Related papers: Limiting characters at ideal points detecting twic…
We give two proofs that appropriately defined congruence subgroups of the mapping class group of a surface with punctures/boundary have enormous amounts of rational cohomology in their virtual cohomological dimension. In particular we give…
We study $\eta$-correction terms in the Kauffman bracket skein algebra of the once-punctured torus $K_t(\Sigma_{1,1})$. While the Frohman--Gelca product-to-sum rule gives an explicit multiplication formula on the closed torus, the…
We present a Hermite interpolation problem via splines of odd-degree which, to the best knowledge of the authors, has not been considered in the literature on interpolation via odd-degree splines. In this new interpolation problem, we…
We confirm the AJ conjecture [Ga04] that relates the A-polynomial and the colored Jones polynomial for those hyperbolic knots satisfying certain conditions. In particular, we show that the conjecture holds true for some classes of…
It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additions. The minimum number of such 1-handles is called the…
We describe limits of line bundles on nodal curves in terms of toric arrangements associated to Voronoi tilings of Euclidean spaces. These tilings encode information on the relationship between the possibly infinitely many limits, and…
We consider the standard site percolation model on the $d$-dimensional lattice. A direct consequence of the proof of the uniqueness of the infinite cluster of Aizenman, Kesten and Newman [Comm. Math. Phys. 111 (1987) 505-531] is that the…
Superconformal Ward identities are revisited in the context of superconformal line defects. Multipoint correlators of topological operators inserted on superconformal lines are studied. In particular, it is known that protected operators…
We study additive double character sums over two subsets of a finite field. We show that if there is a suitable rational self-map of small degree of a set $D$, then this set contains a large subset $U$ for which the standard bound on the…
Given a thin strip of paper, tie a knot, connect the ends, and flatten into the plane. This is a physical model of a folded ribbon knot in the plane, first introduced by Louis Kauffman. We study the folded ribbonlength of these folded…
We establish a Kauffman-Murasugi-Thistlethwaite-type theorem for alternating knots in a solid torus. Specifically, we show that any dotted-reduced alternating diagram of a knot in a handlebody realizes the minimal crossing number, and that…
In this paper, we study certain Kummer characters, which we call the elliptic Soul\'e characters, arising from Galois actions on the pro-$p$ fundamental groups of once-punctured elliptic curves with complex multiplication. In particular, we…
Principal curves are defined as parametric curves passing through the "middle" of a probability distribution in R^d. In addition to the original definition based on self-consistency, several points of view have been considered among which a…
We give a description of several representation varieties of the fundamental group of the complement of the figure eight knot in PGL(3,C) or SL(3,C). We moreover obtain an explicit parametrization of matrices generating the representation…
A torus-covering $T^2$-knot is a surface-knot of genus one determined from a pair of commutative braids. For a torus-covering $T^2$-knot $F$, we determine the number of irreducible metabelian $SU(2)$-representations of the knot group of $F$…
Norm resolvent approximation for a wide class of point interactions in one dimension is constructed. To analyse the limit behaviour of Schr\"odinger operators with localized singular rank-two perturbations coupled with {\delta}-like…
In this work we attempt to generalize our result in [6] [7] for real rings (not just von Neumann regular real rings). In other words we attempt to characterize and construct real closure * of commutative unitary rings that are real. We also…
Given a connected cobordism between two knots in the 3-sphere, our main result is an inequality involving torsion orders of the knot Floer homology of the knots, and the number of local maxima and the genus of the cobordism. This has…
In this paper we study a Kahler structure on finite points. In particular, we study the edge Laplacian of a graph twisted by the Kahler structure introduced in this paper. We also discuss a metric aspect from a twisted holomorphic…
The $k$-truss, introduced by Cohen (2005), is a graph where every edge is incident to at least $k$ triangles. This is a relaxation of the clique. It has proved to be a useful tool in identifying cohesive subnetworks in a variety of…