Max Reinhold Jahnke

I am a postdoctoral researcher at the Federal University of São Carlos. My research interests lie at the intersection of Partial Differential Equations, Several Complex Variables, and Differential Geometry. I am a specialist in local and global solvability for involutive structures, and I have a growing interest in complex and CR structures. I also have experience on how to use algebraic properties of invariant involutive structures on compact Lie groups to understand some analytical properties of such structures. Besides mathematics, my hobbies are cycling, making beer, playing guitar and eventually playing video games.

Education and Professional Preparation

Publications and pre-prints

Research Articles

• G. Hoepfner, M. R. Jahnke and V. Novelli. Normalization, optimal regularity, and solvability in Gevrey classes of vector fields near trapped orbits. To appear at Proceedings of the AMS.
• M. R. Jahnke. Elliptic involutive structures on compact Lie groups. Accepted for publication at Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
• P. D. Cordaro and M. R. Jahnke. Top-degree global solvability in CR and locally integrable hypocomplex structures. The Journal of Geometric Analysis (2021). https://doi.org/10.1007/s12220-020-00573-1
• N. Braun Rodrigues, G. Chinni, P. D. Cordaro and M. R. Jahnke. Lower order perturbation and global analytic vectors for a class of globally analytic hypoelliptic operators. Proceedings of the American Mathematical Society (2016), 144(12), 5159-5170. https://doi.org/10.1090/proc/13178.

Preprints

• H. Jacobowitz and M. R. Jahnke. Levi-flat CR structures on compact Lie groups. Submitted.

• G. Araújo, I. A. Ferra, M. R. Jahnke and L. F. Ragognette. On finiteness of the cohomology spaces of involutive systems on compact manifolds. In preparation.
• G. Araújo, M. R. Jahnke and B. de Lessa Victor. Hypoelliptic involutive structures on compact Lie groups. In preparation.

Complete Work in Conference Proceedings

• P. D. Cordaro and M. R. Jahnke. (2012). Expansão Assintótica em Classes de Gevrey. Atas do VI Simpósio de Iniciação Científica e Pós-graduação do Instituto de Matemática e Estatística da Universidade de São Paulo, São Paulo, Brazil.
• M. V. P. Garcia, S. R. L. Garcia and M. R. Jahnke. (2008). O teorema de Arzelà-Ascoli e aplicações à análise. Atas do IV Simpósio de Iniciação Científica e Pós-Graduação do IME-USP, São Paulo, Brazil.

Extended Abstract in Conference Proceedings

• J. M. P. Soler, A. H. Ribeiro and M. R. Jahnke. (2017). A produção da cerveja produzindo conhecimento. Anais do 3o Congresso de Graduação da Universidade de São Paulo, Pró-Reitoria de Graduação – PRG.

Doctoral Dissertation and Master’s Thesis

• Doctoral dissertation – M. R. Jahnke. (2018). Top-degree solvability for hypocomplex structures and the cohomology of left-invariant involutive structures on compact Lie groups. University of São Paulo, São Paulo, Brazil. DOI: 10.11606/T.45.2019.tde-25032019-092801
• Master’s Thesis – M. R. Jahnke. (2013). A equação de Euler e a análise assintótica de Gevrey. University of São Paulo, Brazil. DOI: 10.11606/D.45.2013.tde-07022014-205830

Talks and posters

• N. Braun Rodrigues, G. Chinni, P. D. Cordaro and M. R. Jahnke. (2017). Global analytic hypo-elliptic operators on compact Lie groups and a perturbation result for a new class of analytic operator on the torus. 2017. Poster presentation in 9th Workshop on GEOMETRIC ANALYSIS OF PDEs and SEVERAL COMPLEX VARIABLES).
• M. R. Jahnke. (2012). Expansão Assintótica de Gevrey. Talk in VI Simpósio de Iniciação Científica e Pós-graduação do IME-USP.
• M. V. P. Garcia, S. R. L. Garcia and M. R. Jahnke. (2008). O Teorema de Arzelà-Ascoli e Aplicações à Análise. Talk in IV Simpósio de Iniciação Científica e Pós-graduação.

Grants and Scholarships

Participation in Conferences and Workshops