Related papers: Self-Intersection Numbers and Random Surfaces on t…
Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling…
We consider free symmetries on cobordisms between knots. We classify which freely periodic knots bound equivariant surfaces in the 4-ball in terms of corresponding homology classes in lens spaces. A key tool is the homology cobordism…
We introduce the concept of pseudo-trisections of smooth oriented compact 4-manifolds with boundary. The main feature of pseudo-trisections is that they have lower complexity than relative trisections for given 4-manifolds. We prove…
A longstanding avenue of research in orientable surface topology is to create and enumerate collections of curves in surfaces with certain intersection properties. We look for similar collections of curves in non-orientable surfaces. A…
The notion of topological entropy can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution $\varepsilon$ within $T$ time units. It can then be formally defined as a limit of a limit…
The term interlacing refers to systematic inequalities between the sequences of eigenvalues of two operators defined on objects related by a specific oper- ation. In particular, knowledge of the spectrum of one of the objects then implies…
This paper constructs a graded-commutative, associative, differential Transverse Intersection Algebra TIA {on the torus (in any dimension) with its cubical decomposition by using a probabilistic wiggling interpretation. This structure…
Let S, T be surfaces in P3. Suppose that S intersect T is set-theoretically a smooth curve C of degree d and genus g. Suppose that S and T have no common singular points. Then if C is not a complete intersection, then deg(S), deg(T) < 2d^4.…
The random vortex world-surface model is an infrared effective model of Yang-Mills dynamics based on center vortex degrees of freedom. These degrees of freedom carry topological charge through writhe and self-intersection of their…
We study the topologically twisted string theory on the general back-ground $AdS_3\times {\cal N}$ which is compatible with the world-sheet N=2 superconformal symmetry and is extensively discussed in the recent works (hep-th/9904024,…
In the projective plane over a finite field of characteristic not equal to 2, we compute the probability that a randomly selected pair of distinct conics $(\mathscr{A},\mathscr{B})$, with $\mathscr{A}$ smooth or singular and $\mathscr{B}$…
We study contact interactions for long world-lines on a curved surface, focusing on the average number of times two world-lines intersect as a function of their end-points. The result can be used to extend the concept of path-ordering, as…
A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics…
We study random tiling models in the limit of high rotational symmetry. In this limit a mean-field theory yields reasonable predictions for the configurational entropy of free boundary rhombus tilings in two dimensions. We base our…
A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of…
This article introduces the notion of L-tangle-free compact hyperbolic surfaces, inspired by the identically named property for regular graphs. Random surfaces of genus g, picked with the Weil-Petersson probability measure, are (a log…
We combine two partons on a random lattice as a vector state. In the ladder approximation, we find that such states have 1/p^2 propagators (after tuning the mass to vanish). We also construct some diagrams which are very similar to 3-string…
Spatial random permutations were originally studied due to their connections to Bose-Einstein condensation, but they possess many interesting properties of their own. For random permutations of a regular lattice with periodic boundary…
A discrete string theory --a theory of embeddings from ${\bf Z}\times {\bf Z}_C\to {\bf R}^D$, where $C$ is the number of components of the string-- is explored. The closure of the algebra of constraints (`${\bf Z}_C$-Virasoro algebra') is…
Statistical mechanics of infinite avalanches is studied in the framework of nonequilibrium random-field Ising model. Critical behavior of the model on a random graph (dilute Bethe lattice) is analyzed in detail. We show that sites with a…