- 2250 Elings Hall
- Q Seminar
One interpretation of contact geometry is that it puts the quasi-classical approximation of quantum mechanics into a simple Hamiltonian formulation. In the past 10 years there have been a number of results in contact geometry with a common theme: objects may have subtle and rich geometric properties, but after crossing a certain threshold size, the geometry dissolves away and all obstructions become purely topological.
This is particularly surprising since it seems that this phenomenon does not occur in symplectic geometry. One might expect that this is related to the uncertainty principle or some kind of micro/macro dichotomy, but so far the results are coming from geometric topology and remain physically uninterpreted. After reviewing the basics of contact geometry and connections with quantum mechanics we will present some results in this theme and explain what it means to reduce contact geometry to topology.