- Series
- Research Horizons Seminar
- Time
- Wednesday, October 23, 2013 - 12:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Dr. John Etnyre – School of Math – etnyre@math.gatech.edu – http://people.math.gatech.edu/~etnyre/
- Organizer
- Robert Rahm
Abstract: Four dimensions is unique in many ways. For example, n-dimensional Euclidean space has a unique smooth structure if and only if n is not equal to four. In other words, there is only one way to understand smooth functions on R^n if and only if n is not 4. There are many other ways that smooth structures on 4-dimensional manifolds behave in surprising ways. In this talk I will discuss this and I will sketch the beautiful interplay of ideas (you got algebra, analysis and topology, a little something for everyone!) that go into proving R^4 has more that one smooth structure (actually it has uncountably many different smooth structures but that that would take longer to explain).