Expositions

Here are some expository writings, surveys, and reading reports on mathematics.

Fixed point properties of group actions on CAT(0) spaces (2026)

An exposition of fixed point properties of groups acting on CAT (0) spaces. We begin with Serre’s study on groups acting on trees, which classified groups that must act with a fixed point on a tree. We then introduce Farb and Bridson’s higher-dimensional analogues for actions on n-dimensional CAT (0) spaces. In particular, we demonstrate the results on reflection groups, arithmetic groups, mapping class groups, and braid groups. PDF

A Riemiannian Geometric Description of Characteristic Classes (2026)

A brief introduction of the Chern–Weil theory of characteristic classes, focusing on connections, curvature, and the geometric interpretation of Chern, Pontryagin, and Euler classes. PDF

Counterexamples to the Stallings Equalizer Conjecture via Colored Stallings Graphs （2026）

A introduction of the Stallings equalizer conjecture and its counterexamples via colored Stallings graphs, including the construction of equalizers of rank at least (2n-2). PDF