Related papers: Carrots for dessert

In his contribution to the Baker's Garden book, Faltings gives a family of examples of irreducible divisors $D$ on $\Bbb P^2$ for which $\Bbb P^2\setminus D$ has only finitely many integral points over any given localization of a number…

We develop a calculus based on graph enumeration for $S_n$-equivariant motivic invariants of graphically stratified moduli spaces. We apply our theory to the Deligne--Mumford moduli space $\overline{\mathcal{M}}_{g, n}$ and to the space of…

Given a manifold M with an action of a quadratic Lie algebra d, such that all stabilizer algebras are co-isotropic in d, we show that the product M\times d becomes a Courant algebroid over M. If the bilinear form on d is split, the choice…

Motivated by quite recent research involving the relationship between the dimension of a poset and graph-theoretic properties of its cover graph, we show that for every $d\geq 1$, if $P$ is a poset and the dimension of a subposet $B$ of $P$…

We consider multifractal Mandelbrot cascades supported on planar $C^2$ curves with nonvanishing curvature and show that their Fourier dimension is as large as possible, i.e., equal to the infimum of the lower pointwise dimension of the…

Braided deformations of (symmetric) monoidal categories are related to Vassiliev theory by a direct generalization of well-known results relating "quantum" knot invariants to Vassiliev invariants. The deformation theory of braidings is…

We use methods from algebra and discrete geometry to study the irreducibility of the dispersion polynomial of a discrete periodic operator associated to a periodic graph after changing the period lattice. We provide numerous applications of…

The category of exploded manifolds is an extension of the category of smooth manifolds related to tropical geometry in which some adiabatic limits appear as smooth families. This paper studies the dbar equation on variations of a given…

We give a necessary, and in some cases sufficient, condition for sliceness inside the family of pretzel knots $P (p_1,...,p_n)$ with one $p_i$ even. The three stranded case yields two interesting families of examples: the first consists of…

We study the special fibers of a certain class of absolutely simple abelian varieties over number fields with endomorphism rings $\bz$ and possessing $l$-adic monodromy groups of the least possible rank. We also study the Dirichlet density…

In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree structure, we establish a gap theorem, a…

Thurston parameterized quadratic invariant laminations with a non-invariant lamination, the quotient of which yields a combinatorial model for the Mandelbrot set. As a step toward generalizing this construction to cubic polynomials, we…

In this paper we consider some families of random Cantor sets on the line and investigate the question whether the condition that the sum of Hausdorff dimension is larger than one implies the existence of interior points in the difference…

We establish a cutting lemma for definable families of sets in distal structures, as well as the optimality of the distal cell decomposition for definable families of sets on the plane in $o$-minimal expansions of fields. Using it, we…

Let M be a complete non-compact connected Riemannian n-dimensional manifold. We first prove that, for any fixed point p in M, the radial Ricci curvature of M at p is bounded from below by the radial curvature function of some non-compact…

In this paper, we prove a result related to the deformation of complex submanifolds, modifying a result of Kodaira (Ann. Math, 75(1), 146-162, 1962).

We establish dimensional thresholds for dot product sets associated with compact subsets of translated paraboloids. Specifically, we prove that when the dimension of such a subset exceeds $ \frac{5}{4} = \frac{3}{2} - \frac{1}{4} $ in…

We introduce new invariants associated to collections of compact subsets of a symplectic manifold. They are defined through an elementary-looking variational problem involving Poisson brackets. The proof of the non-triviality of these…

We investigate using Clifford algebra methods the theory of algebraic dotted and undotted spinor fields over a Lorentzian spacetime and their realizations as matrix spinor fields, which are the usual dotted and undotted two component spinor…

We give a physical realization of the Bala-Carter labels that classify nilpotent orbits of semi-simple Lie algebras, for the case $\mathfrak{g}=A,D,E$. We start from type IIB string theory compactified on an $ADE$ singularity and study the…