperbolic manifolds of finite volume, the eta function of the Dirac operator twisted by any homogeneous vector bu…

Study measures invariant DH on twisted moduli spaces.

This note is to concern a generalization to the case of twisted coefficients of the classical theory of Abelian differentials on a compact Riemann surface. We apply the Dirichlet's principle to a modified energy functional to show the existence of differentials with twisted coefficients of the second and third kinds un…

In this paper, we consider the twisted Kähler-Ricci soliton, and show that the existence of twisted Kähler-Ricci soliton with semi-positive twisting form is closely related to the properness of some energy functionals. We also consider the conical Kähler-Ricci soliton, and obtain some existence results. In particular, …

Topological twists for 4d N=2 theories depend on spacetime type, gerbe connections, and generalized spin-c structures.

Paper studies Landsberg curvature of a specific Finsler metric.

The paper extends inequalities to twisted differential forms on Kähler manifolds.

We calculate the Chern-Simons invariants of the twist knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of the twist knot cone-manifold structures. Following the general instruction of Hilden, Lozano, and Montesinos-Amilibia, we here present the concrete formulae and calc…

Defines and calculates signature invariants for twisted linking forms.

We calculate the Chern-Simons invariants of the hyperbolic double twist knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of cone-manifold structures of double twist knots.

Unified framework designs LK structures using integer twists on non-manifold meshes.

The coefficients of twisted Alexander polynomials of a knot induce regular functions of the $SL_2(\mathbb{C})$-character variety. We prove that the function of the highest degree has a finite value at an ideal point which gives a minimal genus Seifert surface by Culler-Shalen theory. It implies a partial affirmative an…

The paper proves a vanishing identity for twist knots using character varieties.

New method deforms function algebras on manifolds using spectral decomposition.

We develop the theory of twisted L^2-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on the first de Rham cohomology of M and they generalize the standard notions. A new feature of the twisted L^2-cohomology theory is that in addition to sat…

The full 6d Hopf-Wess-Zumino term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying the higher analogue of level quantization familiar from the 2d Wess-Zumino term. We prove that the anomaly cancellation condition is implied by the hypothesis …

Study non-acyclic SL2-representations of twist knots and their L-functions.