2012 Fiscal Year Final Research Report
Gauge theory with infinite group actions
| Project/Area Number |
22540080
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
KATO Tsuyoshi 京都大学, 大学院・理学研究科, 教授 (20273427)
|
|---|
| Project Period (FY) |
2010 – 2012
|
| Keywords | 無限群 / 非コンパクト幾何解析 / スケール変換 |
|---|
| Research Abstract |
Tropical geometry connects discrete dynamical systems with automata. We used it to induce an analytic comparison theorem between mutually different rational dynamics or PDEs. We applied the method to theory of automata groups, particularly to Burnside groups and obtained a new example of infinitely quasi-recursive rational dynamical systems.
We constructed moduli theory of holomorphic curves over infinite dimensional almost Kaehler manifolds with high symmetry. As an application, we constructed Hamiltonian deformation of groups acting on trees, and verified that for some class of Hamiltonians, they must be always uniformly infinite in ours sense.
|
