Category Archives: Topology

AMS Notices Spotlight October 2017

Posted on October 10, 2017 by Taryn Laird

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 →

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Real Numbers Base…Factorials! And A By-product

Posted on September 20, 2017 by Behnam Esmayli

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 →

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

Posted on September 2, 2017 by Irving Dai

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 →

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

Posted on July 24, 2017 by Irving Dai

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 →

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