"Most people would rather die than think; in fact they do so."
Bertrand Russell
As a matter of taste, I am interested in all kinds of physics-inspired beautiful mathematics, especially those with geometric flavors. In principle, I am also interested in some fundamental physics problems, and here is my first attempt in this area.
It is a fact that a lot of beautiful mathematics is hidden behind the embarrassingly simple physics models and some of the technically simple mathematical discoveries in the past had significant impact to the fundamental physics. In recent years I gradually realize that the mathematics behind the Kepler problem is quite rich and some of the new mathematical facts concerning the Kepler problem could be quite relevant to the fundamental physics.
In this project we uncover the rich mathematics hidden behind the Kepler problem and ponder at the physics meaning of the mathematical discoveries at the same time. Here is a list of motivations for this project. Here is a simple derivation of the three Laws of Kepler. Here is a summary of what has been found before 2010, and here is a talk I gave in December 2011. I make a mathematical living by working on this project.
"God always geometrizes", Plato
The goal of this project is to understand the geometric foundation of physics as much as possible. My current primary concern is gravity-related.
In my view, the most interesting and rewarding problem for mathematicians is this one: organize the fundamental physics in a simple, elegant, and logically coherent way. Currently we have bits and pieces scattered around, some pieces are inaccurate or simply wrong. It is like a nearly finished jigsaw puzzle game: we already have lots of pieces put in, though some pieces do not fit well.
The prospective PhD students are advised to click here.
Some interesting articles:
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