
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 GoerssHennMahowaldRezk 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 \( EO_{p1} \) vanishes at height \( n=p1 \).
Preprints
\( K \)theory, reality and duality . Joint with Vesna Stojanoska. We calculate the Anderson dual of \( KO \), and give an algebrogeometric interpretation of this result. Last modified: 14/01/14 
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 \(n=p1\), using the methods of GoerssHennRezk.
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