Related papers: Combinatorial geometry takes the lead
In this expository article we present Rosenlicht's work on geometric class field theory, which classifies abelian coverings of smooth, projective, geometrically connected curves over perfect fields.
Homological Projective duality (HP-duality) theory, introduced by Kuznetsov [42], is one of the most powerful frameworks in the homological study of algebraic geometry. The main result (HP-duality theorem) of the theory gives complete…
It is proposed by Chen et. al. to represent the gauge fields in theories with local symmetries as a sum of "physical" and "pure gauge" fields which to be treated separately. Here we show that after quantization this representation leads to…
This is a concise version of the original article in [arXiv:2203.17115] that will be published in the String Math 2022 Proceedings by the American Mathematical Society.
The new millennium's qualitative advances in relativistic heavy ion physics are in part due to, and are in part causing, a new appreciation for quantitative rigor in both experimental and theoretical work in the field. In these proceedings…
We classify $G$-solid rational surfaces over the field of complex numbers.
By adding or removing appropriate structures to Gauss diagram, one can create useful objects related to virtual links. In this paper few objects of this kind are studied: twisted virtual links generalizing virtual links; signed chord…
Haga's fold in paper folding is generalized. Recent generalization of Haga's theorems and problems in Wasan geometry involving Haga's fold are also generalized.
In this paper the free gauge field theories on a Riemann surface of any genus are quantized in the covariant gauge. The propagators of the gauge fields are explicitly derived and their properties are analysed in details. As an application,…
We generalize the notion of a coloring complex of a graph to linearized combinatorial Hopf monoids. We determine when a linearized combinatorial Hopf monoid has such a construction, and discover some inequalities that are satisfied by the…
The seminal concept of characteristic polygon of an embedded algebroid surface, first developed by Hironaka, seems well suited for combinatorially (perhaps even effectively) tracking of a resolution process. However, the way this object…
This is a chapter in an incoming book on aperiodic order. We review results about the topology, the dynamics, and the combinatorics of aperiodically ordered tilings obtained with the tools of noncommutative geometry.
The field of relativistic heavy-ion collisions is introduced to the high-energy physics students with no prior knowledge in this area. The emphasis is on the two most important observables, namely the azimuthal collective flow and jet…
In this lecture, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker's thesis. We also prove a Hodge decomposition for the twisted cohomology of a compact generalized K\"ahler…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets, and to provide computational tools for multipath…
This is a survey paper about a selection of recent results on the geometry of a special class of Fano varieties, which are called of K3 type. The focus is mostly Hodge-theoretical, with an eye towards the multiple connections between Fano…
It is noteworthy that symmetric teleparallel gravity has attracted considerable attention in recent years. A survey of the literature indicates that this surge of interest became particularly prominent around 2017 and 2018. However,…
This contribution highlights recent results from the PHENIX Collaboration at RHIC. It covers global variables, flow and 2--particle correlations. A second contribution in this issue, by T.C.Awes, covers PHENIX results on heavy quarks,…
Derangements are a popular topic in combinatorics classes. We study a generalization to face derangements of the n-dimensional hypercube. These derangements can be classified as odd or even, depending on whether the underlying isometry is…