Smooth 4-Manifolds

Series: 
Research Horizons Seminar
Wednesday, October 23, 2013 - 12:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
School of Math
,  
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).