Related papers: Poncelet and the arquimedean twins
We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial objects called Ptolemy diagrams which already appeared in our earlier work on…
In this note new properties for the Gossez example are presented in regard to its representability, closedness, and maximal monotonicity with respect to the two dual systems it naturally inhabits.
The classification of Grassmannian cluster algebras resembles that of regular polygonal tilings. We conjecture that this resemblance may indicate a deeper connection between these seemingly unrelated structures.
In this note, we establish a duality result under the residue paring between certain two-dimensional adelic spaces, which are associated to a closed point on an arithmetic surface.
In this paper, using an algebraic approach, it is intended to show that the Goldbach's and Twin primes conjectures are true, building, for each $m>2$, an isomorphism between posets. One of the posets is the set of coprimes less than $m$,…
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
Three types of reciprocity laws for arithmetic surfaces are established. For these around a point or along a vertical curve, we first construct $K_2$ type central extensions, then introduce reciprocity symbols, and finally prove the law as…
Cocycles are constructed by polynomial expressions for Alexander quandles. As applications, non-triviality of some quandle homology groups are proved, and quandle cocycle invariants of knots are studied. In particular, for an infinite…
The algebraic foundation of tropical polynomial algebra provides the framework for the geometric construction of the supplement and the reversal of tropical varieties, thereby inducing a duality of reduced tropical varieties; for classes of…
The Coble cubics were discovered more than a century ago in connection with genus two Riemann surfaces and theta functions. They have attracted renewed interest ever since. Recently, they were reinterpreted in terms of alternating…
Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean…
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
Recent development on non-Abeliann vortices and monopoles is reviewed with an emphasis on their relevance on confinement and duality. A very recent construction of non-Abelian vortices which do not dynamically Abelianize is crucial in this…
We derive some, seemingly new, curious additive relations in the Pascal triangle. They arise in summing up the numbers in the triangle along some vertical line up to some place.
We study equivalence relation of the set of triangles generated by similarity and operation on a triangle to get a new one by joining division points of three edges with the same ratio. Using the moduli space of similarity classes of…
Let X be a smooth elliptic fibration over a smooth base B. Under mild assumptions, we establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an O^* gerbe over a genus one fibration which is a…
We work with completed adelic structures on an arithmetic surface and justify that the construction under consideration is compatible with Arakelov geometry. The ring of completed adeles is algebraically and topologically self-dual and…
We give some equivalent characterizations of $\mathcal{GP}$, the class of Gorenstein $(\mathcal{L}, \mathcal{A})$-projective modules, and construct some model structures associated to duality pairs and Frobenius pairs. Moreover, some rings…
We prove a conjecture of Bhatt-Hansen that derived pushforwards along proper morphisms of rigid-analytic spaces commute with Verdier duality on Zariski-constructible complexes. In particular, this yields duality statements for the…
We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an intersection of certain Laurent polynomial rings.…