Related papers: Markoff Surfaces and Strong Approximation: 1

We construct a moduli space of adequately marked Enriques surfaces that have a supersingular K3 cover over fields of characteristic $p \geq 3$. We show that this moduli space exists as a scheme locally of finite type over $\mathbb{F}_p$.…

We refine metrical statements in the style of the Khintchine-Groshev Theorem by requiring certain coprimality constraints on the coordinates of the integer solutions.

We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…

New exact modular branching rules are obtained for modules over the symmetric groups that are close to completely splittable modules. These results are based on some upper bounds for the Ext^1-spaces between simple modules.

We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…

We prove the modularity of a positive proportion of abelian surfaces over $\mathbf{Q}$. More precisely, we prove the modularity of abelian surfaces which are ordinary at $3$ and are $3$-distinguished, subject to some assumptions on the…

We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and…

We prove the rationality of the coarse moduli spaces of Coble surfaces and of nodal Enriques surfaces over the field of complex numbers.

We prove a "strong" Durfee-type inequality for isolated hypersurface surface singularities, which implies Durfee's strong conjecture for such singularities with non-negative topological Euler number of the exceptional set of the minimal…

We survey a research program on the strong convergence of unitary and permutation representations of discrete groups. We also take the opportunity to flesh out details that have not appeared elsewhere.

We classify completely the infinite, planar triangulations satisfying a weak spatial Markov property, without assuming one-endedness nor finiteness of vertex degrees. In particular, the Uniform Infinite Planar Triangulation (UIPT) is the…

Let K be the function field of a curve over the complex field. Let X be a homogeneous space of a semisimple linear algebraic group. Strong approximation holds for X outside any finite nonempty set of places of K. Strong approximation fails…

It is proved that the number of deformation types of complex structures on a fixed oriented smooth four-manifold can be arbitrarily large. The considered examples are locally simple abelian covers of rational surfaces.

Following [GS22], [LM20] and [CWX20], we study the Brauer-Manin obstruction for integral points on similar Markoff-type cubic surfaces. In particular, we construct a family of counterexamples to strong approximation which can be explained…

We study strong approximation of the equation N_{L/k}(x) = \prod_{i=1}^n p_i(t) where L/k is a finite extension of number fields and p_i(t)'s are distinct irreducible polynomials over k. We prove this equation satisfies strong approximation…

We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…

We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…

The main purpose of this paper is to prove some density results of polynomials in Fock spaces of slice regular functions. The spaces can be of two different kinds since they are equipped with different inner products and contain different…

For prime degree hypersurfaces of dimension at least 3, Mori asked if every smooth proper limit is still a hypersurface. Interestingly in dimensions 1 and 2, this is not the case. For example, Griffin constructed explicit families of…

Suppose $S$ is a smooth projective surface over an algebraically closed field $k$, $\mathcal{L}=\{L_1,\ldots,L_n\}$ is a full strong exceptional collection of line bundles on $S$. Let $Q$ be the quiver associated to this collection. One…