Related papers: Framings for graph hypersurfaces
We introduce, for every surface {\Sigma}, a two-way connection between FO transductions (first-order logical transformations) of the graphs embeddable in {\Sigma} and a certain variant of fan-crossing drawings of graphs in {\Sigma}. If the…
The goal of the present paper is to push forward the frontiers of computations on Farrell-Tate cohomology for arithmetic groups. The conjugacy classification of cyclic subgroups is reduced to the classification of modules of group rings…
We prove the quasimodularity of generating functions for counting torus covers, with and without Siegel-Veech weight. Our proof is based on analyzing decompositions of flat surfaces into horizontal cylinders. The quasimodularity arise as…
This article studies the mixed Hodge structures that appear on the complements of generalized theta divisors inside generalized Jacobians of curves with modulus. For a smooth or nodal curve with an effective modulus, the generalized…
Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…
In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by…
Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and $\varphi^k$ theories. Using dedicated graph theoretic tools…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
We associate to triangulations of infinite type surface a type of flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two triangulations can be related by a sequence of flips. A consequence of…
In this paper we investigate the Schwinger parametric representation for the Feynman amplitudes of the recently discovered renormalizable $\phi^4_4$ quantum field theory on the Moyal non commutative ${\mathbb R^4}$ space. This…
For a variety with a Whitney stratification by affine spaces, we study categories of motivic sheaves which are constant mixed Tate along the strata. We are particularly interested in those cases where the category of mixed Tate motives over…
We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are…
Let $\Gamma$ be a finite graph and let $A(\Gamma)$ be the corresponding right-angled Artin group. From an arbitrary basis $\mathcal B$ of $H^1(A(\Gamma),\mathbb F)$ over an arbitrary field, we construct a natural graph $\Gamma_{\mathcal B}$…
In this paper we give several criteria for the edge polytope of a fundamental FHM-graph to possess a regular unimodular triangulation in terms of some simple data of the the graph. We further apply our criteria to several examples of graphs…
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding…
We describe a technique to determine the automorphism group of a geometrically represented graph, by understanding the structure of the induced action on all geometric representations. Using this, we characterize automorphism groups of…
Using Beilinson's theory of f-categories, we prove that the triangulated category of Tate motives over a field k is equivalent to the bounded derived category of its heart, provided that k is algebraic over the rationals. This answers a…
In this paper we study the homology and cohomology of confguration spaces of two distinct particles on a graph. Our main tool is intersection theory for cycles in graphs. We obtain an explicit description of the cohomology algebra of the…
We consider the Tate cohomology of the circle group acting on the topological Hochschild homology of schemes. We show that in the case of a scheme smooth and proper over a finite field, this cohomology theory naturally gives rise to the…
We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we…