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The inclusion of fermionic loops contribution in Numerical Stochastic Perturbation Theory (NSPT) has a nice feature: it does not cost so much (provided only that an FFT can be implemented in a fairly efficient way). Focusing on Lattice…
A number of proposed extensions of the Standard Model include new strongly interacting dynamics, in the form of SU(N) gauge fields coupled to various numbers of fermions. Often, these extensions allow N = 3 as a plausible choice, or even…
I sketch what it is supposed to mean to quantize gauge theory, and how this can be made more concrete in perturbation theory and also by starting with a finite-dimensional lattice approximation. Based on real experiments and computer…
We discuss the inclusion of fermionic loops contributions in Numerical Stochastic Perturbation Theory for Lattice Gauge Theories. We show how the algorithm implementation is in principle straightforward and report on the status of the…
We present the geometric solutions to some variational problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape…
In memoriam N.G. de Bruijn. In this article I present some highlights of De Bruijn's contributions in combinatorics. This article does not survey his work on eg Penrose tilings, asymptotics or AUTOMATH; other surveys on these topics are…
The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and quantum), quantum field theory and cold atoms physics. The…
Wu's positive $\lambda$-calculus is a recent call-by-value $\lambda$-calculus with sharing coming from Miller and Wu's study of the proof-theoretical concept of focalization. Accattoli and Wu showed that it simplifies a technical aspect of…
Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…
By generalizing our previous work on the parity symmetry, the partition function of a Yang-Mills theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated…
The Graph Brain Project is an experiment in how the use of automated mathematical discovery software, databases, large collaboration, and systematic investigation provide a model for how mathematical research might proceed in the future.…
In this expository note, I present some of the key features of the lattice of torsion classes of a finite-dimensional algebra, focussing in particular on its complete semidistributivity and consequences thereof. This is intended to serve as…
The topic of this treatise is a combinatorial technique called Graph Pebbling. We investigate pebbling numbers, weight functions, flow networks, hypercubes, and the zero-sum conjecture of Erd\H{o}s and Lemke. This investigation is a…
With this work we aim to show how Mathematica can be a useful tool to investigate properties of combinatorial structures. Specifically, we will face enumeration problems on independent subsets of powers of paths and cycles, trying to…
In 2012, Chen Ning Yang received a 90th birthday gift in the form of a black cube inscribed with his 13 most important contributions, which cover four major areas of physics: statistical mechanics, condensed matter physics, particle physics…
Numerical simulations of supersymmetric theories on the lattice are intricate and challenging with respect to their theoretical foundations and algorithmic realisation. Nevertheless, the simulations of a four-dimensional supersymmetric…
This paper aims to recall some of the main contributions of Roberto Petronzio to QCD, with a particular regard to the period we have been working together. His seminal contributions span both the development of analytic computations using…
We use entropy to link fine-structure constant and cosmological constant. We also link nuclear force and gravity. We step on the fundamentals of consciousness for this new millennium with a scientific approach. Statistical and quantum…
Chen-Ning Yang made important contributions to the theory of solvable models in statistical mechanics, including generalizations of the Bethe Ansatz, magnetization in the Ising model, the Lee-Yang circle theorem, and the Yang-Baxter…
To a word $w$, we associate the rational function $\Psi_w = \prod (x_{w_i} - x_{w_{i+1}})^{-1}$. The main object, introduced by C. Greene to generalize identities linked to Murnaghan-Nakayama rule, is a sum of its images by certain…