Main Theme: Mathematical Physics

(In particular, Rigorous theories of **Critical Phenomena and Quantum
Field Theory**)

I have been studying various ** critical phenomena, ** mostly
in a mathematicaly rigorous way. Roughly speaking, *critical
phenomena* occurs in a system consisting of (infinitely) many small
components, as a result of mutual interaction of the components. This is
an interesting topic for Physics, chemistry, and of course for math.

Mathematically, critical phenomena could be seen as representations of some
kind of limit theorems. As such, critical phenomena poses a big challenge
to probability theory, because interesting critical behaviour can be seen
only in systems **with strong correlations**, where familiar
limit theorems (like Central Limit Theorem) are violated.

I have worked on the following different (but mutually related) subjects:

- Classical Spin Systems.
- Self-Avoiding Walks.
- Percolation.
- Lattice Trees and Animals.
- Gravitational collapse.

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Copyright 2000-present, Takashi Hara.