# nLab Yuri Ximenes Martins

I am a PhD student at Departament of Mathematics of Universidade Federal de Minas Gerais (UFMG), Brazil.

I am mainly interested in applying (higher) categorical theory to Physics and Mathematics, and also in some aspects of differential geometry. Previously I was involved with mathematical aspects of Astrophysics.

The best way to contact me is through yurixm@ufmg.br.

I am co-founder of a research group on mathematical-physics and categorification called Math-Phys-Cat Group.

## Writings

### Papers and Preprints

On obstructions to realize gravity (as Einstein–Hilbert–Palatini theories) in geometries other than Lorentzian and Riemannian:

On the classification problem of extensions of Yang-Mills-Type theories:

On the axiomatization problem of Astrophysics:

On a program attempting to get existence and multiplicity results for geometric objects on $C^k$-manifolds fulfilling arbitrarily given regularity conditions.

On an axiomatization proposal to the notion of strong emergence between Lagrangian field theories:

A generalized and simplified version of the above work:

On a functorial extension of Feynman rules from Feynman graphs to structured hypergraphs.

### Textbooks and Lecture Notes

For the complete list, see here.

On an introduction to (algebraic) topology and differential geometry aiming the study of general spherically symmetric black holes (in Brazilian portuguese):

On an introduction to abstract homotopy theory by means of model categories and (infinity,1)-categories (in Brazilian Portuguese):

## Selected Talks

For the complete list, see here.

On the role of higher category theory in the foundations of physics:

• Category Theory in the Foundations of Physics, Colloquium of Mathematics, UFLA, 2016

• Towards an Approach to Hilbert’s Sixth Problem. I SEMAT, UFLA, 2017. Notes available here. See also (hal:02909681)

On a vertical categorification of Lie algebras (called Lie algebroidal categories) and a connection with Lie algebroids. A priori the Lie algebroidal categories differs from Lie 2-algebras of Baez-Crans, but further investigations are needed.

• Lie Algebroidal Categories, Young Algebraist Meeting, UFMG, 2020. (hal-02907904v1)