In mathematics, there are not only theorems. There are, what we call, “philosophies” or “yogas,” which remain vague. Sometimes we can guess the flavor of what should be true but cannot make a precise statement. When I want to understand a problem, I first need to have a panorama of what is around it. A philosophy creates a panorama where you can put things in place and understand that if you do something here, you can make progress somewhere else. That is how things begin to fit together.

Pierre René Deligne

Hello! This is Zhiyuan Liu‘s tiny math home.

I’m a doctoral student at Université Libre de Bruxelles with my research interest in differential geometry, especially for Seiberg-Witten gauge theory. Before that, I did my master degree in pure mathematcis at Université Normale de l’Capitale (Beijing, China), with my master thesis on the symplectic nature of meromorphic connections over the projective line.

I also have some interests in Hamiltonian dynamics (both for real and holomorphic), especially for integrable Hamiltonian systems. The main problem I’m concerning about is how to find the singular locus of the Liouville toric fibration, such as for Hitchin systems.

My tougne language is Chinese, my English CEF level is B2. I’m also learning some French to get used to the life in Belgium.

My mathematics blogs can be found in my blog page, and my PDF notes can be found in the PDF page. For a detailed Resumé, see here.