Some documents below
Click on the title to view
June, 2007
Comment: This is a general investigation of the situation of Quantum Gravity research in 2007. Quantum Gravity has been a main domain of research for me during many years.
June 15, 2008
Comment: This is my Master Thesis, it should have dealt with a vague study of some paper from Tim and Vladimir Dokchishter, I was zealed enough to make a general presentation of the theory underlying L-functions and of what goes with it. It can be useful for students entering the theory of L-functions.
February 8, 2013
Comment: This are general slides, written fast, about the fields of Arithmetic and Diophantine Geometry. It can be used to introduce various questions.
November 28, 2013
Comment: I took the risk to ask a difficult question of "why Mathematics?" are the best suited language for science and therefore progress. This is short but can be interesting, I hope I will develop this further some day.
March 19, 2014
Comment: A short essay about the coming role of geometry in Diophantine contexts. Since the work of Alexander Grothendieck in Algebraic Geometry, settled in the context of Number Fields by Suren Arakelov, Diophantine Geometry has evolved quite a lot in a very few decades. I argue that we are just at the beginning of this geometrization that is full of promises.
2014 (Revised-06-08-2017)
Comment: A (very short) text relating my work on Lang's Conjecture to its mathematical background.
2014
Comment: I tried here to question very general things about Heuristics, this is extremely general.
February 18, 2014
Comment: Here I question what is certainly a main conceptual mistake in current Physics: turning around the maths while forgetting the true issues. The fact is that we have now quite exhausted all the possible mathematical theories to address Physics issues and that it is very improbable that the next step in Physics will be done thanks to the Maths but much more probable that it will be done thanks to a completely new physical insight.
July , 2014
Comment: This is a short text that tends to demonstrate that Alexander Grothendieck has been certainly a much better geometer than RenÃ© Descartes was.
November 26, 2015
Comment: This are the slides from a talk at Institut de MathÃ©matiques de Jussieu.
November 22, 2016
Comment: Official defended version of my Ph.D. Thesis. I mainly prove an explicit lower bound for the Faltings height involving non-archimedean invariants and some consequences. From this, one can conjecture an explicit formula for the Faltings height.
March 6, 2017
Comment: This is a very hard job I did about the proof of Lang's height conjecture. It took me some years of intensive research to do it. This Conjecture was a leading conjecture in the field of Diophantine and Arithmetic Geometry. This work solve the problem completely, both by providing a sharp effective version of the conjecture and by providing in complement an almost optimal bound on the cardinality of the torsion group of elliptic curves (Submitted).