Related papers: An Algebraic Structure for the Central Mexican Rit…

We construct an arithmetic period map for cubic fourfolds, in direct analogy with Rizov's work on K3 surfaces. For each $N\geq 1$, we introduce a Deligne-Mumford stack $\widetilde{\mathcal{C}^{[N]}}$ of cubic fourfolds with level structure…

A perpetual calendar, a calendar designed to find out the day of the week for a given date, employs a rich arithmetical calculation using congruence. Zeller's congruence is a well-known algorithm to calculate the day of the week for any…

We study the statistics of Hamiltonian cycles on various families of bicolored random planar maps (with the spherical topology). These families fall into two groups corresponding to two distinct universality classes with respective central…

We study period integrals of CY hypersurfaces in a partial flag variety. We construct a holonomic system of differential equations which govern the period integrals. By means of representation theory, a set of generators of the system can…

For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmueller space of the surface. On the geometric…

Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the…

A wealth of geometric and combinatorial properties of a given linear endomorphism $X$ of $\R^N$ is captured in the study of its associated zonotope $Z(X)$, and, by duality, its associated hyperplane arrangement ${\cal H}(X)$. This…

This text is an introduction to algebraic enumerative geometry and to applications of tropical geometry to classical geometry, based on a course given during the X-UPS mathematical days, 2008 May 14th and 15th. The aim of this text is to be…

We describe explicitly the algebraic structure of the Terwilliger algebra of wreath products of cyclic schemes.

We investigate a type of lunar calendar known as lists of the 'nights of the moon', found throughout East Polynesia, including Rapa Nui (Easter Island). Using computational methods, we analyzed the lexical and structural divergence of 49…

In this article we study domino tilings of a family of finite regions called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in the four outer sub-regions, every tile lines up with nearby…

Let $W$ be a complex reflection group. We formulate a conjecture relating blocks of the corresponding restricted rational Cherednik algebras and Rouquier families for cyclotomic Hecke algebras. We verify the conjecture in the case that $W$…

We compute the cobordism ring $MU^*(BG)\otimes \mathbb{F}_p$ when $G$ is a Chevalley group. In the particular case of the general linear group, we prove that it agrees with the Chow ring (as defined by Totaro).

We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of intrinsic topological order with the spontaneous breaking of discrete time-translation symmetry. We show…

The group theoretical description of the periodic system of elements in the framework of the Rumer-Fet model is considered. We introduce the concept of a single quantum system, the generating core of which is an abstract $C^\ast$-algebra.…

Accurate electricity consumption forecasting is essential for demand management and smart grid operations. This paper introduces a unified deep learning framework that integrates cyclical temporal encoding with hybrid LSTM-CNN architectures…

We explain how following the representation of 3D crystallographic space groups in geometric algebra it is further possible to similarly represent the 162 socalled subperiodic groups of crystallography in geometric algebra. We construct a…

The so-called Miccinelli documents are a set of documents which were written by Jesuit scholars in Peru within the first half of the 17th century. Among such documents, one contains the depiction of a Quipu, that is, a device made out of…

Let G be a virtually cyclic of the form (Z_a x Z_b) x Z or [Z_a x (Z b x Q_{2^i})] x Z. We compute the integral cohomology ring of G, and then obtain the periodicity of the Farell cohomology of these groups.

We use the subgraph replacement method to investigate new properties of the tilings of regions on the square lattice with diagonals drawn in. In particular, we show that the centrally symmetric tilings of a generalization of the Aztec…