Renan Assimos
Renan Assimos (Martins)
Max Planck Institute for Mathematics in the Sciences
Inselstraße 22, 04103 Leipzig, Germany
assimos@mis.mpg.de
Welcomão! I have graduated on July 2019 from my PhD studies at the Max Planck Institute for Mathematics in the Sciences in the research group Geometry, Analysis and Theoretical Physics . My advisor was Prof. Jürgen Jost.
I am currently a post-doc at the Max Planck Institute for Mathematics in the Sciences in the same research group; moving to industry soon.
I was interested in various topics within geometric analysis, the calculus of variations, differential geometry, and non-linear partial differential equations. In particular harmonic maps and minimal submanifolds of high codimension. Lately, I have `discretized' my interests and divided them into two subcategories. From the geometric view-point, I study harmonic maps defined on graphs, discrete Laplacians, hypergraphs and their applications to topological data analysis. From the analytical view-point, I go more into Stochastic analysis; more precisely, I am enthusiastic about Stochastic harmonic maps and Martingales on manifolds.
Projects and Preprints
- Assimos, R. and Jost, J. - The Geometry of Maximum Principles and a Bernstein Theorem in Codimension 2, 2018. Under Review. Preprint available on arXiv:1811.09869. PDF.
- Assimos, R. and Jost, J. - Harmonic maps from surfaces of arbitrary genus into spheres, 2019. Under Review. Preprint available on arXiv:1910.13966. PDF.
- Assimos, R. and Jost, J. - Spherical Bernstein Theorems for codimension 1 and 2, 2019. Submitted. Preprint available on arXiv:1910.14445. PDF.
- Assimos, R. - On the instersection of minimal hypersurfaces of $S^k$, 2020. Submitted. Preprint available on arXiv:2004.08358.
- Assimos, R.** - Curvature estimates for minimal submanifolds in codimension 2 , 2020. Status: Ready, but since this paper is fully based on the Bernstein theorem for codimension 2 on the pre-print above, we are only waiting for it to get published so we make this available.
Other notes
- Assimos, R. - The Geometry of Maximum Principles and a Bernstein Theorem in Codimension 2. PhD thesis, Leipzig University and the Max Planck Institute for Mathematics in the Sciences, 2019. PDF Photos1,2
- Assimos, R. - Riemannian Holonomy Groups (Based on the book of Dominic Joyce and J. Simons' proof of Berger's classification theorem. In Portuguese!) PDF.
Professional Service
- Referee for: Calculus of Variations and PDE
Invited Talks and Conferences
- Analysis Seminar of the University of Warwick, United Kingdom. May 2019. Organizer: Prof. Peter M. Topping.
Title: The Geometry of Maximum Principles and a Bernstein theorem for codimension 2.
- Analysis Seminar of the Scuola Normale Superiore di Pisa, Italy. April 2019. Organizer: Prof. Andrea Malchiodi. Photos1,2
Title: The Geometry of Maximum Principles and a Bernstein theorem for codimension 2.
- Analysis Seminar of the ETH Zürich, Switzerland. March 2019. Organizer: Prof. Michael Struwe. Photo
Title: The Geometry of Maximum Principles and a Bernstein theorem for codimension 2.
- Canadian Mathematical Society Meeting 2018, Vancouver, Canada. December 2018.
Title: The Geometry of Maximum Principles.
Teaching: Seminars and Lectures
- Sep(2019)-Mar(2020): Topics in Regularity Theory of Elliptic and Parabolic PDEs.
Audience: PhD students and Post-docs, Max Planck Institute for Mathematics in the Sciences.
- Sep(2018)-Mar(2019): Geometric Measure Theory, the regularity of Varifolds.
Audience: PhD students and Post-docs, Max Planck Institute for Mathematics in the Sciences.
- Aug(2017)-Jun(2018): The Analysis of harmonic maps and their heat flows.
Audience: PhD students and Post-docs, Max Planck Institute for Mathematics in the Sciences.
- Sep(2017)-Jul(2018): Coorganizer: Likbez seminar on basic notions of science and mathematics (Geometry and Analysis section).
Audience: PhD and Master students, Max Planck Institute for Mathematics in the Sciences.
- Aug(2013)-January(2015): Lecturer (Professor Substituto) Calculus IV \& Partial Differential Equations.
Audience: Engineering students, Universidade Federal do Rio de Janeiro.
- Aug(2013)-January(2015): Lecturer (Professor Substituto) Calculus I.
Audience: Engineering students, Universidade Federal do Rio de Janeiro.
Short Academic CV
References
- Prof. Jürgen Jost, Max Planck Institue for Mathematics in the Sciences.
- Prof. Camillo de Lellis, Institute for Advanced Study (homepage).
- Prof. Peter Topping, Warwick University (homepage).
- Prof. László Székelyhidi, Leipzig University.
- Prof. Stephan Luckhaus, Leipzig University.