William Balderrama (UIUC Math) Stable Phenomena in Algebraic Topology Abstract: A phenomenon might be called stable if it happens the same way in every dimension. For example, if $C_\bullet$ is a chain complex, then $H_\ast C_\bullet = H_{\ast+1}C_{\bullet+1}$: ``taking homology'' is done the same in every dimension. In some cases, a construction might not be stable, but can be stabilized. For example, if $M$ is a smooth closed manifold, choice of distinct embeddings $i,j\colon M\rightarrow \mathbb{R}^n$ give rise to possibly nonisomorphic choices of normal bundles $N_iM$ and $N_jM$. However, we can stabilize this by adding trivial bundles: $N_iM\oplus k \simeq N_jM \oplus k$ for sufficiently large $k$, leading to the notion of the stable normal bundle. In this talk, I will introduce this notion of stability, and propose spectra, the main objects in stable homotopy theory, as a good way for dealing with it. 
