- Scholarship in 2023 at University of Wisconsin–Madison

**About Amy L Tao’s work**

Amy L Tao is a mathematician whose field of research is algebra, with a particular focus on the Galois module structure of cube power classes for bicubic extensions.

The inverse Galois problem is a question in algebra that asks whether a given group G can be realised as the Galois group of a field extension over a certain base field. Equivariant Kummer theory provides an answer to this problem in a specific scenario. It states that when certain assumptions on the field K are met, elementary p-abelian extensions of K correspond to Fp[G]-submodules of the space J(K) = K*/K*^p, which consists of pth power classes of K.

Recently, researchers have studied the Fp[G]-module structure of J(K) for various small groups G and broken down J(K) into indecomposable submodules using a module-theoretic approach. This approach has been productive and insightful, even when the representation type of Fp[G]-modules is wild.

Building on her undergraduate work in this field, where she began decomposing J(K) for p = 3 and G = Z/3Z + Z/3Z, Tao has obtained a large submodule with an interesting and stratified structure. She intends to continue this decomposition and investigate the field extensions represented by the submodules that appear in the decomposition, as well as exploring the realizability of certain direct summands.

**Biography**

Amy L Tao obtained her BA in Mathematics with honours *summa cum laude* from Wellesley College in 2022. In the same year, she was invited to join the Sigma Xi Scientific Research Honor Society and won the Lewis Atterbury Stimson Prize in Mathematics. She is currently carrying out her PhD studies and research at the University of Wisconsin–Madison.