Research
Research
Research
Research
3,263+ open-access research outputs.
We study the quantum Gromov-Hausdorff convergence of spectral truncations for compact quantum groups. Using a proper length function, we define a Dirac operator and the associated spectral truncations…
We establish a direct connection between the analytic data of weakly isolated mixed singularities and the topology of their associated links. More precisely, we prove that the existence of essential t…
In the previous paper, the author showed that for a smooth family $X \to \mathbb{X} \to B$ of a homotopy $K3$ surface, the obstruction for the tangent bundle along the fibers $T_B \mathbb{X}$ to have …
In this paper, we obtain a weighted trigonometric summation formula which is an extension of the trigonometric summation formula by Grigor'yan, Lin and Yau \cite{GLY}.…
We demonstrate a construction of products on the quantum torus $\mathbb{T}_\theta^2$ that generalises the usual construction of finite Riesz products on the commutative torus $\mathbb{T}^2$. We explai…
We prove a suitable fibration theorem over quasi-trivial tori that, through an approach developed by Harpaz and Wittenberg, implies so-called solvable descent. In particular, this gives a positive ans…
Semiclassical analysis and noncommutative geometry are two pillars of quantum theory. It's only recently that bridges between them have been emerging. In this monograph, we combine various techniques …
Given a thin torus $T_K$ around a knot $K\subset \mathbb{R}^3$, we construct Morse models of cord algebra $Cord(T_K)$ with $\mathbb{Z}$ and loop space coefficients. Using the Multiple time scale dynam…
We study independent sets in strong powers of circulant graphs using a transfer matrix formulation. The compatibility constraints separate into intra-layer and inter-layer components, yielding a trans…
Roman-type domination parameters form an important class of graph invariants that model protection and resource allocation problems on networks. Among them, $[k]$-Roman domination provides a unified f…
We determine the structure of the Kauffman bracket skein module of the connected sum of two genus one handlebodies over the ring of Laurent polynomials $\mathbb Z[q^{\pm 1}]$, thereby proving a conjec…
A torus-covering $T^2$-link of degree $n$ is a surface-link consisting of tori, in the form of an unbranched covering of degree $n$ over the standard torus. We focus on a torus-covering $T^2$-link of …
Motivated by resource defense models in networks, such as protecting territories with varying legion strengths, let $k \geq 2$ be an integer. Roman $k$-domination and strong Roman $k$-domination gener…
We prove that there exist infinitely many embedded tori with a common geometric dual in $T^4\#(S^2\times S^2)$ that are homotopic, diffeomorphic, but not isotopic to each other, even after arbitrary m…
In this paper, we study Morse functions with regular level sets consisting of spheres, tori, or Klein Bottles on $3$-dimensional closed manifolds. We characterize $3$-dimensional manifolds represent…
For pseudo-Anosov mapping tori with co-orientable invariant foliations and monodromies reversing their co-orientations, a family of taut foliations was constructed in previous work on Dehn fillings wi…
Lusztig (2024) recently introduced the space $\mathcal{T}_{>0}$ of totally positive maximal tori of an algebraic group $G$. Each such torus is the intersection of a totally positive Borel subgroup and…
We prove a motivic version of the Poisson formula on the adelic points of a split algebraic torus and apply it to the study of the motivic height zeta function of split projective toric varieties, in …
Using our previous work we give a tropical formula for disk potentials for Lagrangian tori in almost toric four-manifolds, that is, fibrations by Lagrangian tori with only toric and focus-focus singul…
We investigate the stable and retract rationality of multinorm one tori associated to finite {\'e}tale algebras. Our results are organized according to the greatest common divisor $d$ of the degrees o…
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