Topology

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What’s Important About UCSD’s Math Report—And What It Leaves Out
By Kyndall Brown and Robin Wilson As educators who have collectively spent 50-plus years of our lives on improving math teaching, we are normally pleased when math education gets attention in the newspapers. But a recent report from UC San Diego about declining math preparation has been a mixed blessing. Crucially, the report puts a spotlight...

AI solves an 80 year-old Erdős problem.
By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social  Much of the attention on uses of AI has focused of late on Anthropic’s Claude. In particular, Claude’s discovery of 23,000 potential security vulnerabilities across 1,000 Open Source Software products. With evidence like that, we should all assume that any publicly available software product we use has one or more security flaws....
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            Topology: A Categorical Approach

            Instructors of advanced undergraduate and beginning graduate topology courses find themselves with a happy dilemma of having several well-written texts to choose from to accompany their lectures.  Topology by Munkres, Introduction to Topological Manifolds by Lee, and Elementary Topology Problem Textbook by Viro et al., are just a few notable options.   Topology: A Categorical Approach aims to extend this selection even further.  The topological material it presents is fairly standard,...
            Cover of the book "Topology: A Categorical Approach" by Tai-Danae Bradley, Tyler Bryson, and John Terilla. The design features an abstract, dynamic pattern of light trails in red, white, and blue tones against a dark background, conveying a modern and conceptual feel. The title is in red and white text at the top left, with author names in white at the bottom left.

            Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory

            This book is an introduction to the intersection theory of punctured J-holomorphic curves in symplectic 4-manifolds with boundary and applications to symplectic cobordisms and fillings of contact 3-manifolds.  The main theme of the text is the use of the moduli space and intersection theory of punctured J-holomorphic curves to understand the structure of a symplectic 4-manifold, locally as a foliation and globally as a...
            Cover of the book "Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory" by Chris Wendl. The background is solid light blue. The title is written in bold, black capital letters, centered on the page. At the top, it reads “Cambridge Tracts in Mathematics” with the volume number “220.” Below the title, the author's name appears in smaller black text. The Cambridge University Press logo is centered underneath the title, followed by the publisher's name at the bottom.