Related papers: Dynkin Systems and the One-Point Geometry

Let X be an algebraic curve. We study the problem of parametrizing geometric data over X, which is only generically defined. E.g., parametrizing generically defined (aka rational) maps from X to a fixed target scheme Y. There are three…

This article introduces moduli spaces of coloured graphs on which Feynman amplitudes can be viewed as 'discrete' volume densities. The basic idea behind this construction is that these moduli spaces decompose into disjoint unions of open…

In this article we generalise the structure of Connes-Kreimer Hpof algebra consisting of Feynmam diagrams to the situations of abstract finite sets, matrices and star product of scalar field, where the construction for the case of finite…

We sketch a proof of a conjecture of [FFKM] that relates the geometric Eisenstein series sheaf with semi-infinite cohomology of the small quantum group with coefficients in the tilting module for the big quantum group.

We give infinite series of groups Gamma and of compact complex surfaces of general type S with fundamental group Gamma such that 1) Any surface S' with the same Euler number as S, and fundamental group Gamma, is diffeomorphic to S. 2) The…

For simple, simply-connected compact Lie groups, Dynkin embedding indices obey a universal scaling law with a direct topological meaning. Given an inclusion $f:G\hookrightarrow H$, the Dynkin embedding index $j_f$ is characterized…

We consider the moduli space $\mathcal{R}_n$ of pairs of monic, degree $n$ polynomials whose resultant equals $1$. We relate the topology of these algebraic varieties to their geometry and arithmetic. In particular, we compute their…

Let $I \subset R = \mathbb{F}[x_1,x_2]$ be a height two ideal minimally generated by three homogeneous polynomials of the same degree $d$, where $\mathbb{F}$ is a field of characteristic zero. We use the theory of $D$-modules to deduce…

This is an English translation of the author's Ph.D. thesis, accumulating his results on a construction of Cohen-Macaulay modules over a polynomial ring that appeared in the study of Cauchy-Fueter equations. This construction is generalized…

We introduce a method for associating a chain complex to a module over a combinatorial category, such that if the complex is exact then the module has a rational Hilbert series. We prove homology--vanishing theorems for these complexes for…

We develop a version of $\mathrm{G}$-theory for an $\mathbb{F}_1$-algebra (i.e., the $\mathrm{K}$-theory of pointed $G$-sets for a pointed monoid $G$) and establish its first properties. We construct a Cartan assembly map to compare the…

The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…

We explore representing the compact subsets of a given represented space by infinite sequences over Plotkin's $\mathbb{T}$. We show that computably compact computable metric spaces admit representations of their compact subsets in such a…

We generalize a result of J. C. Kelly to the setting of Ahlfors $Q$-regular metric measure spaces supporting a $1$-Poincar\'e inequality. It is shown that if $X$ and $Y$ are two Ahlfors $Q$-regular spaces supporting a $1$-Poincar\'e…

We construct moduli spaces of complex affine and dilation surfaces. Using ideas of Veech, we show that the the moduli space of affine surfaces with fixed genus and with cone points of fixed complex order is a holomorphic affine bundle over…

In this paper, we propose a new method for evaluating scalar one-loop Feynman integrals in generalized D-dimension. The calculations play an important building block for two-loop and higher-loop corrections to the processes at future…

The aim of this paper is to clarify the relation between the following objects: $ (a) $ rank 1 projective modules (ideals) over the first Weyl algebra $ A_1(\C)$; $ (b) $ simple modules over deformed preprojective algebras $…

We consider the moduli space of stable principal G-bundles over a compact Riemann surface C of genus >1, with G a reductive algebraic group. We explicitly construct a map F from the generic fibre of the Hitchin map to a generalized Prym…

This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element…

The complex projective structures considered is this article are compact curves locally modeled on $\mathbb{CP}^1$. To such a geometric object, modulo marked isomorphism, the monodromy map associates an algebraic one: a representation of…