These are notes for a short course and some talks gave at Departament of Mathematics and at Departament of Physics of Federal University of Minas Gerais, based on the author's paper arXiv:1808.09249.… Expand

In this paper we continue the program on the classification of extensions of the Standard Model of Particle Physics started in arXiv:2007.01660. We propose four complementary questions to be… Expand

In this paper we propose an axiomatization for the notion of strong emergence phenomenon between field theories depending on additional parameters, which we call parameterized field theories. We… Expand

In this paper we introduce $B_{\alpha,\beta}^{k}$-manifolds as generalizations of the notions of smooth manifolds with $G$-structure or with $k$-bounded geometry. These are $C^{k}$-manifolds whose… Expand

In this article functorial Feynman rules are introduced as large generalizations of physicists Feynman rules, in the sense that they can be applied to arbitrary classes of hypergraphs, possibly… Expand

In this paper we consider the existence problem of affine connections on $C^{k}$-manifolds $M$ whose coefficients are as regular as one needs. We show that if $M$ admits a suitable subatlas, meaning… Expand