Dr. Benjamin Wagener

maths maths

Natural Reality

My interest for Mathematics and Physics goes as far in the past as I can remember. Reality is absolutely wonderful, infinitely more than what we usually consider in everyday life. I have been blocked on what is perhaps the most wonderful of all, Quantum Gravity, while I found my way through some of the most fundamental Mathematics up to date, Arithmetic and Diophantine Geometry. While I hesitated to continue because there are much more important for Mankind... I will...

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Documents

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  • June, 2007

    Some slides of 2007 on Quantum Gravity(in French)

    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

    A document on some "L"-facts

    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

    Linking Arithmetic and Geometry

    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

    Why Mathematics ?

    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

    Geometric Perspectives in Number Theory: The Revolution Begins

    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)

    Text about and around the proof of Lang's Conjecture.

    Comment: A (very short) text relating my work on Lang's Conjecture to its mathematical background.

  • 2014

    General Heuristics

    Comment: I tried here to question very general things about Heuristics, this is extremely general.

  • February 18, 2014

    Where is Physics?

    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

    Descartes vs Grothendieck

    Comment: This is a short text that tends to demonstrate that Alexander Grothendieck has been certainly a much better geometer than René Descartes was.

  • November 26, 2015

    Slides from an elementary talk about Heights

    Comment: This are the slides from a talk at Institut de Mathématiques de Jussieu.

  • November 22, 2016

    Published version of my Ph.D. Thesis

    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

    Proof of Serge Lang 's Height Conjecture and an almost optimal bound on the Torsion of Elliptic Curves

    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).