• Drew Heard

    About me:

    I am a third year graduate student studying mathematics at Melbourne University. My advisor is Craig Westerland. I am broadly interested in stable homotopy theory with a particular interest in chromatic homotopy theory. Currently I am thinking about the \(K(n)\)-local homotopy category, in particular the construction of so called exotic elements of the Picard group. See the research page for more information.

    Update: New paper uploaded to the arxiv.

  • Notes and Papers

    Note that these notes are very rough, and may (indeed do) contain errors and simplifications introduced by me. Please keep this in mind.

    GHMR Resolution: Slightly expanded version of the talk I gave at the 2013 Talbot on the Goerss-Henn-Mahowald-Rezk resolution of the \( K(2) \)-local sphere at the prime 3.

    The Tate spectrum of higher real \( K \)-theories: Draft of a calulcation that shows that the Tate spectrum associated to \( EO_{p-1} \) vanishes at height \( n=p-1 \).

    Preprints

    \( K \)-theory, reality and duality . Joint with Vesna Stojanoska. We calculate the Anderson dual of \( KO \), and give an algebro-geometric interpretation of this result. Last modified: 14/01/14
  • Links

    Here are some links to fellow algebraic topologists: Aaron Mazel-Gee Craig Westerland Dylan Wilson Eric Peterson Jon Beardsley Kyle Ormsby Mark Behrens Mike Catanzaro Sean Tilson TriThang Tran Vesna Stojanoska Vitaly Lorman
  • Research

    The \(K(n)\)-local stable homotopy category is symmetric monoidal under the \(K(n)\)-local smash product, and hence we can study its group of invertible elements, known as the Picard group, denoted \(\text{Pic}_n\). This admits a cohomological approximation, \(\text{Pic}_n^\text{alg}\) much like the Picard group of a scheme, and there is a natural map  \(\text{Pic}_n \to \text{Pic}_n^\text{alg}\). The kernel of this map forms the group of exotic elements \( \kappa_n \). In general not much is known about these groups; for a fixed \(n\) it is known they vanish for large primes and further information is known at \(n=1,2\). My work involves producing some exotic elements at height \(n=p-1\), using the methods of Goerss-Henn-Rezk.


    I also have various other interests in the stable homotopy category including various forms of duality, the Brauer group of the \(K(n)\)-local category and general compuational methods in homotopy theory.

  • Contact

    Drew Heard

    Richard Berry Building
    Melbourne University
    Victoria, Australia

    E-mail:

    Sample map