Related papers: An equality between two towers over cubic fields

Suppose that \Delta, \Delta' are two buildings each arising from a semisimpe algebraic group over a field, a topological field in the former case, and that for both the buildings the Coxeter diagram has no isolated nodes. We give conditions…

This work starts with the observation of a certain "rule" (up to now unexplored) in the fundamental laws of Nature. We show some evidence of this, and formulate it as a fundamental principle which exhibits a number physical consequences. In…

A twin building consists of two buildings that are twinned by a codistance function. We prove that the local structure of a twin building uniquely determines the two buildings up to isomorphism. This has been known for twin buildings…

We show that even dimensional Fermat cubic hypersurfaces are rational over any field of characteristic different from three by producing explicit rational parametrizations given by polynomials of low degree. As a byproduct of our…

We construct the Effective Field Theory (EFT) of the teleparallel equivalent of general relativity (TEGR). Firstly, we present the necessary field redefinitions of the scalar field and the tetrads. Then we provide all the terms at…

Let $K$ be a function field over a finite field $k$ of characteristic $p$ and let $K_{\infty}/K$ be a geometric extension with Galois group $\mathbb{Z}_p$. Let $K_n$ be the corresponding subextension with Galois group…

We study functors F from C_f to D where C and D are simplicial model categories and C_f is the full subcategory of C consisting of objects that factor a fixed morphism f from A to B. We define the analogs of Eilenberg and Mac Lane's cross…

In arXiv:1409.6313 we proposed a formula for the 3-point structure constants of Toda field theory, derived using topological strings and the AGT-W correspondence from the partition functions of the non-Lagrangian $T_N$ theories on $S^4$. In…

To pave the way for the journey from geometry to conformal field theory (CFT), these notes present the background for some basic CFT constructions from Calabi-Yau geometry. Topics include the complex and Kaehler geometry of Calabi-Yau…

We study the representation theory of three towers of algebras which are related to the symmetric groups and their Hecke algebras. The first one is constructed as the algebras generated simultaneously by the elementary transpositions and…

We study K3 surfaces over non-closed fields and relate the notion of derived equivalence to arithmetic problems.

Let $P$ and $Q$ be polynomials in one variable over an algebraically closed field $k$ of characteristic zero. Let $f$ and $g$ be elements of a function field $\K$ over $k$ such that $P(f)=Q(g).$ We give conditions on $P$ and $Q$ such that…

The paper has two purposes. First, we start to develop a theory of infinite global fields, i.e., of infinite algebraic extensions either of ${\mathbb{Q}}$ or of ${\mathbb{F}}_r(t)$. We produce a series of invariants of such fields, and we…

Two singularity theorems can be proven if one attempts to let a Lorentzian cobordism interpolate between two topologically distinct manifolds. On the other hand, Cartier and DeWitt-Morette have given a rigorous definition for quantum field…

Roth's theorem is extended to finitely generated field extensions of $\Bbb Q$, using Moriwaki's framework for heights.

Let G be a semisimple quasi-split group defined over a global function field. We express the relative Tamagawa number of G in terms of local data including the number of types of special vertices in one orbit of the Bruhat-Tits building…

We give a general construction of topological groups from combinatorial structures such as trees, towers, gaps, and subadditive functions. We connect topological properties of corresponding groups with combinatorial properties of these…

We use real algebraic geometry to construct an affine $\Lambda$-building $B$ associated to the $\mathbb{F}$-points of a semisimple algebraic group, where $\mathbb{F}$ is a valued real closed field. We characterize the spherical building at…

Physics beyond the standard model can affect top-quark physics indirectly. We describe the effective field theory approach to describing such physics, and contrast it with the vertex-function approach that has been pursued previously. We…

An overview of the accomplishments of constructive quantum field theory is provided.