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.
On higher category theory and physics in view of Hilbert's sixth problem:
Yuri Ximenes Martins, Rodney Josué Biezuner, Towards An Approach to Hilbert’s Sixth Problem: A Brief Review, 2020 (hal:02909681, pdf). Submitted
Yuri Ximenes Martins, Categorical and Geometrical Methods in Physics, Master’s thesis, UFMG, 2018. (pdf, slides)
On obstructions to realize gravity (as Einstein–Hilbert–Palatini theories) in geometries other than Lorentzian and Riemannian:
Yuri Ximenes Martins, Rodney Josué Biezuner, Topological and Geometric Obstructions on Einstein-Hilbert-Palatini Theories, Journal of Geometry and Physics Volume 142, August 2019, Pages 229-239. (arXiv:1808.09249)
Yuri Ximenes Martins, Rodney Josué Biezuner, Geometric Obstructins on Gravity, 2019, (arXiv:1912.11198)
On the classification problem of extensions of Yang-Mills-Type theories:
Yuri Ximenes Martins, Luiz Felipe Andrade Campos, Rodney Josué Biezuner, On Extensions of Yang-Mills-Type Theories, Their Spaces and Their Categories, 2020, (arXiv:2007.01660). Submitted
Yuri Ximenes Martins, Luiz Felipe Andrade Campos, Rodney Josué Biezuner, On Maximal, Universal and Complete Extensions of Yang-Mills-Type Theories, 2020, (arXiv:2007.08651). Submitted
On the axiomatization problem of Astrophysics:
Yuri Ximenes Martins, Daniel de Souza Plácido Teixeira, Luiz Felipe Andrade Campos, Rodney Josué Biezuner, Constraints Between Equations of State and Mass-Radius Relationships in General Clusters of Stellar Systems, Phys. Rev. D 99, 023007 (2019). (arXiv:1808.09306)
Yuri Ximenes Martins, Luiz Felipe Andrade Campos, Daniel de Souza Plácido Teixeira, Rodney Josué Biezuner, Existence and Classification of Pseudo-Asymptotic Solutions for Tolman-Oppenheimer-Volkoff Systems, Annals of Physics, v. 409, p. 167929, 2019. (arXiv:1809.02281)
On a program attempting to get existence and multiplicity results for geometric objects on $C^k$-manifolds fulfilling arbitrarily given regularity conditions.
Yuri Ximenes Martins, Rodney Josué Biezuner, Existence of $B^k_{\alpha,\beta}$-Structures on $C^k$-Manifolds, 2019. (arXiv:1908.04442). To appear in São Paulo Journal of Mathematical Sciences
Yuri Ximenes Martins, Rodney Josué Biezuner, Geometric Regularity Results on $B_{\alpha,\beta}^{k}$-Manifolds, I: Affine Connections, 2020. (arXiv:1910.03113). To appear in Methods of Functional Analysis and Topology
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.
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):
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.
Currently I am (co)advising three master students (joint Rodney Josué Biezuner). For past advising, see here.
Mayk Alves de Andrade, Modal Homotopy Type Theory on the Foundations of Physics, started 2019/2
Daniel de Souza Plácido Teixeira, Higher Quantization, started 2020/1
Pedro Brunialti Lima de Andrade, Abstract Stable Homotopy Theory, started 2020/1
Last revised on April 22, 2021 at 14:26:49. See the history of this page for a list of all contributions to it.