Category Archives: Topology

AMS Notices Spotlight October 2017

Hello and welcome to the October AMS Notices Spotlight. As we are now into the swing of the busyness of the semester it is sometimes nice to take a break and think about math not related to our classes. With … Continue reading

Posted in Algebra, AMS, Mathematics in Society, Topology | Tagged , , | Leave a comment

Real Numbers Base…Factorials! And A By-product

PROPOSITION 1:  For a real number  x  there exists a sequence $ x_1, x_2, x_3,…$ of integers such that $ \hspace{4cm} x=x_1 +\frac{x_2}{2!}+\frac{x_3}{3!} + \cdots + \frac{x_n}{n!} + \cdots,  \hspace{2cm} (*) $ where $x_1$ can be any integer, but for … Continue reading

Posted in Math, Topology | Tagged , | Leave a comment

Gauge Theory and Low-Dimensional Topology (Part II: Smooth Four-Manifolds)

In the last post, I attempted to give an overview of the state of affairs in four-manifold topology leading up to the introduction of gauge theory. In particular, we discussed the correspondence between (topological) four-manifolds and their intersection forms afforded by … Continue reading

Posted in Math, Topology | Tagged , | 2 Comments

Donaldson Turns 60

“Donaldson has opened up an entirely new area; unexpected and mysterious phenomena about the geometry of 4-dimensions have been discovered. Moreover, the methods are new and extremely subtle, using difficult nonlinear partial differential equations. On the other hand, this theory … Continue reading

Posted in Algebraic Geometry, Math, Topology | Tagged , , | Leave a comment

Gauge Theory and Low-Dimensional Topology (Part I: Historical Context)

Hi! This month, I thought I would start a brief series of articles describing the uses of gauge theory in mathematics. Rather than discuss current research directions in gauge theory (of which there are many), I hope to give an … Continue reading

Posted in Math, Topology | Tagged , | 1 Comment